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29 pages, 3209 KiB  
Review
Reverse Polarity-Based Soil Electrokinetic Remediation: A Comprehensive Review of the Published Data during the Past 31 Years (1993–2023)
by Ahmed Abou-Shady and Heba El-Araby
ChemEngineering 2024, 8(4), 82; https://doi.org/10.3390/chemengineering8040082 - 15 Aug 2024
Cited by 2 | Viewed by 1187
Abstract
Soil restoration by exploiting the principles and basics of electrokinetic (EK) has been extended to involve several categories, such as electrokinetic remediation in soil (SEKR), soil consolidation, the prevention of soil pollution, reclaiming salt-affected soil, the dewatering/dryness of wet soils, water reuse, seed [...] Read more.
Soil restoration by exploiting the principles and basics of electrokinetic (EK) has been extended to involve several categories, such as electrokinetic remediation in soil (SEKR), soil consolidation, the prevention of soil pollution, reclaiming salt-affected soil, the dewatering/dryness of wet soils, water reuse, seed germination, sedimentation, etc. As an extension of our recently published review articles on the soil electrokinetic (SEK) process intensification/optimization, the present review illustrates the effect of a reverse-polarity mode (RPM) on the efficiency of the SEK. Based on several searches of six database search engines, we did not find any relevant reviews focused on SEK improvements using the RPM. The influences of the RPM are described by various features, including (a) pollutant removal (organic, inorganic, and mixed pollutants) and (b) integration with other processes (phyto/bioremediation and Fenton oxidation), geosynthetics (consolidation, stabilization, and sedimentation), SEK operation conditions, and soil properties. Most of the RPM studies have focused on the remediation of organic pollutants. Several benefits can be gained from applying the RPM, such as (a) controlling the soil’s temperature, pH, and moisture values at desirable levels, (b) reducing a large number of chemical additives, (c) high remediation efficiency, (d) maintaining the indigenous fungal community’s appropriate diversity and abundance, (e) a stable and higher electric current, (f) enhancing microbial growth, etc. However, the hindrances to applying the RPM are (a) reducing the electroosmosis flow, (b) relatively high energy consumption, (c) reducing the diversity of soil microbes with a prolonged experiment period, (d) providing oxygen for a microbial community that may not be desirable for anaerobic bacteria, etc. Finally, the RPM is considered an important process for improving the performance of the SEK, according to experimental endeavors. Full article
(This article belongs to the Special Issue New Advances in Chemical Engineering)
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Figure 1

Figure 1
<p>Design of an electrode matrix with polarity switching to produce the same intensity of an electric field at any point of equal distance from the electrodes, redrawn from the work of Guo et al. [<a href="#B63-ChemEngineering-08-00082" class="html-bibr">63</a>].</p>
Full article ">Figure 2
<p>Schematic diagram of the rotational operation at an interval of 3 h through an electrode array with four couples for one operation cycle, after Luo et al. [<a href="#B39-ChemEngineering-08-00082" class="html-bibr">39</a>] (Elsevier Copyright—License Number 5824280357745). The electrified anode ( ●), cathode (<span class="html-fig-inline" id="ChemEngineering-08-00082-i001"><img alt="Chemengineering 08 00082 i001" src="/ChemEngineering/ChemEngineering-08-00082/article_deploy/html/images/ChemEngineering-08-00082-i001.png"/></span>), and un-electrified electrodes (○) are shown.</p>
Full article ">Figure 3
<p>Schematic diagram of the cyclic and progressive electroosmosis (CPE) approach, redrawn from the work of Sun et al. [<a href="#B65-ChemEngineering-08-00082" class="html-bibr">65</a>].</p>
Full article ">Figure 4
<p>The positive influences of the reverse-polarity mode (RPM) on various factors during the application of soil electrokinetics.</p>
Full article ">Figure 5
<p>The negative influences of the reverse-polarity mode (RPM) on various factors during the application of soil electrokinetic.</p>
Full article ">
14 pages, 2854 KiB  
Article
The Preparation and Evaluation of a Hydrochloride Hydrogel Patch with an Iontophoresis-Assisted Release of Terbinafine for Transdermal Delivery
by Mengfei Li, Xinghao Chen, Xiangxiang Su and Wenyan Gao
Gels 2024, 10(7), 456; https://doi.org/10.3390/gels10070456 - 12 Jul 2024
Viewed by 1247
Abstract
Background: Terbinafine hydrochloride (TEB) is a broad-spectrum antifungal medication commonly used to treat fungal infections of the skin. This study designed a hydrogel patch assisted by an iontophoresis system to enhance the transdermal permeability of TEB, enabling deeper penetration into the skin layers. [...] Read more.
Background: Terbinafine hydrochloride (TEB) is a broad-spectrum antifungal medication commonly used to treat fungal infections of the skin. This study designed a hydrogel patch assisted by an iontophoresis system to enhance the transdermal permeability of TEB, enabling deeper penetration into the skin layers. Methods: The influences of current intensity, pH levels, and drug concentration on the TEB hydrogel patch’s permeability were explored using an adaptive ion electroosmosis system. The pharmacokinetic profile, facilitated by iontophoresis for transdermal permeation, was analyzed through the application of microdialysis technology. Scanning electron microscopy and transmission electron microscopy were employed to assess the impact of ion electroosmotic systems on skin integrity. Results: The cumulative drug accumulation within 8 h of the TEB hydrogel patches, assisted by iontophoresis, was 2.9 and 7.9 times higher than without iontophoresis assistance and TEB cream in the control group, respectively. TEB hydrogel patches assisted by iontophoresis can significantly increase the permeability of TEB, and the AUC(0–8 h) was 3.4 and 5.4 times higher, while the Cmax was 4.2 and 7.3 times higher than the TEB hydrogel patches without iontophoresis, respectively. This system has no significant impact on deep-layer cells. Conclusions: This system may offer a safe and effective clinical strategy for the local treatment of deep antifungal infections. Full article
(This article belongs to the Special Issue Novel Functional Gels for Biomedical Applications)
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Figure 1

Figure 1
<p>Chemical structure of terbinafine hydrochloride (<b>A</b>) and terbinafine hydrochloride hydrogel patch (<b>B</b>).</p>
Full article ">Figure 2
<p>HPLC chromatogram for specificity investigation. (<b>A</b>) Blank mobile phase (methanol–water (0.2% triethylamine and 1% acetic acid) = 7:3). (<b>B</b>) 20% PEG 400-20 mM NaH<sub>2</sub>PO<sub>4</sub>. (<b>C</b>) Reference substance of TEB (6.25 μg/mL, Dissolve in NS). (<b>D</b>) Reference substance of TEB (5.85 μg/mL, Dissolve in 20% PEG 400-20 mM NaH<sub>2</sub>PO<sub>4</sub>). (<b>E</b>) Standard curve of TEB transdermal receiver solution.</p>
Full article ">Figure 3
<p>The effect of different factors influencing the iontophoresis-assisted transdermal permeation of TEB in vitro. (<b>A</b>) Schematic diagram of iontophoresis transdermal delivery in vitro. (<b>B</b>) The effect of current density on the iontophoresis penetration of TEB hydrogel patches (n = 4). (<b>C</b>) The effect of pH on the iontophoresis penetration of TEB hydrogel patches (n = 4). (<b>D</b>) The effect of drug concentration on the iontophoresis penetration of TEB hydrogel patches (n = 4). (<b>E</b>) A comparison of different TEB formulations of percutaneous penetration (n = 4). (<b>F</b>) The skin retention of different TEB formulations. * <span class="html-italic">p</span> &lt; 0.05, as compared with the group of TEB hydrogel patches without iontophoresis; <sup>##</sup> <span class="html-italic">p</span> &lt; 0.01, as compared with the TEB cream group.</p>
Full article ">Figure 4
<p>Microdialysis recovery rate of TEB in vitro and in vivo, and percutaneous pharmacokinetics. (<b>A</b>) Schematic diagram of microdialysis recovery rate in vitro. (<b>B</b>) Schematic diagram of iontophoresis transdermal delivery and microdialysis in vitro. (<b>C</b>) The effect of different flow rates and TEB concentrations on the recoveries of probes in vitro (retrodialysis, n = 4). (<b>D</b>) The effect of different flow rates and TEB concentrations on the recoveries of probes in vivo (retrodialysis, n = 4). (<b>E</b>) Percutaneous pharmacokinetics of different TEB formulations (n = 6).</p>
Full article ">Figure 5
<p>The effect of iontophoresis on the skin microstructure. (<b>A</b>–<b>D</b>) The ultrastructural damage of the epidermis under a scanning electron microscope (SEM) ((<b>A</b>) skin of normal rats (control); (<b>B</b>) the skin of rats with a TEB hydrogel patch; (<b>C</b>) skin of rats with a TEB hydrogel patch under iontophoresis; (<b>D</b>) skin of rats with the TEB cream); (<b>E</b>–<b>H</b>) deeper damage to skin cells under a transmission electronic microscope (TEM) ((<b>E</b>) skin of normal rats (control); (<b>F</b>) skin of rats with a TEB hydrogel patch; (<b>G</b>) skin of rats with a TEB hydrogel patch under iontophoresis; (<b>H</b>) skin of rats with the TEB cream).</p>
Full article ">Figure 6
<p>The preparation process of a TEB hydrogel patch.</p>
Full article ">
32 pages, 5291 KiB  
Article
Analytical Investigation of Thermal Radiation Effects on Electroosmotic Propulsion of Electrically Conducting Ionic Nanofluid with Single-Walled Carbon Nanotube Interaction in Ciliated Channels
by Junaid Mehboob, Rahmat Ellahi and Sadiq Mohammad Sait
Symmetry 2024, 16(6), 717; https://doi.org/10.3390/sym16060717 - 9 Jun 2024
Cited by 3 | Viewed by 749
Abstract
This study examines the behavior of single-walled carbon nanotubes (SWCNTs) suspended in a water-based ionic solution, driven by the combined mechanisms of electroosmosis and peristalsis through ciliated media. The inclusion of nanoparticles in ionic fluid expands the range of potential applications and allows [...] Read more.
This study examines the behavior of single-walled carbon nanotubes (SWCNTs) suspended in a water-based ionic solution, driven by the combined mechanisms of electroosmosis and peristalsis through ciliated media. The inclusion of nanoparticles in ionic fluid expands the range of potential applications and allows for the tailoring of properties to suit specific needs. This interaction between ionic fluids and nanomaterials results in advancements in various fields, including energy storage, electronics, biomedical engineering, and environmental remediation. The analysis investigates the influence of a transverse magnetic field, thermal radiation, and mixed convection acting on the channel walls. The novel physical outcomes include enhanced propulsion efficiency due to SWCNTs, understanding the influence of thermal radiation on fluid behavior and heat exchange, elucidation of the interactions between SWCNTs and the nanofluid, and recognizing implications for microfluidics and biomedical engineering. The Poisson–Boltzmann ionic distribution is linearized using the modified Debye–Hückel approximation. By employing real-world approximations, the governing equations are simplified using long-wavelength and low-Reynolds-number approximation. Conducting sensitivity analyses or exploring the impact of higher-order corrections on the model’s predictions in recent literature might alter the results significantly. This acknowledges the complexities of the modeling process and sets the groundwork for further enhancement and investigation. The resulting nonlinear system of equations is solved through regular perturbation techniques, and graphical representations showcase the variation in significant physical parameters. This study also discusses pumping and trapping phenomena in the context of relevant parameters. Full article
(This article belongs to the Section Mathematics)
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Figure 1

Figure 1
<p>Geometry of the problem.</p>
Full article ">Figure 2
<p>(<b>a</b>–<b>g</b>) illustrate the velocity profiles <span class="html-italic">u</span>(<span class="html-italic">y</span>) for different values of the <span class="html-italic">k</span>, <math display="inline"><semantics> <mi>M</mi> </semantics></math>, <span class="html-italic">Gr</span>, <span class="html-italic">U</span>, <span class="html-italic">Rd</span>, <span class="html-italic">Pr</span>, and <span class="html-italic">Br</span>.</p>
Full article ">Figure 2 Cont.
<p>(<b>a</b>–<b>g</b>) illustrate the velocity profiles <span class="html-italic">u</span>(<span class="html-italic">y</span>) for different values of the <span class="html-italic">k</span>, <math display="inline"><semantics> <mi>M</mi> </semantics></math>, <span class="html-italic">Gr</span>, <span class="html-italic">U</span>, <span class="html-italic">Rd</span>, <span class="html-italic">Pr</span>, and <span class="html-italic">Br</span>.</p>
Full article ">Figure 2 Cont.
<p>(<b>a</b>–<b>g</b>) illustrate the velocity profiles <span class="html-italic">u</span>(<span class="html-italic">y</span>) for different values of the <span class="html-italic">k</span>, <math display="inline"><semantics> <mi>M</mi> </semantics></math>, <span class="html-italic">Gr</span>, <span class="html-italic">U</span>, <span class="html-italic">Rd</span>, <span class="html-italic">Pr</span>, and <span class="html-italic">Br</span>.</p>
Full article ">Figure 3
<p>(<b>a</b>–<b>g</b>): temperature profile <span class="html-italic">θ</span>(<span class="html-italic">y</span>) for different values of the <span class="html-italic">k</span>, <span class="html-italic">Rd</span>, <span class="html-italic">U</span>, <span class="html-italic">Br</span>, <span class="html-italic">Pr</span>, <span class="html-italic">η,</span> and <math display="inline"><semantics> <mi mathvariant="sans-serif">Φ</mi> </semantics></math>.</p>
Full article ">Figure 3 Cont.
<p>(<b>a</b>–<b>g</b>): temperature profile <span class="html-italic">θ</span>(<span class="html-italic">y</span>) for different values of the <span class="html-italic">k</span>, <span class="html-italic">Rd</span>, <span class="html-italic">U</span>, <span class="html-italic">Br</span>, <span class="html-italic">Pr</span>, <span class="html-italic">η,</span> and <math display="inline"><semantics> <mi mathvariant="sans-serif">Φ</mi> </semantics></math>.</p>
Full article ">Figure 4
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">k</span> = 2, (<b>b</b>) <span class="html-italic">k</span> = 2.2, and (<b>c</b>) <span class="html-italic">k</span> = 2.4.</p>
Full article ">Figure 4 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">k</span> = 2, (<b>b</b>) <span class="html-italic">k</span> = 2.2, and (<b>c</b>) <span class="html-italic">k</span> = 2.4.</p>
Full article ">Figure 5
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Br</span> = 2, (<b>b</b>) <span class="html-italic">Br</span> = 4, and (<b>c</b>) <span class="html-italic">Br</span> = 6.</p>
Full article ">Figure 5 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Br</span> = 2, (<b>b</b>) <span class="html-italic">Br</span> = 4, and (<b>c</b>) <span class="html-italic">Br</span> = 6.</p>
Full article ">Figure 6
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Pr</span> = 1, (<b>b</b>) <span class="html-italic">Pr</span> = 2, and (<b>c</b>) <span class="html-italic">Pr</span> = 3.</p>
Full article ">Figure 6 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Pr</span> = 1, (<b>b</b>) <span class="html-italic">Pr</span> = 2, and (<b>c</b>) <span class="html-italic">Pr</span> = 3.</p>
Full article ">Figure 7
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">U</span> = −2, (<b>b</b>) <span class="html-italic">U</span> = 0, and (<b>c</b>) <span class="html-italic">U</span> = 2.</p>
Full article ">Figure 7 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">U</span> = −2, (<b>b</b>) <span class="html-italic">U</span> = 0, and (<b>c</b>) <span class="html-italic">U</span> = 2.</p>
Full article ">Figure 8
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Gr</span> = 6, (<b>b</b>) <span class="html-italic">Gr</span> = 7, and (<b>c</b>) <span class="html-italic">Gr</span> = 8.</p>
Full article ">Figure 8 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Gr</span> = 6, (<b>b</b>) <span class="html-italic">Gr</span> = 7, and (<b>c</b>) <span class="html-italic">Gr</span> = 8.</p>
Full article ">Figure 9
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">M</span> = 0.2, (<b>b</b>) <span class="html-italic">M</span> = 0.7, and (<b>c</b>) <span class="html-italic">M</span> = 1.2.</p>
Full article ">Figure 9 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">M</span> = 0.2, (<b>b</b>) <span class="html-italic">M</span> = 0.7, and (<b>c</b>) <span class="html-italic">M</span> = 1.2.</p>
Full article ">Figure 10
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Rd</span> = 1, (<b>b</b>) <span class="html-italic">Rd</span> = 2, and (<b>c</b>) <span class="html-italic">Rd</span> = 2.</p>
Full article ">Figure 10 Cont.
<p>Streamlines for SWCNT+H<sub>2</sub>O for (<b>a</b>) <span class="html-italic">Rd</span> = 1, (<b>b</b>) <span class="html-italic">Rd</span> = 2, and (<b>c</b>) <span class="html-italic">Rd</span> = 2.</p>
Full article ">Figure 11
<p>(<b>a</b>–<b>g</b>): pressure gradient for variation in <span class="html-italic">k</span>, <span class="html-italic">Gr</span>, <span class="html-italic">U</span>, <span class="html-italic">M</span>, <span class="html-italic">Pr</span>, <span class="html-italic">Br</span>, and <span class="html-italic">Rd</span>.</p>
Full article ">Figure 11 Cont.
<p>(<b>a</b>–<b>g</b>): pressure gradient for variation in <span class="html-italic">k</span>, <span class="html-italic">Gr</span>, <span class="html-italic">U</span>, <span class="html-italic">M</span>, <span class="html-italic">Pr</span>, <span class="html-italic">Br</span>, and <span class="html-italic">Rd</span>.</p>
Full article ">
21 pages, 4158 KiB  
Article
Novel Numerical Investigations of Some Problems Based on the Darcy–Forchheimer Model and Heat Transfer
by Fahir Talay Akyildiz, Fehaid Salem Alshammari and Cemil Tunç
Mathematics 2024, 12(11), 1742; https://doi.org/10.3390/math12111742 - 3 Jun 2024
Viewed by 474
Abstract
In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct [...] Read more.
In this study, we introduced a new type of basis function and subsequently a Chebyshev delta shaped collocation method (CDSC). We then use this method to numerically investigate both the natural convective flow and heat transfer of nanofluids in a vertical rectangular duct on the basis of a Darcy–Brinkman–Forchheimer model and the electroosmosis-modulated Darcy–Forchheimer flow of Casson nanofluid over stretching sheets with Newtonian heating problems. The approximate solution is represented in terms of Chebyshev delta shaped basis functions. Novel error estimates for interpolating polynomials are derived. Computational experiments were carried out to corroborate the theoretical results and to compare the present method with the existing Chebyshev pseudospectral method. To demonstrate our proposed approach, we also compared the numerical solutions with analytic solutions of the Poisson equation. Computer simulations show that the proposed method is computationally cheap, fast, and spectrally accurate and more importantly the obtained approximate solution can easily be used by researchers in this field. Full article
(This article belongs to the Section Computational and Applied Mathematics)
Show Figures

Figure 1

Figure 1
<p>Flow domain and geometry of Problem 1.</p>
Full article ">Figure 2
<p>Flow domain and geometry of Problem 2.</p>
Full article ">Figure 3
<p>Solution of Equation (10) by both methods.</p>
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<p>Differences between the approximate solutions: one obtained from CDSC, the other one from the CP method.</p>
Full article ">Figure 5
<p>(<b>a</b>) Velocity contour graph; (<b>b</b>) Variation in velocity with <span class="html-italic">x</span> and <span class="html-italic">y</span> for <math display="inline"><semantics> <mrow> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> of Problem 1. (<b>c</b>) Temperature contour graph; (<b>d</b>) Variation in temperature with <span class="html-italic">x</span> and <span class="html-italic">y</span> for <math display="inline"><semantics> <mrow> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> of Problem 1.</p>
Full article ">Figure 6
<p>Velocity variation with <math display="inline"><semantics> <mrow> <mi>y</mi> </mrow> </semantics></math> for fixed <math display="inline"><semantics> <mrow> <mi>x</mi> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> <mo> </mo> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mo> </mo> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> <mo>.</mo> </mrow> </semantics></math> Line x = 0, and dash dot x = 0.5.</p>
Full article ">Figure 7
<p>Temperature variation with <math display="inline"><semantics> <mrow> <mi>y</mi> </mrow> </semantics></math> for fixed <math display="inline"><semantics> <mrow> <mi>x</mi> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>0.1</mn> <mo> </mo> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">d</mi> <mo> </mo> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>(<b>a</b>) Velocity contour graph; (<b>b</b>) Variation in velocity with <span class="html-italic">x</span> and <span class="html-italic">y</span> for <math display="inline"><semantics> <mrow> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> of Problem 1. (<b>c</b>) Temperature contour graph; (<b>d</b>) Variation in temperature with <span class="html-italic">x</span> and <span class="html-italic">y</span> for <math display="inline"><semantics> <mrow> <mi>G</mi> <mi>r</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>D</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> of Problem 1.</p>
Full article ">Figure 9
<p>The effect of the Darcy number on <math display="inline"><semantics> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced separators="|"> <mrow> <mi>y</mi> </mrow> </mfenced> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>h</mi> <mi>S</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Effect of electroosmotic <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>h</mi> <mi>S</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> and electromagnetohydrodynamic <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>M</mi> </mrow> </mfenced> </mrow> </semantics></math> forces on the velocity <math display="inline"><semantics> <mrow> <msup> <mi>f</mi> <mo>′</mo> </msup> <mfenced separators="|"> <mrow> <mi>y</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>The effect of electroosmotic <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <msub> <mrow> <mi>U</mi> </mrow> <mrow> <mi>h</mi> <mi>S</mi> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> and electromagnetohydrodynamic <math display="inline"><semantics> <mrow> <mfenced separators="|"> <mrow> <mi>M</mi> </mrow> </mfenced> </mrow> </semantics></math> forces on the velocity temperature distribution for Problem 2.</p>
Full article ">
19 pages, 9237 KiB  
Article
Diffusiophoresis of a Charged Soft Sphere in a Charged Spherical Cavity
by Wei-Zhi Chen and Huan-Jang Keh
Colloids Interfaces 2024, 8(3), 36; https://doi.org/10.3390/colloids8030036 - 2 Jun 2024
Viewed by 1288
Abstract
The quasi-steady diffusiophoresis of a soft particle composed of an uncharged hard sphere core and a uniformly charged porous surface layer in a concentric charged spherical cavity full of a symmetric electrolyte solution with a concentration gradient is analyzed. By using a regular [...] Read more.
The quasi-steady diffusiophoresis of a soft particle composed of an uncharged hard sphere core and a uniformly charged porous surface layer in a concentric charged spherical cavity full of a symmetric electrolyte solution with a concentration gradient is analyzed. By using a regular perturbation method with small fixed charge densities of the soft particle and cavity wall, the linearized electrokinetic equations relevant to the fluid velocity field, electric potential profile, and ionic concentration distributions are solved. A closed-form formula for the diffusiophoretic (electrophoretic and chemiphoretic) velocity of the soft particle is obtained as a function of the ratios of the core-to-particle radii, particle-to-cavity radii, particle radius to the Debye screening length, and particle radius to the permeation length in the porous layer. In typical cases, the confining charged cavity wall significantly influences the diffusiophoresis of the soft particle. The fluid flow caused by the diffusioosmosis (electroosmosis and chemiosmosis) along the cavity wall can considerably change the diffusiophoretic velocity of the particle and even reverse its direction. In general, the diffusiophoretic velocity decreases with increasing core-to-particle radius ratios, particle-to-cavity radius ratios, and the ratio of the particle radius to the permeation length in the porous layer, but increases with increasing ratios of the particle radius to the Debye length. Full article
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Figure 1

Figure 1
<p>Geometric sketch for the diffusiophoresis of a charged soft sphere in a concentric charged spherical cavity.</p>
Full article ">Figure 2
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>01</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the electrophoresis of a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a spherical cavity: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>10</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity with electroosmosis: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the electrophoresis of a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity versus the fixed charge density ratio <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">¯</mo> </mover> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>02</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the chemiphoresis of a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a spherical cavity: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 6
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>11</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>20</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity with chemiosmosis: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 8
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>/</mo> <msup> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>2</mn> </msup> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the chemiphoresis of a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity versus the fixed charge density ratio <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">¯</mo> </mover> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Normalized velocity <math display="inline"><semantics> <mrow> <mi>U</mi> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the diffusiophoresis of a charged porous sphere (<math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>) in a charged spherical cavity with <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mo>−</mo> <mn>0.2</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> versus the charge density <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>01</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the electrophoresis of a charged soft sphere in a spherical cavity versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>10</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a soft sphere in a charged spherical cavity with electroosmosis versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 11 Cont.
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>10</mn> </mrow> </msub> <mo>/</mo> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a soft sphere in a charged spherical cavity with electroosmosis versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>1</mn> </msub> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> <mi>β</mi> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the electrophoresis of a charged soft sphere in a charged spherical cavity with <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> versus the fixed charge density ratio <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">¯</mo> </mover> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>02</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the chemiphoresis of a charged soft sphere in a spherical cavity versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 14
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>11</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a charged soft sphere in a charged spherical cavity versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 15
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mrow> <mn>20</mn> </mrow> </msub> <mo>/</mo> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for a soft sphere in a charged spherical cavity with chemiosmosis versus <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>/</mo> <mi>a</mi> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 16
<p>Normalized velocity <math display="inline"><semantics> <mrow> <msub> <mi>U</mi> <mn>2</mn> </msub> <mo>/</mo> <msup> <mrow> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> <mn>2</mn> </msup> <msup> <mi>U</mi> <mo>*</mo> </msup> </mrow> </semantics></math> for the chemiphoresis of a charged soft sphere in a charged spherical cavity with <math display="inline"><semantics> <mrow> <mi>κ</mi> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>λ</mi> <mi>a</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>/</mo> <mi>b</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> versus the fixed charge density ratio <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>σ</mi> <mo stretchy="true">¯</mo> </mover> <mo>/</mo> <mover accent="true"> <mi>Q</mi> <mo stretchy="true">¯</mo> </mover> </mrow> </semantics></math>.</p>
Full article ">
22 pages, 7806 KiB  
Article
Simulation on the Separation of Breast Cancer Cells within a Dual-Patterned End Microfluidic Device
by Diganta Dutta, Xavier Palmer, Jung Yul Lim and Surabhi Chandra
Fluids 2024, 9(6), 123; https://doi.org/10.3390/fluids9060123 - 25 May 2024
Viewed by 809
Abstract
Microfluidic devices have long been useful for both the modeling and diagnostics of numerous diseases. In the past 20 years, they have been increasingly adopted for helping to study those in the family of breast cancer through characterizing breast cancer cells and advancing [...] Read more.
Microfluidic devices have long been useful for both the modeling and diagnostics of numerous diseases. In the past 20 years, they have been increasingly adopted for helping to study those in the family of breast cancer through characterizing breast cancer cells and advancing treatment research in portable and replicable formats. This paper adds to the body of work concerning cancer-focused microfluidics by proposing a simulation of a hypothetical bi-ended three-pronged device with a single channel and 16 electrodes with 8 pairs under different voltage and frequency regimes using COMSOL. Further, a study was conducted to examine the frequencies most effective for ACEO to separate cancer cells and accompanying particles. The study revealed that the frequency of EF has a more significant impact on the separation of particles than the inlet velocity. Inlet velocity variations while holding the frequency of EF constant resulted in a consistent trend showing a direct proportionality between inlet velocity and net velocity. These findings suggest that optimizing the frequency of EF could lead to more effective particle separation and targeted therapeutic interventions for breast cancer. This study hopefully will help to create targeted therapeutic interventions by bridging the disparity between in vitro and in vivo models. Full article
(This article belongs to the Special Issue Physics and Applications of Microfluidics)
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<p>The microchannel schematic includes electrode placement. The scale of this channel is hundreds of microns wide and thousands of microns long. Electrode placement is asymmetric along the horizontal axis, and their spacing differs depending on which side of the channel is referred.</p>
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<p>COMSOL Multiphysics application provides a mesh to measure velocities at many points along the chamber. The top graph shows a grid independent study.</p>
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<p>The microchannel exhibits a surface graph showing the electric field’s magnitude in various locations throughout the chamber. Color represents the extremities of the voltage on a micro scale.</p>
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<p>While the inlet velocity remains zero, a surface view of the fluid velocity, taken at the 15 s mark, depicts vortical motion corresponding to the 1200 kHz AC applied to the electrodes.</p>
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<p>The surface graph of the velocity at 15 s with a 50 nm/s inlet velocity and 1200 kHz AC exerted on the electrodes.</p>
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<p>The surface graph of velocity at 15 s with a 100 nm/s inlet velocity and 1200 Hz AC exerted on the electrodes.</p>
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<p>With 1200 kHz AC through the electrodes, at 15 s, a 200 nm/s inlet velocity results in a clearer surface view of the ACEO phenomena.</p>
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<p>The graph of maximum velocity over 15 s when the inlet velocity is 0 nm/s.</p>
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<p>The maximum velocity graphed over 15 s using an inlet velocity of 50 nm/s.</p>
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<p>The following graph shows the maximum velocity for each simulation over the course of 15 s.</p>
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<p>This graph shows the largest velocity recorded using our mesh for varying frequencies of AC over the domain of 0 to 15 s.</p>
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<p>Velocity in x direction vs. the channel height (y) graph at the middle of the channel when time is 15 s.</p>
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<p>A diagram of a graph of particles and cell trajectories while the frequency of AC through the electrodes is 100 kHz.</p>
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<p>A diagram of a graph of cell trajectories while the frequency of AC through the electrodes is 800 kHz.</p>
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<p>A diagram of the separation of particles due to the DEP phenomenon produced at 1000 kHz AC.</p>
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<p>The depiction of our microchannel filtering different cells through DEP with a frequency of 1200 kHz.</p>
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<p>The depiction of our cell’s trajectories at 1500 kHz AC through the electrodes.</p>
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<p>The diagram of cell trajectories when the frequency of AC is 1800 kHz.</p>
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<p>The electric field affects the particles shown in this diagram in a unique way when the frequency is 2200 kHz.</p>
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<p>A depiction of the particle trajectories when the AC through the electrodes is 4000 kHz.</p>
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<p>The diagram of our particles’ path of motion when the frequency of electric field is 100,000 kHz.</p>
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22 pages, 33285 KiB  
Article
Rising Damp Treatment in Historical Buildings by Electro-Osmosis: A Case Study
by Aliihsan Koca, Mehmet Nurettin Uğural and Ergün Yaman
Buildings 2024, 14(5), 1460; https://doi.org/10.3390/buildings14051460 - 17 May 2024
Viewed by 1689
Abstract
Throughout the past century, numerous technologies have been suggested to deal with the capillary rise of water through the soil in historic masonry buildings. The aim of this study was to examine the effectiveness of capillary moisture repulsion apparatus that uses the electro-osmosis [...] Read more.
Throughout the past century, numerous technologies have been suggested to deal with the capillary rise of water through the soil in historic masonry buildings. The aim of this study was to examine the effectiveness of capillary moisture repulsion apparatus that uses the electro-osmosis approach over a prolonged period of time. The Gül mosque was selected as a sample historical building affected by structural problems caused by the absorption of water through small channels on its walls due to capillary action. The moisture repulsion mechanism efficiently decreased the moisture level in the walls from a ‘wet’ state to a ‘dry’ state in roughly 9 months. After the installation of the equipment, the water mass ratio of the building decreased from 14.48% to 2.90%. It was determined that the majority of the water in the building was relocated during the initial measurement period. Furthermore, it inhibited the absorption of water by capillary action by protecting the construction elements that were in contact with the wet ground. Lastly, capillary water repulsion coefficients (C) for various measurement durations and time factors were proposed. The average value of C was calculated to be 0.152 kg/m2 s0.5 by measuring the point at which the water repulsion remained nearly constant. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
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<p>Water and salt molecules climbing a structure (The blue arrows indicate the presence of rising damp) [<a href="#B41-buildings-14-01460" class="html-bibr">41</a>].</p>
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<p>The product resulting from the corrosion of steel in a structure and damage to concrete [<a href="#B41-buildings-14-01460" class="html-bibr">41</a>].</p>
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<p>First stage of installation of the capillary moisture treatment device [<a href="#B41-buildings-14-01460" class="html-bibr">41</a>].</p>
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<p>Treatment of rising damp [<a href="#B41-buildings-14-01460" class="html-bibr">41</a>].</p>
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<p>Gül mosque.</p>
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<p>General view inside the mosque.</p>
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<p>Persistent issue of dampness and humidity within the mosque.</p>
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<p>System layout.</p>
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<p>Installation of the capillary rising damp treatment device.</p>
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<p>Electrode mounted on the vertical axis (shown in a red circle).</p>
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<p>Capillary moisture repulsion coefficients obtained according to different time factors (<b>a</b>) The time scale is a second, (<b>b</b>) The time scale is a day.</p>
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<p>Variations in capillary moisture repulsion coefficients at each measurement interval.</p>
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<p>Time-dependent variations in the mass fraction of water in the masonry walls.</p>
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<p>Variations in the mass fraction of water within the masonry wall during different measurement intervals.</p>
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<p>Moisture repulsion performance over time.</p>
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<p>Variations in capillary water repulsion coefficient with mass fraction of water.</p>
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14 pages, 3490 KiB  
Article
Rapid and Sensitive Detection by Combining Electric Field Effects and Surface Plasmon Resonance: A Theoretical Study
by Qijie Qiu and Yan Xu
Micromachines 2024, 15(5), 653; https://doi.org/10.3390/mi15050653 - 15 May 2024
Cited by 1 | Viewed by 1281
Abstract
Surface plasmon resonance (SPR) has been extensively employed in biological sensing, environmental detection, as well as chemical industry. Nevertheless, the performance possessed by conventional surface plasmon resonance (SPR) biosensors can be further limited by the transport of analyte molecules to the sensing surface, [...] Read more.
Surface plasmon resonance (SPR) has been extensively employed in biological sensing, environmental detection, as well as chemical industry. Nevertheless, the performance possessed by conventional surface plasmon resonance (SPR) biosensors can be further limited by the transport of analyte molecules to the sensing surface, noteworthily when small molecules or low levels of substances are being detected. In this study, a rapid and highly sensitive SPR biosensor is introduced to enhance the ability of the target analytes’ collection by integrating AC electroosmosis (ACEO) and dielectrophoresis (DEP). Both the above-mentioned phenomena principally arise from the generation of the AC electric fields. This generation can be tailored by shaping the interdigitated electrodes (IDEs) that also serve as the SPR biomarker sensing area. The effects exerted by different parameters (e.g., the frequency and voltage of the AC electric field as well as microelectrode structures) are considered in the iSPR (interdigitated SPR) biosensor operation, and the iSPR biosensors are optimized with the sensitivity. The results of this study confirm that the iSPR can efficiently concentrate small molecules into the SPR sensing area, such that SPR reactions achieve an order of magnitude increase, and the detection time is shortened. The rapid and sensitive sensor takes on critical significance in the development of on-site diagnostics in a wide variety of human and animal health applications. Full article
(This article belongs to the Special Issue Micromachines for Dielectrophoresis, 3rd Edition)
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<p>Schematic and principle of AC DEP–ACEO-enhanced surface plasmon resonance. Au microelectrodes are first patterned by photolithography and metal liftoff on a glass substrate. With out-of-phase AC voltage applied to the Au electrodes, the electrical double layer horizontally moves along the electrode surfaces. The electrical double-layer motion generates a hydrodynamic rotational flow in the microfluidic channel, and the target analyte is polarized. The hydrodynamic flow (ACEO) and DEP facilitate the transport of the target biomolecules to the sensing surface and their surface binding reaction.</p>
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<p>(<b>a</b>) Numerical simulation of the electric field strength under different electrode gaps. (<b>d</b>) <math display="inline"><semantics> <mrow> <mo>∇</mo> <mo>|</mo> <mi mathvariant="normal">E</mi> <msup> <mrow> <mo>|</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math><sub>max</sub> calculated under different electrode gaps as a linear function of Vpp. (<b>c</b>) Relationship between V<sub>ACEO</sub> and frequency. The AC electroosmotic velocity calculated at locations ‘x’ from the electrode edge under 0.0002 S m<sup>−1</sup>, 1 V. (<b>e</b>) Clausius–Mossotti factor calculated for polystyrene particles (<math display="inline"><semantics> <mrow> <msub> <mrow> <mo>ε</mo> </mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <mo>,</mo> <msub> <mrow> <mo>σ</mo> </mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mi mathvariant="normal">S</mi> <mo>/</mo> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>) in DI water. (<b>b</b>) Calculated distribution of <math display="inline"><semantics> <mrow> <mo>∇</mo> <mo>|</mo> <mi mathvariant="normal">E</mi> <msup> <mrow> <mo>|</mo> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> with a gap distance of E<sub>G</sub> = 10 μm and f = 10<sup>5</sup> Hz. (<b>f</b>) The maximum value of ACEO as a result of increasing V<sub>pp</sub> (f = 10<sup>5</sup> Hz) from 0 to 3 V.</p>
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<p>Simulation of the electric fields for the evaluation of DEP and ACEO. (<b>a</b>) Calculated distribution of ACEO flow on electrode surfaces under V<sub>pp</sub> = 3 V and f = 10<sup>5</sup> Hz. (<b>b</b>) Numerical simulation of the electric field strength in iSPR biochips. (<b>c</b>) Details of the DEP force at distances 5 μm from the electrode edge along the red dashed line in (<b>b</b>). (<b>d</b>) Plot of log10(<math display="inline"><semantics> <mrow> <mrow> <mrow> <msub> <mrow> <mo>|</mo> <mi mathvariant="normal">F</mi> </mrow> <mrow> <mi mathvariant="normal">D</mi> <mi mathvariant="normal">E</mi> <mi mathvariant="normal">P</mi> </mrow> </msub> <mo>|</mo> </mrow> <mo>/</mo> <mrow> <msub> <mrow> <mo>|</mo> <mi mathvariant="normal">F</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">g</mi> </mrow> </msub> <mo>|</mo> </mrow> </mrow> </mrow> </semantics></math>) comparing the forces in vertical direction exerted on PS particles under AC electric field (dielectrophoretic vs. Stokes drag force). (<b>e</b>) The number of captured PS particles in the SPR sensing area at 15 s.</p>
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<p>Target analyte concentration profiles in the iSPR microfluidic channel of the device operated under DEP and ACEO at V<sub>pp</sub> = 3 V f = 10<sup>5</sup> Hz, and with diffusion only, respectively. The flow field direction is shown by the black arrows. The initial concentration for two cases is set at 5 mol/L. The inlet (left edges) and the outlet (right edges) for diffusion-only cases (<b>a</b>) and DEP–ACEO (<b>b</b>) are defined as open boundaries with no target analyte replenishment.</p>
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<p>Simulation (<b>a</b>) and experimental (<b>b</b>–<b>e</b>) results of the pDEP and ACEO effects of polystyrene microbeads. (<b>a</b>) Results of the COMSOL particle tracing temporal study with a 3 V<sub>pp</sub> voltage and the same electrical parameter as previously. A relative buffer permittivity of 80 is used in each model. While positive pDEP typically attracts objects to the edge of electrodes, electro-osmosis can drag microbeads toward the center of the electrodes, which facilitates SPR detection. (<b>b</b>–<b>d</b>) Representative images of polystyrene microbead collection using the iSPR chip (under 10× magnification). ISPR chip with 5 μm diameter polystyrene microbeads at 10<sup>5</sup> Hz and 3 V suspended in 0.0002 S m<sup>−1</sup> media with a low concentration of particles. (<b>e</b>) Comparison of the concentration changes for DEP–ACEO and diffusion only from the COMSOL temporal study.</p>
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17 pages, 4796 KiB  
Article
Experimental Study of Electroosmosis in Rock Cores Based on the Dual Pressure Sensor Method
by Chenggang Yin, Wei Guan and Hengshan Hu
Sensors 2024, 24(9), 2832; https://doi.org/10.3390/s24092832 - 29 Apr 2024
Viewed by 776
Abstract
Electroosmotic experiments obtain the electroosmotic pressure coefficient of a rock sample by measuring the excitation voltage at both ends of the sample and the pressure difference caused by the excitation voltage. The electroosmotic pressure is very weak and buried in the background noise, [...] Read more.
Electroosmotic experiments obtain the electroosmotic pressure coefficient of a rock sample by measuring the excitation voltage at both ends of the sample and the pressure difference caused by the excitation voltage. The electroosmotic pressure is very weak and buried in the background noise, which is the most difficult signal to measure in the dynamic-electric coupling experiment, so it is necessary to improve its signal-to-noise ratio. In this paper, for the low signal-to-noise ratio of electroosmotic pressure, the dual pressure sensor method is proposed, i.e., two pressure sensors of the same type are used to measure electroosmotic pressure. Two different data extraction methods, Fast Fourier Transform and Locked Amplification, are utilized to compare the dual pressure sensor method of this paper with the existing single pressure sensor method. The relationship between the electroosmotic pressure coefficient and the excitation frequency, mineralization, permeability, and porosity is analyzed and discussed. Full article
(This article belongs to the Special Issue Sensors and Geophysical Electromagnetics)
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<p>The schematic of the electroosmotic effect.</p>
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<p>Two pressure sensors were used in the electroosmotic experiment.</p>
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<p>Measurements of the pressure sensor <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> when there is no excitation voltage across the core sample. (<b>a</b>) time domain; (<b>b</b>) frequency domain.</p>
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<p>The correlation coefficient of background noise of the pressure sensor <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> at different frequencies. (<b>a</b>) a point-to-point correlation coefficient; (<b>b</b>) an average correlation coefficient in several measurements.</p>
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<p>The measured signals of the pressure sensor <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math> when the excitation voltage is applied across the sample. (<b>a</b>) time domain; (<b>b</b>) frequency domain.</p>
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<p>Comparisons between the measured signal with electroosmotic pressure <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>A</mi> </mrow> </msub> </mrow> </semantics></math> and the corrected background noise <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>C</mi> </mrow> <mrow> <mi>p</mi> <mi>t</mi> </mrow> </msub> <mo>Δ</mo> <msub> <mrow> <mi>P</mi> </mrow> <mrow> <mi>B</mi> </mrow> </msub> </mrow> </semantics></math>. (<b>a</b>) time domain; (<b>b</b>) frequency domain.</p>
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<p>The electroosmotic pressure after weighted difference of the measured signals of two pressure sensors. (<b>a</b>) time domain; (<b>b</b>) frequency domain.</p>
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<p>The electroosmotic pressure by the double pressure sensor method. (<b>a</b>) time domain; (<b>b</b>) frequency domain.</p>
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<p>Comparison between single method (solid line) and double method (dashed line).</p>
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<p>Comparison between single + LIA method (black solid line) and double + LIA method (red solid line) in the electroosmotic experiment. The dashed line is a reference signal. (<b>a</b>) pressure amplitude; (<b>b</b>) pressure phase.</p>
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<p>The electroosmotic pressure coefficient with the varying frequency.</p>
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<p>The electroosmotic pressure coefficient with the varying mineralization.</p>
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<p>The electroosmotic pressure coefficient with the varying gas permeability of sandstone samples in different salinities.</p>
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<p>The electroosmotic pressure coefficient with the varying porosity of sandstone samples in different salinities.</p>
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22 pages, 4338 KiB  
Article
Non-Invasive Delivery of Negatively Charged Nanobodies by Anodal Iontophoresis: When Electroosmosis Dominates Electromigration
by Phedra Firdaws Sahraoui, Oscar Vadas and Yogeshvar N. Kalia
Pharmaceutics 2024, 16(4), 539; https://doi.org/10.3390/pharmaceutics16040539 - 13 Apr 2024
Viewed by 1572
Abstract
Iontophoresis enables the non-invasive transdermal delivery of moderately-sized proteins and the needle-free cutaneous delivery of antibodies. However, simple descriptors of protein characteristics cannot accurately predict the feasibility of iontophoretic transport. This study investigated the cathodal and anodal iontophoretic transport of the negatively charged [...] Read more.
Iontophoresis enables the non-invasive transdermal delivery of moderately-sized proteins and the needle-free cutaneous delivery of antibodies. However, simple descriptors of protein characteristics cannot accurately predict the feasibility of iontophoretic transport. This study investigated the cathodal and anodal iontophoretic transport of the negatively charged M7D12H nanobody and a series of negatively charged variants with single amino acid substitutions. Surprisingly, M7D12H and its variants were only delivered transdermally by anodal iontophoresis. In contrast, transdermal permeation after cathodal iontophoresis and passive diffusion was <LOQ. The anodal iontophoretic delivery of these negatively charged proteins was achieved because electroosmosis was the dominant electrotransport mechanism. Cutaneous deposition after the anodal iontophoresis of M7D12HWT (wild type), and the R54E and K65E variants, was statistically superior to that after cathodal iontophoresis (6.07 ± 2.11, 9.22 ± 0.80, and 14.45 ± 3.45 μg/cm2, versus 1.12 ± 0.30, 0.72 ± 0.27, and 0.46 ± 0.07 µg/cm2, respectively). This was not the case for S102E, where cutaneous deposition after anodal and cathodal iontophoresis was 11.89 ± 0.87 and 8.33 ± 2.62 µg/cm2, respectively; thus, a single amino acid substitution appeared to be sufficient to impact the iontophoretic transport of a 17.5 kDa protein. Visualization studies using immunofluorescent labeling showed that skin transport of M7D12HWT was achieved via the intercellular and follicular routes. Full article
(This article belongs to the Special Issue Transdermal Delivery: Challenges and Opportunities)
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<p>Iontophoretic transport is governed by the contributions of electromigration (EM) and electroosmosis (EO). Their magnitude and relative contribution is a function of the permeant (anion or cation) in the donor compartment, the isoelectric point of the skin (pI), and the type of iontophoresis (anodal or cathodal). They can act in conjunction or in opposition.</p>
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<p>3D structure of the 7D12 nanobody displaying the electrostatic potential onto the molecular surface (Connolly surface). Blue and red colors represent regions of high positive and negative charge density, respectively. Software used: AlphaFold2.ipynb for protein structure prediction and Pymol for visualization.</p>
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<p>Plasmid map of M7D12H<sub>WT</sub> and its corresponding sequence.</p>
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<p>Plasmid maps of the mono-substituted variants and their corresponding sequences.</p>
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<p>(<b>a</b>) 3D structure of the 7D12 nanobody and its variants displaying the electrostatic potential on the molecular surface (Connolly surface). Blue and red colors represent regions of high positive and negative charge density, respectively; (<b>b</b>) coloration of protein residues according to the Eisenberg hydrophobicity scale. Red and white colors represent regions of high hydrophobicity and high hydrophilicity, respectively. Software used: AlphaFold2.ipynb for protein structure prediction and Pymol for visualization.</p>
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<p>(<b>a</b>) Skin deposition of M7D12H<sub>WT</sub> nanobody and its variants following 8 h cathodal iontophoresis at 0.5 mA/cm<sup>2</sup> across porcine skin and a comparison between S102E deposition with the wild-type protein and R54E and K65E mutants. (<b>b</b>) Extraction from saline bridges after cathodal iontophoresis, (Mean ± SD; <span class="html-italic">n</span> = 3 for iontophoresis and <span class="html-italic">n</span> = 2 for passive control). ** indicates a <span class="html-italic">p</span> value ≤ 0.01.</p>
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<p>(<b>a</b>) Skin deposition of M7D12H<sub>WT</sub> nanobody and its variants following 8 h cathodal iontophoresis at 0.5 mA/cm<sup>2</sup> across porcine skin and a comparison between S102E deposition with the wild-type protein and R54E and K65E mutants. (<b>b</b>) Extraction from saline bridges after cathodal iontophoresis, (Mean ± SD; <span class="html-italic">n</span> = 3 for iontophoresis and <span class="html-italic">n</span> = 2 for passive control). ** indicates a <span class="html-italic">p</span> value ≤ 0.01.</p>
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<p>(<b>a</b>) Cumulative protein permeation (M7D12H<sub>WT</sub> and its variants) as a function of time during 8 h of transdermal iontophoresis at 0.5 mA/cm<sup>2</sup> across porcine skin; (<b>b</b>) total amounts permeated after 8 h of iontophoresis; (<b>c</b>) skin deposition; and (<b>d</b>) total delivery of M7D12H<sub>WT</sub> and its variants after anodal iontophoresis. (Mean ± SD; <span class="html-italic">n</span> = 3 for iontophoresis and <span class="html-italic">n</span> = 2 for passive control). * indicates a <span class="html-italic">p</span> value ≤ 0.05, *** indicates a <span class="html-italic">p</span> value ≤ 0.001.</p>
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<p>Comparison of anodal and cathodal iontophoretic delivery. (Mean ± SD; <span class="html-italic">n</span> = 3). ** indicates a <span class="html-italic">p</span> value ≤ 0.01, *** indicates a <span class="html-italic">p</span> value ≤ 0.001, and **** indicates a <span class="html-italic">p</span> value ≤ 0.0001.</p>
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<p>(<b>a</b>) Cumulative acetaminophen permeation as a function of time during 8 h of transdermal iontophoresis at 0.5 mA/cm<sup>2</sup> across porcine skin in the presence and the absence of M7D12H<sub>WT</sub> and its variants and (<b>b</b>) cumulative amounts delivered after 8 h of iontophoresis. (Means ± SD; <span class="html-italic">n</span> = 3 for iontophoresis and <span class="html-italic">n</span> = 2 for passive control). * indicates a <span class="html-italic">p</span> value ≤ 0.05, *** indicates a <span class="html-italic">p</span> value ≤ 0.001.</p>
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<p>Immunofluorescence labeling studies of M7D12H<sub>WT</sub> distribution across porcine skin (longitudinal sections) following either 8 h of constant current anodal or cathodal iontophoresis at 0.5 mA/cm<sup>2</sup> ((<b>a</b>) and (<b>b</b>), respectively), passive diffusion for 8 h (<b>c</b>), and untreated porcine skin (control) (<b>d</b>). The samples were labeled with Alexa Fluor™ 594 goat anti-mouse IgG antibody, and cell nuclei were stained with DAPI. The images contain an overlay (superimposition) of M7D12H<sub>WT</sub> (red) and nuclei (blue). They were taken with a widefield scanner Zeiss Axioscan.Z1 at 10× magnification and treated with ImageJ software. VE: viable epidermis; UD: upper dermis; LD: lower dermis. Scale bar = 500 µm.</p>
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<p>Localization of M7D12H<sub>WT</sub> nanobody in hair follicles after anodal iontophoresis, cathodal iontophoresis, and passive delivery. Blank: porcine skin incubated with primary and secondary antibodies. HF: hair follicle; ORS: outer root sheath; IRS: inner root sheath; HS: hair shaft. Images were obtained with a widefield scanner Zeiss Axioscan.Z1 at 10× magnification and treated with ImageJ software. Scale bar 100 μm.</p>
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15 pages, 4347 KiB  
Article
A Novel DC Electroosmotic Micromixer Based on Helical Vortices
by Sri Manikandan Saravanakumar, Mohsen Jamshidi Seresht, Ricardo Izquierdo and Paul-Vahe Cicek
Actuators 2024, 13(4), 139; https://doi.org/10.3390/act13040139 - 9 Apr 2024
Viewed by 1214
Abstract
This work introduces a novel direct current electroosmosis (DCEO) micromixer designed for rapid and efficient fluid mixing. This micromixer demonstrates excellent capability, achieving approximately 98.5% mixing efficiency within a one-second timespan and 99.8% efficiency within two seconds, all within a simple channel of [...] Read more.
This work introduces a novel direct current electroosmosis (DCEO) micromixer designed for rapid and efficient fluid mixing. This micromixer demonstrates excellent capability, achieving approximately 98.5% mixing efficiency within a one-second timespan and 99.8% efficiency within two seconds, all within a simple channel of only 1000 µm in length. A distinctive feature of this micromixer is its ability to generate robust and stable helical vortices by applying a controlled DC electric field. Unlike complex, intricate microfluidic designs, this work proposes a simple yet effective approach to fluid mixing, making it a versatile tool suitable for various applications. In addition, through simple modifications to the driving signal configuration and channel geometry, the mixing efficiency can be further enhanced to 99.3% in one second. Full article
(This article belongs to the Special Issue Actuators in 2024)
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<p>Proposed micromixer topology: (<b>a</b>) isometric view; (<b>b</b>) cross-section showing configuration for electrical actuation.</p>
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<p>Flow of the PDMS channel formation process: (<b>a</b>) photoresist application; (<b>b</b>) grayscale photolithographic exposure; (<b>c</b>) photoresist development; (<b>d</b>) PDMS casting; (<b>e</b>) PDMS mold separation.</p>
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<p>Fabricated half-channel mold: (<b>a</b>) top-view micrograph, (<b>b</b>) 3D contact profilometry, and (<b>c</b>) linear profilometry of the cross-section.</p>
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<p>Flow of the micromixer fabrication process: (<b>a</b>) copper deposition; (<b>b</b>) electrode patterning; (<b>c</b>) PDMS half-channel bonding.</p>
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<p>Initial concentration distribution along the channel before applying an external electric field.</p>
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<p>Electric potential distribution on the channel cross-section.</p>
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<p>Streamline contour plot: (<b>a</b>) channel view and (<b>b</b>) cross-section view.</p>
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<p>Concentration profiles (Re = 0.0865) after mixing has been turned on for (<b>a</b>) 0 s, (<b>b</b>) 250 ms, (<b>c</b>) 500 ms, (<b>d</b>) 750 ms, and (<b>e</b>) 1 s.</p>
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<p>Impact of the maximum mesh element size on the mixing index: (<b>a</b>) time domain; (<b>b</b>) after exactly 1 s.</p>
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<p>Mixing index at the channel outlet for different Reynolds numbers: (<b>a</b>) transient response right after mixing activation; (<b>b</b>) transient response until mixing is settled; (<b>c</b>) after exactly 1 s.</p>
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<p>Distance required to achieve MI = 95% for different values of Re.</p>
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<p>Influence of the actuation potential on the mixing efficiency at the mixing channel outlet: (<b>a</b>) transient response; (<b>b</b>) after 1 s.</p>
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<p>Modified cross-section geometries: (<b>a</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Def</mi> </mrow> <mi>p</mi> </msub> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Def</mi> </mrow> <mi>n</mi> </msub> </semantics></math>.</p>
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<p>Electric potential distribution for the modified geometries: (<b>a</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Def</mi> </mrow> <mi>p</mi> </msub> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Def</mi> </mrow> <mi>n</mi> </msub> </semantics></math>.</p>
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<p>Transient response of mixing index for the different cross-section geometries.</p>
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<p>Electric potential distribution for the modified electrode configurations: (<b>a</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Conf</mi> </mrow> <mrow> <mn>3</mn> <mi>V</mi> </mrow> </msub> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <msub> <mrow> <mi>Conf</mi> </mrow> <mrow> <mn>7</mn> <mi>V</mi> </mrow> </msub> </semantics></math>.</p>
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1 pages, 135 KiB  
Retraction
RETRACTED: Musharavati, F. A Study on Life Cycle Impact Assessment of Seawater Desalination Systems: Seawater Reverse Osmosis Integrated with Bipolar-Membrane-Enhanced Electro-Dialysis Process. Sustainability 2023, 15, 16673
by Farayi Musharavati
Sustainability 2024, 16(8), 3097; https://doi.org/10.3390/su16083097 - 9 Apr 2024
Viewed by 1037
Abstract
The Sustainability Editorial Office retracts the article, “A Study on Life Cycle Impact Assessment of Seawater Desalination Systems: Seawater Reverse Osmosis Integrated with Bipolar-Membrane-Enhanced Electro-Dialysis Process” [...] Full article
12 pages, 2983 KiB  
Article
A Light-Powered Micropump with Dynamic Collective Behavior for Reparation
by Yunyu Sun, Hao Wang, Jiwei Jiang, Hui Zhang, Limei Liu, Keying Zhang, Bo Song and Bin Dong
Nanomaterials 2024, 14(6), 517; https://doi.org/10.3390/nano14060517 - 14 Mar 2024
Viewed by 1231
Abstract
Inspired by the collective behaviors of active systems in nature, the collective behavior of micromotors has attracted more and more attention in recent years. However, little attention has been paid to the collective behavior of the immobilized micromotor, i.e., the micropump. In this [...] Read more.
Inspired by the collective behaviors of active systems in nature, the collective behavior of micromotors has attracted more and more attention in recent years. However, little attention has been paid to the collective behavior of the immobilized micromotor, i.e., the micropump. In this paper, a unique pentacene-based micropump is reported, which demonstrates dynamic collective behavior activated by white light irradiation. The light irradiation may generate the photochemical reactions between pentacene and water, leading to the electroosmotic flow. As a result, this micropump is capable of pumping the surrounding solution inward along the substrate surface based on the electroosmosis mechanism. Intriguingly, the inward pumping causes the agglomeration of the tracer particles on the surface of the micropump. In addition, the aggregation can migrate following the change in the light irradiation position between two adjacent micropumps. Based on the aggregating and migrating behaviors of this pentacene-based micropump, we have achieved the conductivity restoration of the cracked circuit. Full article
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<p>Fabrication and characterization of the pentacene-based micropump. (<b>a</b>) Schematic illustration showing the fabricating process of the micropump based on pentacene. (<b>b</b>) Schematic illustration and (<b>c</b>) scanning electron microscope (SEM) image of the micropump. (<b>d</b>) The EDX analysis of the micropump for carbon element. (<b>e</b>) Atomic force microscopy (AFM) image and (<b>f</b>) the section analysis showing the surface morphology and the thickness of the micropump. (<b>g</b>) Enlarged SEM image of the micropump. (<b>h</b>) Enlarged AFM image of the micropump. (<b>i</b>) The section analysis of the surface shown in (<b>g</b>). (<b>j</b>) UV–Vis–NIR spectrum of the pentacene.</p>
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<p>(<b>a</b>) Schematic illustration and (<b>b</b>) overlaid optical microscopic image showing the pumping behavior of the micropump. White balls: tracer particles. Blue arrows: the direction of pumping behavior. (<b>c</b>) The average velocity of tracer particles as a function of the distance from the border of the pentacene micropump. Light intensity: 0.6 W/cm<sup>2</sup>. (<b>d</b>) The average velocity of tracer particles under different light intensities. (<b>e</b>) The aggregating–dispersing recycles of tracers based on the same micropump. I and II represent the aggregation and dispersion states, respectively. Light intensity: 1.2 W/cm<sup>2</sup>.</p>
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<p>(<b>a</b>,<b>b</b>) Schematic illustration of mechanism of the light-activated pumping behavior. (<b>c</b>) The pH of the solution changes with the illuminating time (light intensity 1.2 W/cm<sup>2</sup>). (<b>d</b>) The velocity of the tracer particles decreases as the concentration of NaCl solution increases.</p>
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<p>Schematic (<b>a</b>) and overlaid image (<b>b</b>,<b>c</b>) showing the aggregating behaviors of tracer particles on the focus spot in a system consisting of two adjacent pentacene microstructures. (<b>d</b>–<b>f</b>) Schematic showing dynamic migration of the aggregation tuned by the light. (<b>g</b>–<b>i</b>) The corresponding optical microscopic images of migrating process. Light intensity: 1.2 W/cm<sup>2</sup>.</p>
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<p>(<b>a</b>) Schematic showing the application in light-controlled reparation of the cracked conductive path. (<b>b</b>,<b>c</b>) The optical microscopic images obtained from <a href="#app1-nanomaterials-14-00517" class="html-app">Video S6 in the Supporting Information</a> showing the dynamic repairing process. The red circles are the micropumps.</p>
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17 pages, 4204 KiB  
Article
Bidirectional and Stepwise Rotation of Cells and Particles Using Induced Charge Electroosmosis Vortexes
by Shaoxi Wang, Zhexin Zhang, Xun Ma, Yuanbo Yue, Kemu Li, Yingqi Meng and Yupan Wu
Biosensors 2024, 14(3), 112; https://doi.org/10.3390/bios14030112 - 20 Feb 2024
Viewed by 1522
Abstract
The rotation of cells is of significant importance in various applications including bioimaging, biophysical analysis and microsurgery. Current methods usually require complicated fabrication processes. Herein, we proposed an induced charged electroosmosis (ICEO) based on a chip manipulation method for rotating cells. Under an [...] Read more.
The rotation of cells is of significant importance in various applications including bioimaging, biophysical analysis and microsurgery. Current methods usually require complicated fabrication processes. Herein, we proposed an induced charged electroosmosis (ICEO) based on a chip manipulation method for rotating cells. Under an AC electric field, symmetric ICEO flow microvortexes formed above the electrode surface can be used to trap and rotate cells. We have discussed the impact of ICEO and dielectrophoresis (DEP) under the experimental conditions. The capabilities of our method have been tested by investigating the precise rotation of yeast cells and K562 cells in a controllable manner. By adjusting the position of cells, the rotation direction can be changed based on the asymmetric ICEO microvortexes via applying a gate voltage to the gate electrode. Additionally, by applying a pulsed signal instead of a continuous signal, we can also precisely and flexibly rotate cells in a stepwise way. Our ICEO-based rotational manipulation method is an easy to use, biocompatible and low-cost technique, allowing rotation regardless of optical, magnetic or acoustic properties of the sample. Full article
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<p>(<b>a</b>) A 3D schematic of the device. (<b>b</b>) The top view of the ITO electrodes under the main channel. (<b>c</b>) A schematic of the experimental setup. The illustration of the basic physics behind ICEO: (<b>d</b>) as soon as the electric field is applied, the electric field lines perpendicularly intersect the center electrode at the beginning. (<b>e</b>) Then, ions in solution are driven to the center electrode. When the double layer is fully formed, the electric field will be screened from the center electrode and paralleled to the surface of the electrode. The ions in the double layer will be driven to generate slip velocity and two counterrotating vortexes. (<b>f</b>) When the center electrode is energized with Vg (Vg &lt; V/2), a positively charged double layer forms, which drives the fluid away towards the grounded electrode and builds asymmetric vortexes. (<b>g</b>) Photograph of the assembled device. (<b>h</b>) A microscopy image of the black dashed line area in (<b>g</b>) showing the main channel and the ITO electrodes. Scale bar, 200 μm.</p>
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<p>(<b>a</b>) The distribution of ICEO velocity (top) and DEP velocity (bottom) in the microchannel under an AC field of V = 10 V, V<sub>g</sub> = floating and f = 500 Hz. There are two vortexes above the center electrode which are symmetrical and rotating in opposite directions. Another two vortexes are respectively above the driving electrodes. They rotate in opposite directions symmetrically. Red and blue colors indicate high and low velocity of ICEO (top) and DEP (bottom), respectively. The direction of ICEO (top) and DEP (bottom) streaming lines is indicated by the red arrows. Yellow and black dashed lines show the position of the vortex center. (<b>b</b>) The distribution of ICEO velocity in the microchannel under an AC field of <span class="html-italic">V</span> = 10 V, <span class="html-italic">V</span><sub>g</sub> = 1 V and <span class="html-italic">f</span> = 500 Hz. The rotation directions of four vortexes are the same as in (<b>a</b>), but they become asymmetrical. (<b>c</b>) Real parts of the CM factors as a function of frequency for yeasts, 10 μm PS particles and 15 μm PS particles at suspending medium conductivity of 8 mS/m. (<b>d</b>) Frequency-dependent electrode surface average velocity of ICEO and DEP of yeasts under an AC field of V = 10 V and V<sub>g</sub> = floating. (<b>e</b>) Voltage-dependent electrode surface average velocity of ICEO and DEP of yeasts under an AC field of V<sub>g</sub> = floating and f = 500 Hz. (<b>f</b>) ICEO velocity of y–z plane at black dashed line in (<b>a</b>). (<b>g</b>) ICEO velocity of y-z plane at yellow dashed line in (<b>a</b>). (<b>h</b>) Relationship between the average velocity of ICEO at surfaces of left driving electrode and the applied voltages of V<sub>g</sub> under an AC field of V = 10 V and f = 500 Hz.</p>
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<p>Schematic of the device in operation. (<b>a</b>) Schematic and image sequences showing that the yeast is continuously rotated clockwise at up driving electrode (Movie 1). (<b>b</b>) Schematic and image sequences showing that the yeast is continuously rotated counterclockwise at top edge of floating electrode, clockwise at bottom edge of floating electrode. Some yeasts are focused in the middle of floating electrode (Movie 2). (<b>c</b>) Schematic and image sequences showing that the yeast is continuously rotated counterclockwise at down driving electrode (Movie 1). Red arrows indicate a specific point on yeast cells. Black scale bar, 5 μm. White scale bar, 100 μm.</p>
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<p>(<b>a</b>) Plot of the rotation speed against voltage of a yeast cell under an AC field of V<sub>g</sub> = floating and f = 500 Hz. (<b>b</b>) Plot of the rotation speed against frequency of a yeast cell under an AC field of V = 10 Vpp and V<sub>g</sub> = floating. (<b>c</b>) Plot of the rotation speed against quantity of yeast under an AC field of V = 10 Vpp, V<sub>g</sub> = floating and f = 500 Hz. (<b>d</b>) Plot of the rotation speed against diameter of manipulated object under an AC field of V = 10 Vpp, V<sub>g</sub> = floating and f = 500 Hz. Scale bar, 2 μm.</p>
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<p>(<b>a</b>) Real parts of the CM factors as a function of frequency for K562 cells at suspending medium conductivities of 8 mS/m, 19 mS/m. (<b>b</b>) Frequency-dependent driving electrode surface average velocity of ICEO of K562 cells under an AC field of V = 10 Vpp and V<sub>g</sub> = floating. (<b>c</b>) Plot of the rotation speed against frequency under an AC field of V = 10 Vpp, V<sub>g</sub> = floating. (<b>d</b>,<b>e</b>) Image sequence showing that the K562 cell is continuously rotated clockwise at suspending medium conductivities of 19 mS/m (Movie 3), 8 mS/m. Red arrows indicate a specific point on K562 cells and black arrows show the rotation direction. Scale bar, 3 μm.</p>
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<p>Rotating yeast cells in opposite directions using ICEO. (<b>a</b>) Image sequences showing that the yeast is continuously rotated counterclockwise at the bottom edge of BPE. Black arrow displays the rotation direction. (<b>b</b>) Image sequences showing the process of moving yeast rotating at the bottom edge of BPE to the top edge of BPE. The red circles display the yeast cells. (<b>c</b>) Image sequences showing that the yeast cell is continuously rotated clockwise at the top edge of BPE (Movie 4). (<b>d</b>) The simulation results of DEP velocity distribution in the microchannel under an AC field of V = 10 V, V<sub>g</sub> = 1 V and f = 500 kHz. The direction of DEP streaming lines is indicated by the red arrows. Scale bar, 5 μm. (<b>e</b>) Image of yeasts focused in the middle of center electrode (left panel), at the top edge of center electrode (center panel) and at the bottom edge of center electrode (right panel). Scale bar, 50 μm.</p>
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<p>Image sequences showing the stepwise rotation of yeasts when supplied with 500 Hz 10 Vpp pulsed signals of (<b>a</b>) 0.6 s duration and (<b>b</b>) 0.2 s duration (Movie 5). Red arrows indicate a specific point on cells Scale bar, 2 μm.</p>
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15 pages, 1903 KiB  
Article
Electrodeionization for Wastewater Reuse in Petrochemical Plants
by Andréia Barros dos Santos, Alexandre Giacobbo, Marco Antônio Siqueira Rodrigues and Andréa Moura Bernardes
Water 2024, 16(3), 401; https://doi.org/10.3390/w16030401 - 25 Jan 2024
Cited by 1 | Viewed by 2408
Abstract
This study investigated a hybrid membrane and electro-membrane separation process for producing demineralized water from tertiary petrochemical effluent, reusing it as feeding water for high-pressure boilers for steam generation. The effluents were treated in a pilot plant with a 1 m3 h [...] Read more.
This study investigated a hybrid membrane and electro-membrane separation process for producing demineralized water from tertiary petrochemical effluent, reusing it as feeding water for high-pressure boilers for steam generation. The effluents were treated in a pilot plant with a 1 m3 h−1 capacity by using a hybrid process of ultrafiltration (UF), reverse osmosis (RO), and electrodeionization (EDI). The physicochemical parameters of interest and maximum limits in industrial water were pre-determined by the industries. Operating parameters such as flow rate, pressure, percentage of recovery, and electric current were monitored, along with the frequency of chemical cleaning. The UF and RO systems operated with average permeate fluxes of 17 ± 4.06 L h−1 m−2 and 20.1 ± 1.9 L h−1 m−2, respectively. Under optimal operating conditions (flow rate of 600 L h−1, voltage of 22.2 ± 0.7 V, and electric current of 1.3 A), EDI produced high-quality water with an average electrical conductivity of 0.22 μS cm−1. Thus, the industrial water produced reached the quality required for reuse as make-up water for high-pressure boilers in the petrochemical industry. In addition, the specific energy consumption; the use of chemicals, spare materials, equipment; and labor costs were determined to support the technical feasibility study for implementing an industrial plant with a 90 m3 h−1 producing capacity. This resulted in a cost of USD 0.64 per cubic meter of demineralized water produced, a cost similar to values reported in the literature. Full article
(This article belongs to the Special Issue Novel Membrane Processes for Water Treatment)
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<p>Schematic diagram of the hybrid demineralized water production system in pilot scale. Adapted from [<a href="#B15-water-16-00401" class="html-bibr">15</a>].</p>
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<p>Portfolio and Project Management Methodology used by industries in the South Petrochemical Complex. PA: project authorization, approval to carry out basic engineering. APE: authorization for execution, approval for project execution. FEL: Front-End Loading, project definition phase. DR: design review, assessment gates with the project team. Adapted from [<a href="#B27-water-16-00401" class="html-bibr">27</a>].</p>
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<p>Conceptual framework of the demineralized water production plant in industrial scale.</p>
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<p>Behavior of the flux, turbidity, and pH of the UF permeate over the operating time.</p>
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<p>Flux and electrical conductivity of the RO permeate over the operating time.</p>
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<p>Concentration values (in logarithmic scale) of the major ions monitored throughout this study after each treatment stage: stabilization pond 8 (SP8), ultrafiltration (UF), reverse osmosis (RO), and electrodeionization (EDI).</p>
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<p>Percentages of the total annual cost of a UF/RO/EDI plant for tertiary petrochemical wastewater treatment with a capacity of 90 m<sup>3</sup> h<sup>−1</sup>.</p>
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