Soft Sensor Development For Real-Time Process Moni
Soft Sensor Development For Real-Time Process Moni
Soft Sensor Development For Real-Time Process Moni
Article
Soft Sensor Development for Real-Time Process Monitoring of
Multidimensional Fractionation in Tubular Centrifuges
Marvin Winkler *,† , Marco Gleiss † and Hermann Nirschl †
Institute of Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology (KIT),
Strasse am Forum 8, 76131 Karlsruhe, Germany; marco.gleiss@kit.edu (M.G.); hermann.nirschl@kit.edu (H.N.)
* Correspondence: marvin.winkler2@kit.edu; Tel.: +49-721-608-42408
† Current address: Strasse am Forum 8, 76131 Karlsruhe, Germany.
Abstract: High centrifugal acceleration and throughput rates of tubular centrifuges enable the solid–
liquid size separation and fractionation of nanoparticles on a bench scale. Nowadays, advantageous
product properties are defined by precise specifications regarding particle size and material com-
position. Hence, there is a demand for innovative and efficient downstream processing of complex
particle suspensions. With this type of centrifuge working in a semi-continuous mode, an online ob-
servation of the separation quality is needed for optimization purposes. To analyze the composition
of fines downstream of the centrifuge, a UV/vis soft sensor is developed to monitor the sorting of
polymer and metal oxide nanoparticles by their size and density. By spectroscopic multi-component
analysis, a measured UV/vis signal is translated into a model based prediction of the relative solids
volume fraction of the fines. High signal stability and an adaptive but mandatory calibration routine
enable the presented setup to accurately predict the product’s composition at variable operating
conditions. It is outlined how this software-based UV/vis sensor can be utilized effectively for chal-
Citation: Winkler, M.; Gleiss, M.; lenging real-time process analytics in multi-component suspension processing. The setup provides
Nirschl, H. Soft Sensor Development insight into the underlying process dynamics and assists in optimizing the outcome of separation
for Real-Time Process Monitoring of tasks on the nanoscale.
Multidimensional Fractionation in
Tubular Centrifuges. Nanomaterials
Keywords: solid–liquid separation; multidimensional particle features; tubular centrifuge; process
2021, 11, 1114. https://doi.org/
monitoring; soft sensor; UV/vis; chemometrics
10.3390/nano11051114
2. Theory
2.1. Fractionation of Nanoparticles in Tubular Centrifuges
A smooth, dispersed solid matter in creeping motion inside a tubular centrifuge
experiences mass and frictional forces as it settles along the radial and axial coordinates
inside a fluid reservoir. The suspension is fed into the centrifuge rotor with a constant
volumetric flow rate V̇f . By assuming plug flow, a particles residence time
π · rb2 − rw
2 ·l
V
tres = = (1)
V̇f V̇f
Nanomaterials 2021, 11, 1114 3 of 21
traveling a distance l inside the centrifuge is altered by the liquid throughput V̇f and
the available surface area A = π · rb2 − rw 2 of the formed liquid pool. A graphical
representation of this cross section and two exemplary settling paths are shown on the
left hand side in Figure 1. The tubes length L, wall rb and weir radius rw constitute the
geometric boundaries during separation.
rb
ω
Inlet l L Overflow
Figure 1. Schematic view of a tubular centrifuge rotor illustrating the separation zone with its length L, exemplary settling
paths of two suspended materials (left) and an axial cross section (right).
2
A second process parameter denoted as the centrifugal number C = ωg·r indicates
the amplified gravitational field strength and is calculated with the angular velocity of the
rotor ω, a reference radius r and the gravitational constant g. In the following, the wall
radius rb is used to calculate C. For uncharged, spherical colloids in an infinitely diluted
suspension with no solid–liquid or solid–solid interactions, the state of force equilibrium
between drag, buoyancy, and centrifugal force yields
xP2 · (ρP − ρf ) · C · g
uP = , (2)
18 · ηf
an expression for the sedimentation velocity along the radial axis valid at sufficiently low
Reynolds numbers (Re P 1). Particles with small diameters xP and a low solid density ρP
traverse a fluid with viscosity ηf slower, whereas larger or heavier particles can reach the
rotor wall faster. Integrating the Stokes settling velocity (Equation (2)) over the liquid pond
depth results in an expression for the settling time tsed of a particle. Substituting tres with
tsed in Equation (1) leads to an approximated settling distance
rb · ln rrwb · 18ηf · V̇f
l= (3)
π rb2 − rw2 · x2 · (ρ − ρ ) · C · g
P P f
for each particle in a collective where density and size might be distributed over a certain
range. Therefore, fractions with sufficiently low settling rates are transported beyond the
rotor weir since l = f ( xP , ρP , . . . ) ≥ L. Note that Equation (3) depicts the process in a
streamlined manner because it is, in addition to the previous mentioned assumptions,
based on the simplification that every particle is introduced at the inlets liquid surface.
Moreover, the fluid is considered pre-accelerated in the inlet zone and radial turbulent
back mixing is also neglected. Nonetheless, Equation (3) clarifies important influencing
parameters of nanoparticle fractionation on the basis of which the results of this paper
are discussed.
It is defined by the measurable ratio of light intensity before ( I0 ) and after the sample
( ) considering that monochromatic light in the wavelength range of 200 nm ≤ λ ≤ 800 nm
I
passes through a layer with thickness d containing homogeneously distributed particles [53].
Each suspended material with its respective volume fraction φn and PSD contributes to the
attenuation by absorption and scattering phenomena. In a generalized approximation, an
effective extinction cross section per unit volume CV,n,λ captures the physical and chemical
properties of the bulk resulting in a unique attenuation coefficient
for every nth component [54]. Substituting αn,λ in Equation (4) expresses the linear change
in extinction
d · CV,n,λ
Eλ = ∑ φn = ∑(φn k n ) (6)
n ln(10) n
with increasing or decreasing φn , assuming otherwise constant optical properties of the bulk
suspension. Expanding Equation (6) to p analytic wavelengths enables the determination
of n concentrations in multi-component systems with one spectrum. However, this requires
knowledge of a corresponding set of extinction coefficients k λ,n , which are not directly
specifiable for arbitrary suspensions. Hence, multivariate regression models are used in a
practical environment to estimate these proportionality factors by conducting a calibration
procedure. The theoretical background of practical spectroscopic multi-component analysis
summarized below is covered in detail in the literature [55,56]. Here, an inverse calibration
is proposed in which the concentrations are calibrated to the extinction at several wave-
lengths. In this approach, the spectroscopic information Eλ in the evaluated λ-range lose
their theoretical background, but the statistics remain present. This enables the practical
construction of regression models, which describe the relationship between the targeted
concentration of a sample and its unique UV/vis spectrum.
The general concept is as follows: spectroscopic extinction data of m calibration standards
at p wavelengths containing n different solids are structured in a (m × p + 1)-dimensional
matrix X. To complete the system of linear equations, the ( p + 1 × m)-dimensional coeffi-
cient matrix β is multiplied with X to receive an expression for the (m × n)-dimensional
target matrix
Y = Xβ (7)
here shown in matrix notation. Note that a nonzero intercept fit requires the addition
of vector u = [1, 1, . . . , 1] with size (1 × p) to the extinction matrix and an extra column
of regression parameters in β. During calibration, each individual extinction spectrum
T
X = E1m , . . . , E pm is labeled with the known target concentrations Y = [φm1 , . . . , φmn ] T .
Using the generalized least squares (OLS) approach, the best possible solution for β in
overdetermined systems ( p > n) is given by
−1
β = XT X XT Y (8)
Ŷ = X̂β. (9)
Nanomaterials 2021, 11, 1114 5 of 21
particles do not tend to form agglomerates. The preliminary suspension treatment served
the purpose of ensuring that both the light and heavy material are in a similar size range.
Bubble trap
Waste
Feed suspension
The separated fine fraction passes over the overflow weir into a collection tray and is
ejected irregularly into the process downstream. A bubble trap separates the suspension–
air mixture into a product and waste stream. The fine material, freed from micron sized
bubbles, is fed into the UV/vis hardware sensor with a peristaltic pump and a volumetric
flow rate of 60 mL min−1 . Sampling takes place at the sensor outlet with no dead time in
Nanomaterials 2021, 11, 1114 7 of 21
relation to spectral data acquisition. The sensor hardware (Ocean Insight former Ocean
Optics, Orlando, FL, USA) used to enable high-speed multi-wavelength extinction mea-
surements consists of a Flame S-XR1 UV/vis spectrometer, a deuterium-halogen DH-2000
light source and a set of optical fibers, which guide the light to both a cross flow cell and
back to the detector.
Between two fused silica windows, monochromatic light passes a one millimeter thick
suspension layer and becomes attenuated by the excitation of molecules and scattering
phenomena induced by dispersed particles. The schematic structure of the sensor is shown
in (Figure 4b). Every 400 ms one spectrum is recorded and locally saved as a text file.
The extinction Eλ is measured in a wavelength range of 200 nm ≤ λ ≤ 800 nm. Each
measurement can be assigned to a process time outlining the change in extinction at several
wavelengths. Regarding sensor calibration with samples of known concentration, the
hardware setup is slightly altered, as outlined in Figure 4a. Here, dispersion is continuously
stirred and cycled through the cross flow cell. A pre-calculated and gradual dilution with
demineralized water or suspension in multiple steps allows a time efficient acquisition of
calibration data sets. This procedure is described more thoroughly in the supplementary
material of this paper.
(a) (b)
Sampling
step i
⁞ D D
from
step 2 overflow
step 1 data data
.txt export .txt export
peristaltic pump light source detector bubble trap UV/vis cross flow cell
Figure 4. Illustration of the calibration setup (a) and the experimental setup (b) of the hardware sensor. Components are depicted and
named in the bottom legend.
Regarding mixtures of both solids (n = 2), only the total solid mass – removed – can be
evaluated with this technique. In order to infer the proportional mass of both PMMA
and ZnO after separation, an inductively coupled plasma optical emission spectrometry
(ICP-OES) analysis was carried out. The analytical technique measured the content of
pure zinc in each sample, which allowed a stoichiometric approximation of the zinc oxide
concentration. Since the total amount of solids (TAS) mTAS is composed of zinc oxide and
PMMA under exclusion of the stabilizing agents mass, the nanoplastic content can be
quantified with the closing condition as follows:
ICP-OES data used for the practical estimation of zinc oxide mass are available as SI
(Supplementary Materials).
Besides the holistic contemplation of material separation, the grade efficiency
µn,weir ( xP )
Tn ( xP ) = 1 − (12)
µn,feed ( xP )
of component n is the second quantity to help evaluate the density fractionation experi-
ments. The separation probability is calculated by the ratio of material specific relative mass
µn per particle size xP in weir and feed samples. In regard to the described measurement
principles of the CPS disk centrifuge it was not possible to measure the relative mass of
both dispersed materials at the same time. In a preliminary experiment it was observed
that ZnO can be successfully stabilized by sodium hexametaphosphate. Moreover, the
preliminary examination revealed that a further increase in the stabilizer concentration
to 4.5 mM resulted in the complete dissolution of the ZnO particles. Consequently, the
samples turbidity vanished and the corresponding extinction spectrum was congruent
with the measured background of demineralized water. Crucially, the PMMA NPs are
not affected by the increased concentration of the stabilizing agent. Therefore, sodium
hexametaphosphate was added to a mixed suspension before analyzing it in the CPS disk
centrifuge. The resulting dissolution of ZnO NPs enables an interference-free measurement
of the PSD and, therefore, the grade efficiency of the suspended polymer.
most relevant variables in X with the help of a filter method. For this study, a univariate
mutual information (MI) statistic was chosen and implemented via the scikit-learn API. It
T
computes the relatedness between each individual signal Xp = Ep1 , Ep2 , . . . , Epm and
response Yn = [φn1 , φn2 , . . . , φnm ] T column-wise with a nearest neighbor method [64]. The
algorithm thus points to those wavelengths that are most likely to increase the correlation
between the measured data and the target variable, quantifying it with a dimensionless MI
index. In light of this, data reduction is performed manually by discarding wavelengths
with low MI values, generating an adjusted matrix X with size m × d. To justify this selec-
tion, the model is then evaluated based on an intrinsic cross validation method described
in the following section.
for each individual component comparing the solids volume fractions φ̈n,j with the corre-
sponding model prediction φ̈ˆ . Here, φ̈¯ n denotes the mean of each column in Ÿ. Values
n,j
of R2n close to unity suggest a high prediction strength of the regression model [65]. If the
correlation is not satisfactory, X can be adjusted manually in further iterations of the cali-
bration pipeline, as outlined in Figure 5. Lastly, a chosen adjusted calibration set calculates
the coefficient matrix β substituted in Equation (9) to quantify the composition Ŷ(t) of in
situ acquired process samples.
Ẋ Ẏ MLR model
z
X Y MI filter X Y
m m d n n
q Ẍ Ÿ d
β̇ n
Figure 5. Graphical representation of the sensor software setup described in Sections 3.2.1 and 3.2.2. Matrices are denoted as
brackets with their dimensions drawn on the top and left. The inner loop (solid arrows) highlights the calibration procedure
including supervised feature selection with an MI filter, model training and diagnostic measures. The outer loop (dashed
arrows) visualizes the translation of raw UV/vis process data Ŷ(t) into a prediction of the suspension composition X̂(t).
Nanomaterials 2021, 11, 1114 10 of 21
4. Results
This chapter elaborates on a documented field test of the developed soft sensor used
in real-time suspension analysis at the overflow of a tubular centrifuge. The experimental
endeavor includes the processing of PMMA in single-component suspension (expC-1) and
the fractionation of both PMMA and ZnO in a mixture (expF). A short-time experiment
(expC-2), in which a ZnO suspension is processed at C = 10,000, is used for comparative
purposes only to analyze the grade efficiency in the CPS disc centrifuge.
An overview of the initial solids volume fractions in the product feeds as well as the
corresponding operating parameters is shown in Table 1. Low initial particle concentrations
ensure an inferior influence of the sediment build-up on the overflow monitoring. During
classification (expC-1) at a constant centrifugation number, signal stability and separation
efficiency is observed. In fractionation (expF) on the other hand, a ramp up in rotor
speed is set to monitor changes in multivariate suspension composition under varying
process conditions. The soft sensor is set to predict the solids volume fraction φ̂n in an
effort to quantify the specific product loss (Equation (10)) in real-time. Unless otherwise
stated, separation proceedings were carried out two-fold. Consequently, the predictive
sensor output is based on two unique extinction signals per unit of time in the centrifuge
overflow. Similarly, lab scale reference measurements on suspension composition are
repeated at least three times to obtain a mean and standard deviation. The first part
highlights the sensor calibration procedure and model framework used to monitor the
separation process, whereas the second part focuses on the soft sensor application and
separation outcome evaluation.
Operating Parameters
Experiment Feed Concentration Volumetric Flow Rate Centrifugal Number Process Time
φPMMA /- φZnO /- V̇f /mL · min−1 C1 /- C2 /- C3 /- t/min
expC-1 1.359 × 10−3 0 100 30,000 - - 60
expC-2 0 9.264 × 10−5 100 10,000 - - 15
expF 1.631 × 10−3 7.181 × 10−5 100 10,000 30,000 50,000 35
Figure 6. Overview of collected calibration spectra for classification (caC) and fractionation (caF).
(a) (c)
(b)
Figure 7. Outcome of applied data pre-processing and model diagnostic. On the left in the background, three selected
data segmentation zones are displayed: feature range FR1 (blue, hatched sideways from top to bottom), FR2 (red, hatched
sideways from bottom to top) and FR3 (green, cross hatched). (a) Mean extinction of calibration data set caC and caF drawn
over the wavelength range of interest. (b) Mutual information for components PMMA and ZnO at every wavelength.
(c) Visual inspection of model suitability plotting predicted φ̈ˆ n,m against known φ̈n,m concentrations. Data points are
normalized to the highest volume fraction in each column of matrix Ÿ. For every component, the coefficient of determination
R2n is displayed.
overflow. In comparison, Figure 8b highlights the rotor speed ramp up with three distinct
plateaus of constant light attenuation during fractionation. A detailed view of speed level
settings against the process time is shown in Figure 9c.
(a) (b)
(c)
expC-1
expF
Sampling of roughly 200 mL of fines takes place in a period of two minutes at the
sensor outlet. Each individual time of extraction is marked with small arrows and red dash
dotted lines. A reference is only taken when the system is in a steady state indicated by a
constant UV/vis signal. Four of these samples and their corresponding feed dispersions
are shown in the lower half of Figure 8. Qualitative inspection with the human eye shows
a stronger turbidity in mixed suspension, caused by the dispersed ZnO particles and their
high refractive index. Overall, the transmittance increases with rotor speed due to more
solids being deposited at the rotor wall.
Nanomaterials 2021, 11, 1114 14 of 21
(a)
(b)
(c)
Figure 9. Comparison of sensor output (solid symbols) and laboratory analysis (half-filled symbols) of the product loss in
fractionation (a) and classification (b) monitoring over the elapsed process time. The set centrifugation number is drawn on
shared abscissa (c). The soft sensor output is based on the corresponding calibration data set of feature range FR2.
Figure 10. Summary of grade efficiency plots for PMMA after fractionation at three C-values (diamonds) and classification
at a constant rotor speed (circles). An additional classification run of a pure ZnO suspension at C = 10,000 yields the leftmost
partition curve (triangles).
loss (small symbols) is given for both classification and fractionation experiments on the
y-axis. Here, raw extinction data were reduced according to feature range FR2. Prediction
results of domains FR1 and FR3 are visualized in two similar plots in the SI (Supplementary
Materials). The abscissa is shared between the subfigures and shows the elapsed process
time. For de-cluttering purposes, every 15th datapoint is shown. Furthermore, each
individual marker is displaced 1.42 minutes to the left due to the observed dead time
between the centrifuge outlet and sensor inlet. Superposed large symbols represent the
offline reference P̃n . Further details on the laboratory analysis performed to determine the
relative solids volume fraction in each sample, and thus the corresponding true product
loss, can be found in Section 3.1.3. Horizontal error bars symbolize the time it took to
gather the samples.
In the following, P̂n and P̃n of each component are discussed individually based on the
introduced theory of nanoparticle separation written in Section 2.1. Contemporaneously,
the sensor performance is specified by the mean prediction error (MPE):
φ̃n − φ̂n
MPEn = × 100% (14)
φ̃n
and summarized for each individual feature range and material in Table 2.
In Figure 9b, the sensor translates unseen extinction spectra (Figure 8a) into the
corresponding product loss of PMMA during classification. Centrifugation at a C-value of
30,000 results in a constant product loss of around 60%. Predictive and reference measures
prove that no significant rise of product loss takes place during classification. This can be
explained by the consciously chosen, low feed concentrations. The sediment formed in the
rotor does not affect the deposition of the polymer since its volume does not shorten the
particles residence time, resulting in a constant separation efficiency.
The determined product loss of all samples taken during this time period coincides
with the values generated by the MLR predictor with an MPE of just 5.913%. The other fea-
ture ranges perform slightly worse, although the inclusion of wavelengths where extinction
shows a lower signal-to-noise ratio seems counter-intuitive. Rather, it is more reasonable to
evaluate spectral data at wavelengths where most of the chemical information is located in
interference-free signals. This is the case for FR2 incorporating multiple wavelengths with
high MI indices.
Assuming that random errors in the recording of the spectra during processing or
analysis errors of the reference measurements are negligible, a systematic error can be
observed. With few exceptions, the soft sensor output tends to underestimate the true
product loss in the centrifuge overflow. These deviations can be explained by the attenua-
tion coefficient expressed in Equation (5). Therein, both absorption and scattering cross
sections define CV,n,λ as an optical constant of the analyzed suspension. As highlighted in
Figure 10, PSDs of both materials are adjusted during separation, emphasizing a possible
change in the effective extinction cross section of the bulk suspension. Strictly speaking,
the linear relationship defined in Equation (6), therefore, no longer applies to the in situ
extinction analysis of the fine fraction samples. According to fundamentals, the wavelength
dependent scattering intensity is altered by the materials refractive index and scales with
particle size to the power of six [68]. Hence, the induced separation of the coarser fraction
in classification and fractionation affects the shape of a measured extinction spectrum.
Yet, the MPE regarding the online monitoring of PMMA classification is low although the
systems PSD is altered. One explanation is that differences in the mean volume weighted
diameter of the feed (103 nm ± 1 nm) and the overflow samples (89 nm ± 0.5 nm) are
very small. This leads towards the assumption that the scattered light intensity does not
change significantly enough to hurt the suitability of the established linear soft sensor
model. Similar observations were made during studies establishing a continuous overflow
monitoring based on measurements of scattered light [39]. Here, calibration data sets were
also recorded from dilutions of the product feed, which failed to sensitize the underlying
model with respect to the changes in the materials PSD.
Nanomaterials 2021, 11, 1114 17 of 21
Table 2. Prediction error for the solids volume fraction φ specified for each material (PMMA, ZnO)
as well as the combined amount of suspended solids (TAS) excluding the mass of stabilizing agent
Na6P6O18. The row related to the chosen feature range FR2 has the lowest MPE.
The second experiment to assess is the density fractionation of both PMMA and ZnO
in mixture highlighted in Figure 8a. The overall product loss analyzed by gravimetric
offline measurements is depicted by half filled, blue diamonds. Note that the TAS here
refers to the corrected mass of both PMMA and ZnO in the dried sample excluding the
weight of Na6P6O18 crystals. It is clearly shown that the ramp up in rotor speed leads
to a better separation of the suspended solids. The sensor can therefore identify changes
in the operating parameters with little delay. With Equation (11), this information was
used in conjunction with the ICP-OES analysis to compute the true relative solids volume
fraction of both materials. In direct comparison, ZnO is separated more effectively at
each of the three C-values due to its higher density and faster radial movement in the
centrifuge rotor according to Equation (2). Consequently at C = 30,000, 6.0% of the heavy
material remains in the product stream. At C = 50,000, mere traces of ZnO are measurable
exclusively by the conducted ICP-OES analysis, verifying a product loss of 3.4%. Online
monitoring as well as lab scale reference measurements outline reproducible magnitudes
of product loss at the three distinct plateaus with constant rotor speed. When reviewing
the MSE, a moderate prediction error of 4.698% in the case of the light polymer can be
observed, which is comparable to the prediction quality in classification. Regarding the
heavy metal oxide ZnO, however, predictions for P̂ZnO underestimate the true solids
volume fraction in the overflow by 8.5%. Error discussion jet involves basic theory of
light scattering by an ensemble of particles. In the case of ZnO, the feed distribution is
broader and therefore the particles effective extinction cross section is accompanied by a
more pronounced scattering part. It is likely that the removal of coarse particle fractions
during centrifugation results in a considerable alteration of the bulks’ optical properties.
Because the sensor software is only capable of modeling linear dependence of extinction
and concentration at constant PSD, this effect could explain the more inaccurate predictions
of the sensor in regard to the product loss of ZnO. Several studies [69,70] list the impact of
changing PSDs as a confounding factor in quantitative spectroscopic analysis of particle-
loaded fluids. Possible adjustments to the model may include an empirically determined
correction factor that adjusts the sensor output in accordance to the change in scattering
properties of the sample. It is also conceivable that a more diverse calibration data set could
be recorded based on collected overflow samples at variable operating parameters. The
results of a preliminary study highlight the potential benefit in prediction accuracy when
incorporating classified samples in the calibration procedure regarding spectroscopic multi-
component analysis [43]. The disadvantage here, however, is the increased effort required
to calibrate the UV/vis sensor. In light of this, multiple regression at several carefully
chosen wavelengths marks a supportive approach presented in this paper. In the future, it
is imaginable to evaluate the extinction spectra of samples with known concentrations and
PSD to be able to perform more precise estimations of the fine fractions composition.
Taken altogether, the data presented here provide strong evidence that the developed
soft sensor is able to monitor the solids volume fraction in the overflow of a tubular
centrifuge. Despite error prone predictions regarding the material ZnO, the product
loss is monitored qualitatively and plausibly according to induced changes in operating
Nanomaterials 2021, 11, 1114 18 of 21
parameters. In the case of PMMA NPs separation, accurate predictions are achievable
when following the suggested method (Figure 5) of sensor calibration.
5. Conclusions
The demand for polydisperse particle systems in the nanometer range, which have
defined properties in regard to their PSD and material composition, is steadily increasing.
Tubular centrifuges offer an approach for bench scale classification and fractionation of
these particles. Due to their semi-continuous operation mode, however, process monitoring
is needed to assist further optimization endeavors. For this reason, the presented study
involves a UV/vis soft-sensor, which was installed in the tubular centrifuges overflow. Its
hardware part continuously acquired an extinction spectrum of processed fines containing
either polymer NPs (PMMA), suspended metal oxide particles (ZnO) or a mixture of
both. Furthermore, a multivariate regression model scheme was developed and connected
to the raw extinction data processing. For this purpose, a sensor calibration procedure
with feed samples of known concentration and material composition was mandatory.
Extinction values measured at wavelengths that contributed to the regression model
quality were identified and manually separated from statistically insignificant inputs.
This enabled parallel, real-time model-based predictions of the solids volume fraction of
both processed materials in the centrifuge overflow. When compared to offline sampling
and costly laboratory analysis, the model has a low prediction error with respect to the
approximation of the solids volume fraction of PMMA. In the case of ZnO, a significantly
greater degree of material separation at increasing rotor speeds is observed. Accompanied
by a more drastic shift in the PSD, the precise computation of the solids volume fraction
of metal oxide NPs was complicated. This was explained by fundamental theory of light
scattering by small particles and the influence of the changing extinction cross section
due to induced separation of coarser fractions. Continuing studies may include the same
soft-sensor setup but follow a different routine in calibration data acquisition. This could
successfully improve the model based on a correction factor if inconsistent scattering
properties of the analyzed fines are expected. Nonetheless, the presented setup enables the
efficient online monitoring of both classification and material sorting in tubular centrifuges
at low particle concentrations. Because a fast response to changes in operating parameters
was achieved, the soft sensor setup leads to an improved understanding of the separation
process and its underlying mechanics. Finally, its integration opens up new perspectives
regarding real-time process control for product quality maintenance.
Acknowledgments: The authors would like to thank Carl Padberg Zentrifugenbau GmbH (CEPA) for
providing the Z11 type tubular centrifuge and Evonik Industries AG for donating the PMMA NPs. We
also thank the Institute of Functional Interfaces (IFG, KIT) for performing the ICP-OES analysis. We
acknowledge support by the KIT-Publication Fund of the Karlsruhe Institute of Technology. Funding
by the Deutsche Forschungsgemeinschaft (DFG; NI 414/31-2) is also gratefully acknowledged.
Conflicts of Interest: The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported in this paper.
Abbreviations
The following abbreviations are used in this manuscript:
References
1. Wong, A.; Liu, Q.; Griffin, S.; Nicholls, A.; Regalbuto, J.R. Synthesis of ultrasmall, homogeneously alloyed, bimetallic nanoparticles
on silica supports. Science 2017, 358, 1427–1430. [CrossRef]
2. Alegret, N.; Criado, A.; Prato, M. Recent Advances of Graphene-based Hybrids with Magnetic Nanoparticles for Biomedical
Applications. Curr. Med. Chem. 2017, 24, 529–536. [CrossRef] [PubMed]
3. Adair, J.H.; Suvaci, E. Morphological control of particles. Curr. Opin. Colloid Interface Sci. 2000, 5, 160–167. [CrossRef]
4. Zhang, J.; Yang, S.; Chen, Z.; Yan, Y.; Zhao, J.; Li, J.; Jiang, Z. In Situ synthesis of SiC-graphene core-shell nanoparticles using wet
ball milling. Ceram. Int. 2018, 44, 8283–8289. [CrossRef]
5. Malamatari, M.; Taylor, K.M.; Malamataris, S.; Douroumis, D.; Kachrimanis, K. Pharmaceutical nanocrystals: production by wet
milling and applications. Drug Discov. Today 2018, 23, 534–547. [CrossRef] [PubMed]
6. Ramos, A.P.; Cruz, M.A.E.; Tovani, C.B.; Ciancaglini, P. Biomedical applications of nanotechnology. Biophys. Rev. 2017, 9, 79–89.
[PubMed]
7. Liu, W.T. Nanoparticles and their biological and environmental applications. J. Biosci. Bioeng. 2006, 102, 1–7. [CrossRef] [PubMed]
8. Zhang, X. Gold Nanoparticles: Recent Advances in the Biomedical Applications. Cell Biochem. Biophys. 2015, 72, 771–775.
[CrossRef]
9. Geszke-Moritz, M.; Moritz, M. Solid lipid nanoparticles as attractive drug vehicles: Composition, properties and therapeutic
strategies. Mater. Sci. Eng. C 2016, 68, 982–994. [CrossRef]
10. Panigrahi, S.; Basu, S.; Praharaj, S.; Pande, S.; Jana, S.; Pal, A.; Ghosh, S.K.; Pal, T. Synthesis and Size-Selective Catalysis
by Supported Gold Nanoparticles: Study on Heterogeneous and Homogeneous Catalytic Process. J. Phys. Chem. C 2007,
111, 4596–4605. [CrossRef]
11. Narayanan, R.; El-Sayed, M.A. Shape-Dependent Catalytic Activity of Platinum Nanoparticles in Colloidal Solution. Nano Lett.
2004, 4, 1343–1348. [CrossRef]
12. He, Z.; Zhang, Z.; Bi, S. Nanoparticles for organic electronics applications. Mater. Res. Express 2020, 7, 012004. [CrossRef]
13. Shen, W.; Zhang, X.; Huang, Q.; Xu, Q.; Song, W. Preparation of solid silver nanoparticles for inkjet printed flexible electronics
with high conductivity. Nanoscale 2014, 6, 1622–1628. [CrossRef] [PubMed]
14. Bliznyuk, V.; Ruhstaller, B.; Brock, P.J.; Scherf, U.; Carter, S.A. Self-Assembled Nanocomposite Polymer Light-Emitting Diodes
with Improved Efficiency and Luminance. Adv. Mater. 1999, 11, 1257–1261. [CrossRef]
15. Plüisch, C.S.; Wittemann, A. Shape-Tailored Polymer Colloids on the Road to Become Structural Motifs for Hierarchically
Organized Materials. Macromol. Rapid Commun. 2013, 34, 1798–1814. [CrossRef]
16. Maneeprakorn, W.; Malik, M.A.; O’Brien, P. Developing Chemical Strategies for the Assembly of Nanoparticles into Mesoscopic
Objects. J. Am. Chem. Soc. 2010, 132, 1780–1781. [CrossRef]
Nanomaterials 2021, 11, 1114 20 of 21
17. Wang, H.; Brandl, D.W.; Nordlander, P.; Halas, N.J. Plasmonic Nanostructures: Artificial Molecules. Accounts Chem. Res. 2007,
40, 53–62. [CrossRef]
18. Cheon, J.Y.; Kim, S.J.; Rhee, Y.H.; Kwon, O.H.; Park, W.H. Shape-dependent antimicrobial activities of silver nanoparticles. Int. J.
Nanomed. 2019, 14, 2773–2780. [CrossRef] [PubMed]
19. Suchomel, P.; Kvitek, L.; Prucek, R.; Panacek, A.; Halder, A.; Vajda, S.; Zboril, R. Simple size-controlled synthesis of Au
nanoparticles and their size-dependent catalytic activity. Sci. Rep. 2018, 8. [CrossRef]
20. Tong, S.; Quinto, C.A.; Zhang, L.; Mohindra, P.; Bao, G. Size-Dependent Heating of Magnetic Iron Oxide Nanoparticles. ACS
Nano 2017, 11, 6808–6816. [CrossRef] [PubMed]
21. Woźniak, A.; Malankowska, A.; Nowaczyk, G.; Grześkowiak, B.F.; Tuśnio, K.; Słomski, R.; Zaleska-Medynska, A.; Jurga, S. Size
and shape-dependent cytotoxicity profile of gold nanoparticles for biomedical applications. J. Mater. Sci. Mater. Med. 2017, 28, 92.
[CrossRef] [PubMed]
22. Cao, S.; Tao, F.F.; Tang, Y.; Li, Y.; Yu, J. Size- and shape-dependent catalytic performances of oxidation and reduction reactions on
nanocatalysts. Chem. Soc. Rev. 2016, 45, 4747–4765. [CrossRef] [PubMed]
23. Patsula, V.; Moskvin, M.; Dutz, S.; Horák, D. Size-dependent magnetic properties of iron oxide nanoparticles. J. Phys. Chem.
Solids 2016, 88, 24–30. [CrossRef]
24. Adams, C.P.; Walker, K.A.; Obare, S.O.; Docherty, K.M. Size-Dependent Antimicrobial Effects of Novel Palladium Nanoparticles.
PLoS ONE 2014, 9, e85981. [CrossRef] [PubMed]
25. Zhang, S.; Li, J.; Lykotrafitis, G.; Bao, G.; Suresh, S. Size-Dependent Endocytosis of Nanoparticles. Adv. Mater. 2009, 21, 419–424.
[CrossRef] [PubMed]
26. Plüisch, C.S.; Bössenecker, B.; Dobler, L.; Wittemann, A. Zonal rotor centrifugation revisited: new horizons in sorting nanoparticles.
RSC Adv. 2019, 9, 27549–27559. [CrossRef]
27. Sun, X.; Tabakman, S.; Seo, W.S.; Zhang, L.; Zhang, G.; Sherlock, S.; Bai, L.; Dai, H. Separation of Nanoparticles in a Density
Gradient: FeCo@C and Gold Nanocrystals. Angew. Chem. Int. Ed. 2009, 48, 939–942. [CrossRef] [PubMed]
28. Fagan, J.A.; Becker, M.L.; Chun, J.; Nie, P.; Bauer, B.J.; Simpson, J.R.; Hight-Walker, A.; Hobbie, E.K. Centrifugal Length Separation
of Carbon Nanotubes. Langmuir 2008, 24, 13880–13889. [CrossRef] [PubMed]
29. Novak, J.P.; Nickerson, C.; Franzen, S.; Feldheim, D.L. Purification of Molecularly Bridged Metal Nanoparticle Arrays by
Centrifugation and Size Exclusion Chromatography. Anal. Chem. 2001, 73, 5758–5761. [CrossRef] [PubMed]
30. Spelter, L.E.; Meyer, K.; Nirschl, H. Screening of Colloids by Semicontinuous Centrifugation. Chem. Eng. Technol. 2012,
35, 1486–1494. [CrossRef]
31. Lohse, S.E.; Eller, J.R.; Sivapalan, S.T.; Plews, M.R.; Murphy, C.J. A Simple Millifluidic Benchtop Reactor System for the High-
Throughput Synthesis and Functionalization of Gold Nanoparticles with Different Sizes and Shapes. ACS Nano 2013, 7, 4135–4150.
[CrossRef] [PubMed]
32. Segets, D.; Komada, S.; Butz, B.; Spiecker, E.; Mori, Y.; Peukert, W. Quantitative evaluation of size selective precipitation of
Mn-doped ZnS quantum dots by size distributions calculated from UV/Vis absorbance spectra. J. Nanopart. Res. 2013, 15.
[CrossRef]
33. Spelter, L.E.; Steiwand, A.; Nirschl, H. Processing of dispersions containing fine particles or biological products in tubular bowl
centrifuges. Chem. Eng. Sci. 2010, 65, 4173–4181. [CrossRef]
34. Spelter, L.E.; Nirschl, H. Classification of Fine Particles in High-Speed Centrifuges. Chem. Eng. Technol. 2010, 33, 1276–1282.
[CrossRef]
35. Konrath, M.; Brenner, A.K.; Dillner, E.; Nirschl, H. Centrifugal classification of ultrafine particles: Influence of suspension
properties and operating parameters on classification sharpness. Sep. Purif. Technol. 2015, 156, 61–70. [CrossRef]
36. Konrath, M.; Gorenflo, J.; Hübner, N.; Nirschl, H. Application of magnetic bearing technology in high-speed centrifugation.
Chem. Eng. Sci. 2016, 147, 65–73. [CrossRef]
37. Kohsakowski, S.; Seiser, F.; Wiederrecht, J.P.; Reichenberger, S.; Vinnay, T.; Barcikowski, S.; Marzun, G. Effective size separation
of laser-generated, surfactant-free nanoparticles by continuous centrifugation. Nanotechnology 2019, 31, 095603. [CrossRef]
[PubMed]
38. Flegler, A.; Schneider, M.; Prieschl, J.; Stevens, R.; Vinnay, T.; Mandel, K. Continuous flow synthesis and cleaning of nano
layered double hydroxides and the potential of the route to adjust round or platelet nanoparticle morphology. RSC Adv. 2016,
6, 57236–57244. [CrossRef]
39. Konrath, M.; Hackbarth, M.; Nirschl, H. Process monitoring and control for constant separation conditions in centrifugal
classification of fine particles. Adv. Powder Technol. 2014, 25, 991–998. [CrossRef]
40. Frank, U.; Wawra, S.E.; Pflug, L.; Peukert, W. Multidimensional Particle Size Distributions and Their Application to Nonspherical
Particle Systems in Two Dimensions. Part. Part. Syst. Charact. 2019, 36, 1800554. [CrossRef]
41. Kadlec, P.; Gabrys, B.; Strandt, S. Data-driven Soft Sensors in the process industry. Comput. Chem. Eng. 2009, 33, 795–814.
[CrossRef]
42. Souza, F.A.; Araújo, R.; Mendes, J. Review of soft sensor methods for regression applications. Chemom. Intell. Lab. Syst. 2016,
152, 69–79. [CrossRef]
43. Winkler, M.; Sonner, H.; Gleiss, M.; Nirschl, H. Fractionation of ultrafine particles: Evaluation of separation efficiency by UV–vis
spectroscopy. Chem. Eng. Sci. 2020, 213, 115374. [CrossRef]
Nanomaterials 2021, 11, 1114 21 of 21
44. Rhein, F.; Scholl, F.; Nirschl, H. Magnetic seeded filtration for the separation of fine polymer particles from dilute suspensions:
Microplastics. Chem. Eng. Sci. 2019, 207, 1278–1287. [CrossRef]
45. Paramelle, D.; Sadovoy, A.; Gorelik, S.; Free, P.; Hobley, J.; Fernig, D.G. A rapid method to estimate the concentration of citrate
capped silver nanoparticles from UV-visible light spectra. Analyst 2014, 139, 4855. [CrossRef]
46. Liu, F.K.; Ko, F.H.; Huang, P.W.; Wu, C.H.; Chu, T.C. Studying the size/shape separation and optical properties of silver
nanoparticles by capillary electrophoresis. J. Chromatogr. A 2005, 1062, 139–145. [CrossRef]
47. Shah, D.; Wang, J.; He, Q.P. A feature-based soft sensor for spectroscopic data analysis. J. Process. Control. 2019, 78, 98–107.
[CrossRef]
48. Rüdt, M.; Vormittag, P.; Hillebrandt, N.; Hubbuch, J. Process monitoring of virus-like particle reassembly by diafiltration with
UV/Vis spectroscopy and light scattering. Biotechnol. Bioeng. 2019, 116, 1366–1379. [CrossRef] [PubMed]
49. Bartosiak, M.; Giersz, J.; Jankowski, K. Analytical monitoring of selenium nanoparticles green synthesis using photochemical vapor
generation coupled with MIP-OES and UV–Vis spectrophotometry. Microchem. J. 2019, 145, 1169–1175. [CrossRef]
50. Rato, T.J.; Reis, M.S. Building Optimal Multiresolution Soft Sensors for Continuous Processes. Ind. Eng. Chem. Res. 2018,
57, 9750–9765. [CrossRef]
51. Hendel, T.; Wuithschick, M.; Kettemann, F.; Birnbaum, A.; Rademann, K.; Polte, J. Correction to In Situ Determination of Colloidal
Gold Concentrations with UV–Vis Spectroscopy: Limitations and Perspectives. Anal. Chem. 2015, 87, 5846–5847. [CrossRef]
[PubMed]
52. Sinn, T.; Flegler, A.; Wolf, A.; Stübinger, T.; Witt, W.; Nirschl, H.; Gleiß, M. Investigation of Centrifugal Fractionation with
Time-Dependent Process Parameters as a New Approach Contributing to the Direct Recycling of Lithium-Ion Battery Components.
Metals 2020, 10, 1617. [CrossRef]
53. Mäntele, W.; Deniz, E. UV—VIS absorption spectroscopy: Lambert-Beer reloaded. Spectrochim. Acta Part A 2017, 173, 965–968.
[CrossRef] [PubMed]
54. Bohren, C.F.; Huffman, D.R. Absorption and Scattering of Light by Small Particles; Wiley-VCH: Weinheim, Germany, 2004.
55. Otto, M.V. Chemometrics: Statistics and Computer Application in Analytical Chemistry, 3rd ed.; Wiley-VCH: Weinheim, Germany, 2017.
56. Maris, M.A.; Brown, C.W.; Lavery, D.S. Nonlinear multicomponent analysis by infrared spectrophotometry. Anal. Chem. 1983,
55, 1694–1703. [CrossRef]
57. Senoussaoui, N.; Krause, M.; Müller, J.; Bunte, E.; Brammer, T.; Stiebig, H. Thin-film solar cells with periodic grating coupler.
Thin Solid Film. 2004, 451–452, 397–401. [CrossRef]
58. Pizzini, S.; Buttá, N.; Narducci, D.; Palladino, M. Thick Film ZnO Resistive Gas Sensors: Analysis of Their Kinetic Behavior. J.
Electrochem. Soc. 1989, 136, 1945–1948. [CrossRef]
59. Müller, J.; Weißenrieder, S. ZnO-thin film chemical sensors. Fresenius’ J. Anal. Chem. 1994, 349, 380–384. [CrossRef]
60. Kołodziejczak-Radzimska, A.; Jesionowski, T. Zinc Oxide—From Synthesis to Application: A Review. Materials 2014, 7, 2833–2881.
[CrossRef] [PubMed]
61. Mie, G. Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Ann. Der Phys. 1908, 330, 377–445. [CrossRef]
62. Harris, C.R. Array programming with NumPy. Nature 2020, 585, 357–362. [CrossRef] [PubMed]
63. Buitinck, L.; Louppe, G.; Blondel, M.; Pedregosa, F.; Mueller, A.; Grisel, O.; Niculae, V.; Prettenhofer, P.; Gramfort, A.; Grobler, J.;
et al. API design for machine learning software: Experiences from the scikit-learn project. arXiv 2013, arXiv:1309.0238.
64. Ross, B.C. Mutual Information between Discrete and Continuous Data Sets. PLoS ONE 2014, 9, e87357. [CrossRef] [PubMed]
65. Renaud, O.; Victoria-Feser, M.P. A robust coefficient of determination for regression. J. Stat. Plan. Inference 2010, 140, 1852–1862.
[CrossRef]
66. Yoshikawa, H.; Adachi, S. Optical Constants of ZnO. Jpn. J. Appl. Phys. 1997, 36, 6237–6243. [CrossRef]
67. Srikant, V.; Clarke, D.R. Optical absorption edge of ZnO thin films: The effect of substrate. J. Appl. Phys. 1997, 81, 6357–6364.
[CrossRef]
68. Seinfeld, J.H.V. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 3rd ed.; Wiley: Hoboken, NJ, USA, 2016.
69. Gippel, C.J. Potential of turbidity monitoring for measuring the transport of suspended solids in streams. Hydrol. Process. 1995,
9, 83–97. [CrossRef]
70. Eerdenbrugh, B.V.; Alonzo, D.E.; Taylor, L.S. Influence of Particle Size on the Ultraviolet Spectrum of Particulate-Containing
Solutions: Implications for In-Situ Concentration Monitoring Using UV/Vis Fiber-Optic Probes. Pharm. Res. 2011, 28, 1643–1652.
[CrossRef]