Tarea 5 Masa N

Tarea 5
Transferencia de masa por difusión y balance macroscópico de masa
1. The efficacy of pharmaceutical products is reduced by prolonged exposure to high temperature, light,
and humidity. For water vapor-sensitive consumer products that are in tablet or capsule form, and
might be stored in humid environments such as bathroom medicine cabinets, blister packaging is
used to limit the exposure of the medicine to humid conditions until immediately before their use.
Consider tablets that are contained in a blister package composed of a flat lidding sheet and a second,
formed sheet that includes troughs to hold each tablet. The formed sheet is L = 50 µm thick and is
fabricated of a polymer material. Each trough is of diameter D = 5 mm and depth h = 3 mm. The
lidding sheet is fabricated of aluminum foil. The binary diffusion coefficient for water vapor in the
polymer is DAB = 6×10-14 m2/s while the aluminum may be assumed to be impermeable to water
vapor. For molar concentrations of water vapor in the polymer at the outer and inner surfaces CA,s1 =
4.5×10-3 kmol/m3 and CA,s2 = 0.5×10-3 kmol/m3, respectively, determine the rate at which water vapor
is transferred through the trough wall to the tablet. Since polymer sheet is thin relative to the
dimensions of the trough, diffusion may be analyzed as though it occurs through a plane wall.
2. Helium gas is stored at 20˚C in a spherical container of fused silica (SiO2), which has a diameter of
0.2 m and a wall thickness of 2 mm. If the container is charged to an initial pressure of 4 bars, what is
the rate at which this pressure decreases with time?
Since D>>L, diffusion may be approximated as being one-dimensional through a plane wall.
Additionally, assume quasi-steady diffusion. Concentration of helium in the silica (on the gas-solid
interface) is related to the helium pressure through the equation cA = SpA where S is the solubility and
is equal to 0.45×10-3 kmol/m3·bar. Molecular diffusivity of helium in fused silica is equal to 0.4×10-13
m2/s. Helium pressure outside the tank can be considered to be negligible.
3. Hydrogen gas is maintained at 3 bars and 1 bar on opposite sides of a plastic membrane, which is 0.3
mm thick. The temperature is 25˚C, and the binary diffusion coefficient of hydrogen in the plastic is
8.7×10-8 m2/s. The solubility of hydrogen in the membrane is 1.5×10-3 kmol/m3·bar. What is the mass
diffusive flux of hydrogen through the membrane?
4. Haciendo un análisis similar al que se realizó en clase, obtenga la ecuación de continuidad para la
especie A con c y DAB constantes en un sistema diluido (ecuación convectiva-difusiva) en
coordenadas cilíndricas.
5. A spherical oxygen (A) bubble of radius a dissolves into a stagnant aqueous solution. In the surface
of the bubble, oxygen is present at a saturation condition C0 while far away from the bubble the
concentration of oxygen is C. Using the pseudo-steady state approximation, derive the oxygen
concentration profile in the aqueous solution. Also obtain an expression to describe the change in the
bubble radius with time. Finally, corroborate that the pseudo-steady state approximation is valid.
6. Ultra-pure hydrogen is required in applications ranging from the manufacturing of semiconductors to

powering fuel cells. The crystalline structure of palladium allows only the transfer of atomic
hydrogen (H) through its thickness, and therefore palladium membranes are used to filter hydrogen
from contaminated streams containing mixtures of hydrogen and other gases. Hydrogen molecules
(H2) are first adsorbed onto the palladium’s surface and are then dissociated into atoms (H), which
subsequently diffuse through the metal. The H atoms recombine on the opposite side of the
membrane, forming pure H2. The surface concentration of H takes the form CH  K s pH0.52 , where Ks =
1.4 kmol/m3·bar0.5 is known as the Sievert’s constant. Consider an industrial hydrogen purifier
consisting of an array of palladium tubes with one tube end connected to a collector plenum and the
other end closed. The tube bank is inserted into a shell. Impure H2 at T = 600 K, p = 15 bars,
xH 2  0.85 is introduced into the shell while pure H2 at p = 6 bars, T = 600 K is extracted through the
tubes. Determine the production rate of pure hydrogen (kg/h) for N = 100 tubes which are of inside
diameter Di = 1.6 mm, wall thickness t = 75 µm, and length L = 80 mm. The mass diffusivity of
hydrogen (H) in palladium at 600 K is approximately DAB = 7×10-9 m2/s. Use cylindrical coordinates
to solve this problem.
7. Many biological tissues have layers with different extracellular matrix components and different
orientations of these components. As a result, diffusion coefficients vary from region to region.
Consider the steady-state, one dimensional diffusion of a protein across a tissue that consists of an
acellular and a cellular phase. There are no chemical reactions. An example of such tissue is an elastic
artery that contains an elastic lamina of thickness L1 and a layer of smooth muscle cells of thickness
L2. (Actually, an artery consists of repeating layers of elastin and smooth muscle cells, but for the
present discussion, consider a single layer of each). The protein diffusion coefficients of the two
layers are Di,1 and Di,2, respectively. The concentration of protein at the surface (x = 0) is C0, and the
concentration at x = L1 + L2 = L is CL. Determine the concentration of protein as a function of position
x and the flux across the tissue. The partition coefficients are Φ1 (elastin layer) and Φ2 (muscle layer).
8. Busque en la literatura dos correlaciones para estimar el coeficiente convectivo de transferencia de

masa para diferentes geometrías. Indique bajo qué condiciones aplican esas correlaciones.

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Tarea 5

Transferencia de masa por difusión y balance macroscópico de masa

6. Ultra-pure hydrogen is required in applications ranging from the manufacturing of semiconductors to

8. Busque en la literatura dos correlaciones para estimar el coeficiente convectivo de transferencia de

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