4 wrf 26 3 hollow cylinder drug delivery system learning objective sim

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4) WRF 26.3: Hollow cylinder drug delivery system
Learning Objective: Simplify the generalized species equation of continuity to solve a mass transfer problem in a
cylindrical coordinate system.
26.3 Consider the hollow cylinder for drug delivery release
shown in the figure below. The hollow center contains a lump of
solid solute A (drug) in a liquid. Solute A dissolves in the liquid
to a maximum concentration CA* = 0.05 mmole A/cm³ and then
diffuses radially through the gel layer to the surrounding liquid,
which is maintained at a constant concentration, CA∞ = 0.01
mmole A/cm³. In the present system, the effective diffusion
coefficient of solute A in the gel layer is De = 1.2 x 105 cm²/s,
the thickness of the gel layer (R, -R) is 0.50 cm, the length is 1.5
cm, and the outer radius (R) is 0.75 cm. You may assume that
the concentrations of solute A are dilute, the liquid within the
hollow portion of the cylinder has constant concentration of CA*,
and the edges of the cylinder are sealed. As long as the solid
solute A inside the hollow cylinder has not completely dissolved
away, the mass transfer process has a constant source and a
constant sink with respect to solute A.
a. What are reasonable boundary conditions for the mass transfer?
b. What are reasonable assumptions for the mass transfer
process?
c. Estimate the total transfer rate of solute A exiting cylinder atr=
Ro, WA, in units of mmole A/s. As part of your analysis, state the
appropriately-simplified differential forms of the Flux Equa-
tion and the General Differential Equation for Mass Transfer.
d. Based on your result for part (c), if the initial loading of solid
solute A within the hollow center is mA = 0.20 mmole A,
and the liquid within the hollow center is always at concen-
tration CA*, how many hours will it take for the solid A to be
completely dissolved?
L = 1.5 cm
Sealed ends
DA 1.2 x 105 cm²/s
CA = 0.05 mmole/cm³
Solid
Gel
layer
CA =0.01 mmole/cm³
solute A I
(0.2 mmol)!
DAe
ICA'
CA
r = Ro
r=0 r R (0.75 cm)
(0.25 cm)
Solution hints for part c: Start by simplifying WRF Eq. 25-11 and show/explain these steps:
0-("N-)
dr
By continuity NR=NA
NA constant along
Then substitute Fick's law (noting that convective velocity can be neglected) and integrate