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Consider unsteady diffusion across a membrane of thickness L . Initially, the concentration of solute in the membrane is zero. At time zero, the concentration
Consider unsteady diffusion across a membrane
of thickness L Initially, the concentration of solute in the
membrane is zero. At time zero, the concentration at
is raised to and the concentration at is
maintained at zero.
a Use the following dimensionless variables:
Show that the solution for can be rewritten as
where is the steadystate solution. State
boundary conditions for the problem. Show that
b Show that can be solved by separation of
variables, and obtain the following solution for
:
exp
c Use Equation to assess the time required
for the membrane to reach steady state. Compare
this result with the result obtained from the quasi
steadystate analysis.
d The following relation is derived from a mass balance:
where is the concentration on side of the
membrane, as shown in Figure At
Show that the solution for is
The problem pertains to one side of
the membrane. You may assume that
volume to be
please write clearly and label all parts of the solution
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