Project. The laminar fluid diffusion interface device introduced in Problem 10.27 is to be used when

Project. The laminar fluid diffusion
interface device introduced in Problem 10.27 is to be used when both a
metabolite (taken here as creatinine) and protein (taken here as albumin) enter
in the sample. Using the same specifications from Problem 10.27, but extending
the dimensionless length by 10, solve for the concentration profiles of both
creatinine and albumin when both enter with a dimensional concentration of 1.0.
Now the viscosity depends upon the albumin concentration: η = 1 + 0.6cA
mPa s (cA = 1 is the maximum albumin concentration). Since the viscosity
depends upon the albumin concentration, even in fully developed flow the
velocity profile will not be quadratic (Bird et al., 2002, pp. 56–68), and the
analytical solution there (when the interface is halfway between the two sides)
is extended to more general cases in “Poiseuille Flow of Two Immiscible Fluids
Between Flat Plates with Applications to Microfluidics” on the book website.
The diffusivities of creatinine and albumin in both serum and water are taken
as 9.19 10^{−10} m^{2}/s and 6.7 10^{−11} m^{2}/s,
respectively. Determine the enhancement factor if the stream in the upper half
at the outlet is collected.

Problem 10.27

Suppose one has done experiments with water
flowing in straight channels measuring 300 × 120 mm. The average flow rate is
0.01 m/s. The inlet concentration takes the value 1.0 in the bottom half and
0.0 in the top half and the diffusivity is 10^{−8} m^{2}/s.
It is desired to scale up to 2.5 × 1 mm, that is, a scale-up by a factor of
8.5, keeping the average velocity at 0.01 m/s. What are the Reynolds number and
Peclet number in both devices? Do you expect the solutions to be the same?
Calculate the variance out of each device.