Problem #$2.$ Darcy's Law of Diffusion. Diffusion limit can be determined using confined compression

testing using Darcy's Law. Below represents the relationship between permeability across the

membrane within the testing chamber and the pressure difference applied by the testing machine.

Assume a $2mm$ thick biopsy punch with a diameter of $12mm$ that was tested under confined

compression. Coefficient of friction of synovial fluid is $0\mathrm{.}02.$

Darcy's Law:

$Q=\frac{kA}{L}p$

Define each term and its units.

$L$ in our case would be $h,$ height.

Use unit cancellation in each step of the problem to

show you have performed the appropriate steps.

a$.$ Consider the data for $0\mathrm{.}342$MPa compressed to $8\%$ strain. What is the $h$ of the sample at

this time under this loading condition?

b$.$ Calculate the instantaneous flow rate, $q$ of the fluid being exuded out of the cartilage using the

relationship of permeability.

c$.$ Repeat the problem for $1\mathrm{.}723$MPa when at $40\%$ strain.

d$.$ Generally speaking, how does the permeability, $k,$ change with respect to

i$.$ the applied compressive strain $(\%)$ and

ii$.$ the increasing compressive pressure $($MPa$)?$