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( a ) Flow of body fluids across biological tissues is often represented mathematically using theories from flow through porous media. One of the key

(a) Flow of body fluids across biological tissues is often represented mathematically
using theories from flow through porous media. One of the key characteristics of a
porous medium is the porosity. Discuss why different tissues with the same porosity
may exhibit different behaviors in transporting water and solutes across them.
(b) Assume that a biological tissue has two types of empty spherical pores within a solid
matrix; while both types of pores are spherical in shape, their diameters are different,
with the diameters of pore type 1 and 2 being d1 and d2 respectively. What are the
specific surface s and the porosity 6 of the tissue. Assume that the number of spherical
pores per unit volume is n4, and the ratio of the number of pores with d1 to that with
d2 is R.
(c) Darcy's law states that the velocity through a porous medium vec(v) is equal to the
negative of the hydraulic conductivity K, multiplied by the pressure gradient vec(grad)P.
What does K depend on?
(d) Please discuss how Darcy's law needs to be modified, as the pore size of the
biological tissue increases such that the pore sizes are no longer much smaller than
the overall size of the biological tissues.
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