Simulation of Interstitial Fluid Flow in Ligaments: Comparison among Stokes,Brinkman and Darcy Models

In this paper, we use Stokes, Brinkman and Darcy equations to approximate the porous continuum media of ligament tissues respectively, simulate the flow field with FLUENT software, and study the shear stress on the cell surface due to the interstitial fluid flow. Since the Brinkman equation approaches Stokes equation well in high hydraulic permeability (k_p) condition (k_p ≥1.0×10^-8 m² in our numerical simulation), and it is an approximation to Darcy model in low k_p condition (k_p ≤5.0×10^-12 m² in our numerical simulation), we used the Brinkman model to simulate the interstitial fluid flow in the ligament where k_p is approximately 1.0×10^-16 m². It shows k_p and anisotropic property have a little effect on the flow field, but have a great effect on the shear stress on the membrane of interstitial cells (τ_cell). There is a linear relationship between τ_cell and , when k_p =1.0×10^-16 m² and the maximum τ_cell (τ_cell,max) is approximately 10 Pa. The anisotropic property will affect τ_cell''s distribution on the cell surface. When k_x/k_y>1, low τ_cell dominates the cell, while when k_x/k_y<1, high τ_cell dominants the cell.