Multiphysics simulation

All shapes were designed in SOLIDWORKS® software and then implemented in COMSOL Multiphysics® simulation software. The governing equations of the blood fluid flow are the Navier-Stokes equation for the incompressible laminar flow, continuity, viscosity, and particle tracking. $\rho \left(\frac{\partial u}{\partial t}+\left(u.\mathrm{\nabla }\right)u\right)=\mathrm{\nabla }.\left[-PI+\mu \left(\mathrm{\nabla }u+{\left(\mathrm{\nabla }u\right)}^T\right)-\frac{2}{3}\mu \left(\mathrm{\nabla }.u\right)I\right]+\rho g$ $\frac{\partial \rho }{\partial t}+\mathrm{\nabla }.\left(\rho u\right)=0$
Where P, μ and ρ are the pressure, dynamic viscosity,y and density of the fluid respectively. u is the velocity vector, t is time and g is the gravitational acceleration, and I is the identity matrix.
Blood is a non-Newtonian fluid, but it is represented in our simulations as a Newtonian fluid. The corresponding dynamic viscosity μ in Eq. (1) is calculated based on the non-Newtonian power law equation from the following equation. $\mu =m{\left(\stackrel{.}{\gamma }\right)}^{n-1}$
And $\stackrel{.}{\gamma }=\max \left(\sqrt{D:D},\underset{\min }{\overset{.}{\gamma }}\right)$
with $D=\frac{1}{2}\left[\mathrm{\nabla }u+{\left(\mathrm{\nabla }u\right)}^T\right]$
Where m, n and $\stackrel{.}{\gamma }$ are the fluid consistency coefficient, flow behaviour index, and lower shear rate limit respectively.
To verify the numerical method, each model was implemented 3 times under equal simulated conditions and the differences between the results obtained were examined. In the next step, we increased the input speed to the chip at a constant rate in 4 steps and evaluated the results. If the trend of the results is proportional to the rate of acceleration rate, the accuracy of the simulations performed is supported.