Inertial Focusing

I want to get the projectile of microspheresc in microfluidic chip.

I am trying to get a complete solution to Navier and Stokes equations at low (unity) Reynold number. (viscous and inertial ).

is there any model that I can use to simulate the fluid behavior ??
anyone has an idea about how should I go with the microspheresc path tracing?

Thank you in advance