A Numerical Model of Viscoelastic Flows in Microchannels

D. Trebotich, P. Colella, G. Miller and D. Liepmann
Lawrence Livermore National Laboratory, US

Keywords: microfluidics, viscoelasticity

Abstract:
We present a numerical method to model non-Newtonian, viscoelastic flow at the microscale. The equations of motion are the incompressible Navier-Stokes equations coupled with the Oldroyd-B constitutive equation. This constitutive equation is chosen to model a Boger fluid which is representative of complex biological solutions exhibiting elastic behavior due to macromolecules in the solution (e.g., DNA solution). Our numerical approach is a projection method to impose the incompressibility constraint and a Lax-Wendroff method to predict velocities and stresses while recovering both viscous and elastic limits. The method is second-order accurate in space and time, free-stream preserving, has a time step constraint determined by the advective CFL condition, and requires the solution of only well-behaved linear systems amenable to the use of fast iterative methods. We demonstrate the method for viscoelastic incompressible flow in simple microchannels (2D) and microducts (3D).

NSTI Nanotech 2003 Conference Technical Program Abstract