Modeling and Simulation of Transient Poiseuille Blood Flow in Microfluidic Tubes

Last year we discussed the development of an efficient methodology for numerical simulation of viscoelastic and thixotropic flows in tubular geometries using a pseudo-spectral method based on Chebyshev orthogonal polynomial approximations. This method has been validated showing that it produces results that follow with high fidelity the analytical solution of Newtonian and upper-convected Maxwell fluids in oscillatory Poiseuille flows.

We employ this methodology here to simulate the oscillatory Poiseuille flow of blood within microfluidic tubes.  To model the viscoelastic and thixotropic rheology of blood we represent the stress as a combination of contributions that involve an elastic (thixotropic) and a viscoelastic contribution from the rouleaux aggregates that develop and break in the flow and a viscoelastic contribution due to the deformation of individual red blood cells.  The rouleaux effect depends on a scalar structure parameter for which a kinetic equation is used based on microscopic considerations.  We also examine the effect of stress and wall-induced migration modeled through a variant of the Phillips et al. [Phys. Fluids 4 (1992) 30-40] model.  The sensitivity of the results to the various model parameters is going to be discussed.