Towards a continuum model for particle-induced velocity fluctuations in suspension flow through a stenosed geometry

Non-particulate continuum descriptions allow for computationally efficient modeling of suspension flows at scales that are inaccessible to more detailed particulate approaches. It is well known that the presence of particles influences the effective viscosity of a suspension and that this effect has thus to be accounted for in macroscopic continuum models. The present paper aims at developing a non-particulate model that reproduces not only the rheology but also the cell-induced velocity fluctuations, responsible for enhanced diffusivity. The results are obtained from a coarse-grained blood model based on the lattice Boltzmann method. The benchmark system comprises a flow between two parallel plates with one of them featuring a smooth obstacle imitating a stenosis. Appropriate boundary conditions are developed for the particulate model to generate equilibrated cell configurations mimicking an infinite channel in front of the stenosis. The averaged flow field in the bulk of the channel can be described well by a non-particulate simulation with a matched viscosity. We show that our proposed phenomenological model is capable to reproduce many features of the velocity fluctuations. Keywords: E¿ective di¿usion; continuous blood modeling; channel ¿ow; boundary conditions; lattice Boltzmann method