Low Reynolds number steady state flow through a branching network of rigid vessels: II. A finite element mixture model

Abstract

This research aims at formulating and verifying a finite element mixture formulation for blood perfusion. The equations derived in a companion paper [Huyghe, J.M., Oomens, C.W., Campen, D.H., van Heethaar, R.M., A mixture theory of low Reynolds steady state flow through a branching network of rigid vessels. Biorheology, submitted for publication, 1988.] are discretized according to the Galerkin method. A flow experiment in a rigid model of a vascular tree of about 500 vessels is performed in order to verify the finite element mixture formulation. Although the comparison of numerical results and experimental measurements is not conclusive as far as the validity of the theory is concerned, the results do suggest that the finite element model has predictive power in the case of low Reynolds number steady state flow of a Newtonian fluid in a rigid vascular tree.