Mathematical Problems in Engineering 
Volume 2008 (2008), Article ID 579172, 30 pages
doi:10.1155/2008/579172
Review Article

An Anisotropic Constitutive Equation for the Stress Tensor of Blood Based on Mixture Theory

Mehrdad Massoudi1 and James F. Antaki2

 1National Energy Technology Laboratory (NETL), U.S. Department of Energy, P.O. Box 10940, Pittsburgh, PA 15236, USA
2Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Received 20 June 2008; Accepted 18 July 2008

Recommended by K. R. Rajagopal

Abstract

Based on ideas proposed by Massoudi and Rajagopal (M-R), we develop a model for blood using the theory of interacting continua, that is, the mixture theory. We first provide a brief review of mixture theory, and then discuss certain issues in constitutive modeling of a two-component mixture. In the present formulation, we ignore the biochemistry of blood and assume that blood is composed of red blood cells (RBCs) suspended in plasma, where the plasma behaves as a linearly viscous fluid and the RBCs are modeled as an anisotropic nonlinear density-gradient-type fluid. We obtain a constitutive relation for blood, based on the simplified constitutive relations derived for plasma and RBCs. A simple shear flow is discussed, and an exact solution is obtained for a very special case; for more general cases, it is necessary to solve the nonlinear coupled equations numerically.