An anisotropic constitutive equation for the stress tensor of blood based on mixture theory

Journal Article · Tue Jan 01 04:00:00 EST 2008 · Mathematical Problems in Engineering

DOI:https://doi.org/10.1155/2008/579172· OSTI ID:1012389

Massoudi, M; Antaki, J

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.

• Research Organization: National Energy Technology Laboratory - In-house Research; National Energy Technology Laboratory (NETL), Pittsburgh, PA, and Morgantown, WV (United States)
• Sponsoring Organization: USDOE Assistant Secretary for Fossil Energy (FE-1)
• OSTI ID: 1012389
• Report Number(s): NETL-TPR-2339
• Journal Information: Mathematical Problems in Engineering, Journal Name: Mathematical Problems in Engineering Vol. 2008; ISSN 1024-123X
• Publisher: Hindawi Publishing Corporation
• Country of Publication: United States
• Language: English

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97 MATHEMATICS AND COMPUTING