Article

Bulletin of Mathematical Biology

, Volume 50, Issue 4, pp 329-344

First online:

A couple stress model of blood flow in the microcirculation

  • Dulal PalAffiliated withUGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Bangalore University
  • , N. RudraiahAffiliated withUGC-DSA Centre in Fluid Mechanics, Department of Mathematics, Bangalore University
  • , Rathna DevanathanAffiliated withDepartment of Applied Mathematics, Indian Institute of Science

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Abstract

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.