Unsteady solute dispersion in small blood vessels using a two-phase Casson model

Abstract

This study explores the transport of a solute in an unsteady blood flow in small arteries with and without absorption at the wall. The Casson fluid model is suitable for blood flow in small vessels. Owing to the aggregation of red cells in the central region of the small vessels, a two-phase model is considered in this investigation. Using the generalized dispersion model (Sankarasubramanian & Gill 1973 Proc. R. Soc. Lond. A 333 , 115–132. (doi:10.1098/rspa.1973.0051)), the convection, dispersion and mean concentration of the solute are analysed at all times in small arteries of different radii. The effects of the yield stress, wall absorption, the amplitude of the fluctuating pressure gradient component, the peripheral layer thickness, the Womersley frequency parameter, the Schmidt number and the Peclet number on the dispersion process are discussed. A comparative study of solute dispersion among single- and two-phase fluid models is presented. For small vessels, a significant difference between these models is observed during the solute dispersion; however, this difference becomes insignificant for large vessels. The mean concentration of solute reduces with increasing radius of the vessels. The present investigation is more realistic for understanding the transportation process of drugs in blood flow in small arteries using the non-Newtonian fluid model.