Flow of couple stress fluid through narrow tubes by sigma phenomenon and marginal zone theory with applications to blood flow 1

Abstract

Blood flow through narrow tubes has been studied by two theoretical models, viz., sigma phenomenon and marginal zone theory. The analysis for the latter model, developed by the author elsewhere, has been used to obtain the marginal zone thickness; the sigma phenomenon theory for the flow of couple stress fluid has been developed here. It is found that the marginal zone thickness ε and the thickness of the unsheared laminae δ are very complicated functions of tube radius. Therefore, to get some insight into their relation with tube radius, the approximate expressions of ε and δ have been obtained. These approximate expressions of ε and δ contain their corresponding expressions for Newtonian fluids, given by Haynes analysis, as their limiting cases. A comparison of the theoretically predicted numerical values of ε and δ, obtained from the present and Haynes analysis, with the experimental values shows that the results obtained by the present analysis are in better agreement with the experimental results than those obtained by Haynes analysis. In contrast to Haynes conclusion (ε and δ are independent of tube radius), it is found that both the analyses (present and Haynes) indicate the dependence of the value of ε and δ on the tube radius. Further, it appears that ε in comparison to δ is a weaker function of tube radius. It is of interest to note that the nature of the variation of ε with tube radius in experiments is opposite to the one obtained from both the analyses. The reasons for this discrepancy are not clear. Finally, some physiological implications of the present analysis have been cited.