A two-fluid model for blood flow through small diameter tubes

Abstract

The present problem deals with a two-fluid model for blood flow through small diameter tubes. The two-fluid model consists of a core (suspension of red cells) and a peripheral red cell free plasma layer. The core has been considered as a couple stress fluid and the plasma layer as a Newtonian fluid. Using appropriate boundary conditions, analytic expressions for velocity profile, flow rate, percentage marginal flow rate and effective viscosity have been obtained. It is found that the velocity profiles obtained from this model are in better agreement with the experimental results of Bugliarello and Sevilla than the velocity profiles given by other models. A critical study of other models and their comparison with the present model have been presented. It is observed that, for some reason, in these models, only one aspect of the flow, i.e., either velocity profiles or viscosity, has been studied, whereas for blood flow, both are equally important. It is shown that many of the existing two-fluid models are included in the present model as its special cases. It is of interest to note that the effective viscosity computed from the present model increases with tube radius; thus this model exhibits ‘Fahraeus-Lindquist Effect’ (FLE). Perhaps, the most important feature of this model is: it gives an analytic formula to determine the core viscosity experimentally, which so far, at least to authors’ knowledge, has not been determined. Finally, some biological implications of this theoretical investigation have been indicated.