A study on two-layered model (Casson-Newtonian) for blood flow through an arterial stenosis: Axially variable slip velocity at the wall

The present paper sheds some light on a mathematical model for blood flow through stenosed arteries with axially variable peripheral layer thickness and variable slip at the wall. The model consists of a core region of suspension of all the erythrocytes assumed to be a Casson fluid and a peripheral layer of plasma as a Newtonian fluid. For such models, in literature, the peripheral layer thickness and slip velocity are assumed a priori based on experimental observations. In the present analysis, new analytic expressions for the thickness of the peripheral layer, slip velocity and core viscosity have been obtained in terms of measurable quantities (flow rate (Q), centerline velocity (U), pressure gradient (−dp/dz), plasma viscosity (μp) and yield stress (θ)). Using the experimental values of Q, U, (−dp/dz), μp and θ, the values of the peripheral layer thickness, core viscosity, and slip velocity at the wall have been computed. The theoretically obtained peripheral layer thickness has been compared with its experimental value. It is found that the agreement between the two is very good (error<1.4%). Further, a comparison between theoretical and experimental values of core viscosity is made and it is observed that the error between the two becomes 3.7465% in the case of two-layered model (Casson-Newtonian) for tube diameter 40 μm. The analysis developed here could be used to determine the more accurate values of the apparent viscosity of blood, agreeability, rigidity and deformability of red cells. This information of blood could be useful in the development of new diagnosis tools for many diseases.