Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

Abstract

Abstract:The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index = 1 and the yield stress τ 0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters ( 1 and 2 ) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

The flow of Newtonian and power law fluids in elastic tubes

“…An example of the former is the widely used one-dimensional (1D) Navier-Stokes flow model in deformable tubes [1][2][3][4][5][6], while an example of the latter is the attempt of Vajravelu et al [7] to model the flow of Herschel-Bulkley fluids in elastic tubes. Other attempts have also been made to deal with more special cases of non-Newtonian flow using mainly numerical methods [8,9].…”

Effect of slip on Herschel–Bulkley fluid flow through narrow tubes

“…The equations governing the flow of Herschel-Bulkley fluid for the present problem (Maruthi Prasad and Radhakrishnamacharya [18] and Vajravelu et al [20]) are given by…”

“…Taliadorou et al [19] derived approximate semi-analytical solutions of the axisymmetric and plane Poiseuille flows of weakly compressible Herschel-Bulkley fluid with no slip at the wall. Vajravelu et al [20] studied a mathematical model for a HerschelBulkley fluid flow in an elastic tube. Gorla et al [21] investigated the combined convection from a slotted vertical plate to Micropolar fluids with slip.…”

“…The objective of this paper was to study the slip effect on Herchel-Bulkley fluid flow through narrow tubes. Following the analysis of Chaturani and Upadhya [10] and Vajravelu et al [20], the linearized equations of motion have been solved and analytical solution has been obtained. The analytical expressions for velocity, flow rate, effective viscosity, core hematocrit and mean hematocrit have been obtained.…”

The yield condition in the mobilization of yield-stress materials in distensible tubes

“…There are some other studies (e.g. [35]) that investigated the flow of yield-stress fluids in distensible conduits but the focus of these studies is not on the yield condition but on the flow of these materials assuming they have already reached a fluid phase state by satisfying the mobilization condition.…”