GENERALISED HERSCHEL MODEL APPLIED TO BLOOD FLOW MODELLING

Abstract

This paper introduces a new rheological model of blood as a certain generalisation of the standard Herschel-Bulkley model (Herschel W H and Bulkley R 1926 Kolloid-Zeitschrift 39 (4) 291). This model is a rheological constitutive equation and belongs to the group of the so-called generalised Newtonian fluids. Experimental data (Yeleswarapu K K et al. 1998 Mech. Res. Comm. 25 (3) 257) is compared with the results obtained from the new model, to demonstrate that it allows obtaining the best agreement together with the Luo-Kuang model (Luo X and Kuang Z B 1992 J. Biomechanics 25 (8) 929; Easthope P L and Brooks D E 1980 Biorheology 17 235). The new model may be easily implemented into commercial CFD codes, which is not that obvious for more complicated models such as differential, integral and rate type fluids (Astarita G and Marrucci G 1974 Principles of non-Newtonian Fluid Mechanics London, McGraw-Hill; Tesch K 2012 Selected Topics of Blood Flows and Microclimate Modelling in Protective Suits Gdansk, Gdansk University of Technology Press). What is more, it allows modelling of such phenomena as shear thinning, yield stress and constant viscosity values at high shear rates.