A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow

Abstract

The earlier constitutive model of Fang & Owens (2006) and Owens (2006) is extended in scope to include non-homogeneous ows of healthy human blood. Application is made to steady axisymmetric ow in rigid walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus-Lindqvist eect (Fåhraeus & Lindqvist (1931)) whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in suciently small vessels. That this is due to the development of a slippage layer of cell-depleted uid near the vessel walls and a decrease in the tube hematocrit (Fåhraeus (1929)) is demonstrated from the numerical results. Although clearly inuential, the reduction in tube hematocrit observed in small vessel blood ow (the so-called Fåhraeus eect) does not therefore entirely explain the Fåhraeus-Lindqvist eect.

Viscoelasticity of blood and viscoelastic blood analogues for use in polydymethylsiloxane in vitro models of the circulatory system

“…Although scarcer, viscoelastic models are necessary for more complete descriptions of blood rheology, and often some of its parameters are dependent on the evolution of structures formed by the erythrocytes. 2,[5][6][7]57 Here, the viscoelastic moduli and the steady viscosity data were fitted using two viscoelastic multi-mode differential constitutive equations: the simplified Phan-Thien-Tanner (sPTT) and Giesekus models 58,59 with a Newtonian solvent contribution of viscosity g s , but without the use of structure-dependent parameters. These two multi-mode models can be compactly written as…”

“…These non-Newtonian properties of blood have long been recognized, measured, and modelled. [4][5][6][7] The non-Newtonian behavior of blood, which affects its flow in both large, but mostly in small vessels characteristic of the microcirculation, is closely related to incident cardiovascular events like ischaemic heart disease and stroke. [8][9][10] Therefore, a fundamental understanding of the detailed fluid dynamics of blood flow and of the distribution of the wall shear stress in small vessels is essential to help detect cardiovascular diseases and to develop preventive measures and design suitable treatments.…”

A two-phase model of blood flow in large and small blood vessels

“…В работе [5] для объяснения эффекта Фареуса-Линдквиста рассматривалась модель упруго деформирующихся "монетных столбиков" (англ. dumbbells) из эритроцитов.…”

A non-homogeneous constitutive model for human blood

“…In particular, the zero shear-rate steady viscosity is chosen to be smaller than in [11] and no articial slip condition is needed. Even more recently, in Part I of this work, Moyers-Gonzalez et al [17] have described a non-homogeneous blood model, that predicts particle migration away from vessel walls and thus allows for a cell depleted slip layer to develop there. In the present paper we use this model in the numerical simulation of oscillatory blood ow and the improvement of the results over those obtained with the simpler model of Fang and Owens [11] demonstrates the importance of wall eects in tubes of the size considered.…”

“…Section 2 of this paper is recapitulative and summarizes from Part I of this work [17] the model equations and the boundary conditions appropriate for tube ow. A simple second-order nite element method for the solution of the equation set is then outlined in the next section.…”