Towards a unified model of elasto-thixotropy of biofluids

Abstract

Biofluids as concentrated suspensions exibit (at fixed shear rate $\dot{\mathit{\gamma }}$ ) a steady shear viscosity η which critically depends on (i) the volume fraction of particles ϕ, and (ii) the ability the particles have to form more or less loose structural units (flocs, aggregates or parts of network). The latter can be quantified by some effective packing volume fraction ϕ_p which reflects the actual compacity of structural units. A special η–ϕ relationships which involves such a packing fraction will be discussed.

Changes of structural units as shear rate $\dot{\mathit{\gamma }}$ (or shear stress σ) varies lead to ${\mathit{\varphi }}_{\mathrm{p}}={\mathit{\varphi }}_{\mathrm{p}}\mathrm{(}\dot{\mathit{\gamma }}\mathrm{)}$ i.e. to non-newtonian viscosity. This shear-thinning behaviour is believed to result from some dynamical equilibrium between formation and destruction of structural units, in the presence of both brownian motions of particles and the shear stresses the suspending fluid exerts on them. A (simple) rate equation (from reaction kinetics) gives a quantitative description of ϕ_p-dependences in $\dot{\mathit{\gamma }}$ and time t. Under steady conditions, the present approach is capable not only to model shear-thinning behaviour but also plastic and shear thickening (dilatant) ones. Time variations under transient shear rate (i.e. thixotropy) can be described with ϕ_p(t) deduced from the same rate equation. Extension to visco-elastic behaviour has been obtained using a Maxwell-model with instantaneous values of viscosity and elasticity which both are functionals of the structural variable ${\mathit{\varphi }}_{\mathrm{p}}\mathrm{(}\mathrm{t}\mathrm{,}\dot{\mathit{\gamma }}\mathrm{)}$ .