Linear Stability Analysis for Plane-Poiseuille Flow of an Elastoviscoplastic fluid with internal microstructure

We study the linear stability of Plane Poiseuille flow of an elastoviscoplastic fluid using a revised version of the model proposed by Putz and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the microstructure upon a gradual increase of the external forcing is governed by a structural variable (the concentration of solid material elements) which decays smoothly from unity to zero as the stresses are gradually increased beyond the yield point. Stability results are in close conformity with the ones of a pseudo-plastic fluid. Destabilizing effects are related to the presence of an intermediate transition zone where elastic solid elements coexist with fluid elements. This region brings an elastic contribution which does modify the stability of the flow

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

The earlier constitutive model of Fang & Owens (Biorheology, vol. 43, 2006, p. 637) and Owens (J. Non-Newtonian Fluid Mech. vol. 140, 2006, p. 57) is extended in scope to include non-homogeneous flows of healthy human blood. Application is made to steady axisymmetric flow in rigid-walled tubes. The new model features stress-induced cell migration in narrow tubes and accurately predicts the Fåhraeus-Lindqvist effect whereby the apparent viscosity of healthy blood decreases as a function of tube diameter in sufficiently small vessels. That this is due to the development of a slippage layer of cell-depleted fluid near the vessel walls and a decrease in the tube haematocrit is demonstrated from the numerical results. Although clearly influential, the reduction in tube haematocrit observed in small-vessel blood flow (the so-called Fåhraeus effect) does not therefore entirely explain the Fåhraeus-Lindqvist effec

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread remarkably similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasionsComment: 13 pages, 18 figure

Thin-film flow of a Bingham fluid over topography with a temperature-dependent rheology

We consider the flow of a viscoplastic fluid on a horizontal or an inclined surface with a flat and an asymmetric topography. A particular application of interest is the spread of a fixed mass – a block – of material under its own weight. The rheology of the fluid is described by the Bingham model which includes the effect of yield stress, i.e. a threshold stress which must be exceeded before flow can occur. Both the plastic viscosity and the yield stress are modelled with temperature-dependent parameters. The flow is described by the lubrication approximation, and the heat transfer by a depthaveraged energy conservation equation. Results show that for large values of the yield stress, only the outer fraction of the fluid spreads outward, the inner fraction remaining unyielded. We also present an analysis which predicts the threshold value of the yield stress for which partial slump occurs