Three Experiments on Complex Fluids

The behaviour of complex fluids is fundamentally interesting and important in many applications. This thesis reports on three experiments on the thermal and rheological behaviour of complex fluids. The first is a study of the rheological properties of and heat transport in a saline solution of hydroxyethyl cellulose. This material has been used as a tissue phantom in testing the behavior of medical devices in MRI scanners. We find it behaves as a typical entangled polymer, and flows in response to local heating, such as could occur due to eddy-current heating of metallic devices in an MR scanner. We use laboratory experiments and numerical simulations to determine the convective and conductive contributions to the heat transport in a simple model of this system. Our results indicate that convective heat transport is of the same order of magnitude as conductive transport under conditions typical of MRI device tests. The second project is an investigation of the start-up flow and yielding of a simple yield-stress fluid (Carbopol 940) in a vertical pipe. The Carbopol was displaced from below by an immiscible Newtonian liquid (Fluorinert FC-40) injected at a constant, controlled rate. Rough and smooth-walled pipes were used to study the effects of wall boundary conditions. In the rough-walled pipe, the yielding involved a long transient with several steps: elastic deformation, the onset of wall slip, yielding at the wall, and finally a steady-state plug flow that is well-described by the predictions of the Herschel-Bulkley model. In contrast, in the smooth-walled pipe, the wall shear stress never exceeded the yield stress. In the third project, we study the flow of Carbopol solutions confined to square microchannels with sides ranging from 500 down to 50 um. In the larger channels, the measured velocity profiles agreed well with simulations based on the bulks-scale rheology of the Carbopol and the Herschel-Bulkley model. In contrast, in microchannels with sides less than 150 um the velocity profiles could not be fitted by a model with a finite yield stress, but instead were described by a power-law model with zero yield stress. We explain the vanishing of the yield stress in terms of the confinement of the Carbopol’s microstructure by the microchannels

Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane

In this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions

A review of implicit algebraic constitutive relations for describing the response of nonlinear fluids

We review the class of implicit algebraic constitutive relations for fluids which includes in its ambit those whose material properties depend on the invariants of the stress, the symmetric part of the velocity gradient, as well as their mixed invariants. Such constitutive relations can describe the response of complex fluids whose material properties depend on the mechanical pressure, shear rate, etc. The class of models under consideration can describe the non-monotone relationship between the shear stress and the shear rate observed in experiments on colloids, as well as other novel response characteristics of non-Newtonian fluids. Constitutive relations for power-law fluids, generalized Stokesian fluids and Piezo-viscous fluids are special sub-classes of the class of fluids considered herein