Smoluchowski theory for concentrated colloidal dispersions far from equilibrium

This thesis develops a theory for the analytical prediction of microstructure of concentrated Brownian suspensions of spheres in simple-shear flow. The computed microstructure is used in a prediction of the suspension rheology. Following an introduction in Chapter 1, the theoretical framework is given in Chapter 2; the remaining chapters involve different extensions of the theory and more detailed analysis of the variables included in it.;In Chapter 2, a near-hard-sphere suspension is studied for solid volume fractions. The method developed determines the steady pair distribution function from a solution of the Smoluchowski equation (SE) reduced to pair level. To account for the influence of the surrounding bath of particles on the interaction of a pair, an integro-differential form of the pair SE is developed; the integral portion represents the forces due to the bath which drive the pair interaction. Hydrodynamic interactions are accounted in a pairwise fashion, based on the dominant influence of pair lubrication interactions for concentrated suspensions. The pair SE is heuristically modified to include the influence of shear-induced relative diffusion, and this is found to be crucial for success of the theory; a simple model based on understanding of the shear-induced self-diffusivity is used for this property.;In Chapter 3, an extension of the theory for hard-sphere sheared suspensions is given to study structure and rheology of colloidal suspensions with soft repulsive interactions. ASD simulations are carried out to provide insight and to enable direct comparison with theoretical predictions. The effect of extended range repulsive interactions is studied by considering repulsive interactions with different steepness in the range of 0.1 ≤ Pe ≤ 100The predicted g(r) and shear viscosity are in good agreement with simulations before the onset of a shear-induced ordering transition in simulations of the soft colloids.;In Chapter 4, an alternative formulation based on pair-wise summation of relative velocities for hydrodynamic interactions is developed. Also, based on ASD results, a modified form is proposed for modeling shear-induced relative diffusion. These modifications result in considerable improvement in the agreement of structure and rheology with simulations. The primary focus of this chapter is to consider the the pair relative velocity predicted by the theory in comparison to Stokesian Dynamics simulations, as well as to evaluate quantities related to the hydrodynamic dispersion needed in the theoretical approach.;In Chapter 5, the theoretical framework constructed for sheared colloidal suspensions is extended to study the active microrheology, wherein the motion of a spherical probe driven through a bath of colloidal suspension by application of a fixed external force or velocity is studied. The theory gives predictions of microstructure in form of g(r), which here is the normalized likelihood of observing the colloidal bath particles at a relative distance r with respect to the probe. The differences between the two scenarios of pulling the probe with constant force and fixing the velocity are elucidated. The results indicate a noticeable difference between the two methods both for microstructure and rheology. In general, although active microrheology gives a similar qualitative picture of variations of viscosity with &phis; and Pe, quantitative agreement of the computed micro-viscosity with shear flow viscosity is not achieved in all conditions.;The last chapter presents preliminary results related to two other extensions of the theory. The results suggest that the theory can be applied to non-Brownian suspensions with different types of interparticle interactions. Predictions of g(r) and rheology are presented for linear flows ranging from pure straining motion with no vorticity to motions dominated by vorticity. This is pursued by fixing the magnitude of straining motion and changing the strength of the rotational component of the linear flow. These results show a steep reduction in the magnitude of normal stress differences with increase of the rotational component of the flow. (Abstract shortened by UMI.).