Multiscale investigation of fundamental rheological phenomena in particulate suspensions based on flow-microstructure interactions

Beris, Antony N.Wagner, Norman J.Suspensions and dispersions are an important class of complex fluids frequently encountered in a variety of industrial processes and are prominent in many consumer products such as beauty creams and food dressing. The extensive use of suspensions can be partly attributed to their unique rheological properties such as shear-induced normal stresses, yield stress, time-dependent viscosity and shear thinning. These rheological properties are a direct result of the interplay between the suspension microstructure and flow and have consequences for material processing. The quantitative understanding of suspension rheology so far has been dominated by empirical models. However, such models are either very specialized to particular flows, involve numerous/unphysical parameters, or are inadequate to describe rheological phenomena such as normal stresses. Alternatively, microscopic approaches have primarily been successful in addressing idealized cases and/or small length/time scales. Therefore, the goal of this thesis is to develop new and improved classes of continuum models that clearly connect the suspension microstructure under flow to the observed macroscopic rheology. ☐ In this thesis, new, generally multiscale methods are applied towards developing robust constitutive models for suspension rheology. Two primary modeling approaches are employed to advance the modeling of suspension rheology in this thesis. First is a bottom-up approach that starts from a microscopic description of the suspension microstructure (e.g., the evolving aggregate size distribution) that is then coupled to an empirical/phenomenological equation to allow for the evaluation of the shear stress. The shortcoming of using a phenomenological stress expression is counterbalanced by the accurate microstructure picture provided by a microscopic framework. The second technique is a top-down approach that starts from a macroscopic description of the system through the use of state variables whose dynamic equations are developed within the Hamiltonian-enhanced Non-Equilibrium Thermodynamics framework. The key benefit of this latter approach is that the expressions for the stress tensor and microstructure, with the latter represented by a second rank tensor, emerge self-consistently from the framework. Moreover, the generated equations are applicable to general flows. The multiscale nature of suspension microstructure implies that depending on the phenomena of interest, one or the other or a combination of the two approaches may be favored. Regardless of the approach taken, a recurrent theme in this work is the clear association of the observed macroscopic rheological behavior with an underlying microscopic picture. Finally, for all the suspensions emphasized in this thesis i.e., thixotropic, polydisperse, noncolloidal and emulsions, the corresponding rheological models developed are validated against experimental/simulation data revealing their predictive capability. ☐ A number of important specific accomplishments are achieved in this thesis. To begin with, a population balance-based constitutive model for thixotropic suspensions is developed. Unlike alternative phenomenological models currently in use, a population balance-based model incorporates parameters with clear physical meaning. As a result, the resultant model holds promise for inverse design of thixotropic materials such as pastes that are used in many industrial processes. Next, the use of a conformation tensor as an internal variable to represent changes in suspension microstructure during material deformation is also demonstrated. For the first time, a comprehensive conformation tensor-based framework for suspensions, with a rigor approaching that performed previously for polymeric system, is realized. When applied to dilute emulsions, the conformation tensor-based rheological model that results is in exact agreement with existing asymptotic microscopic theory. In the same emulsion system, effects of microinertia and Ostwald ripening have also been included within a conformation tensor-based model for the first time. In concentrated suspensions, the conformation based theory has been shown to be capable of describing emerging secondary structure in the particle configuration leading to first and second normal stress differences that are both negative. Additional advances have also been made to develop self-consistent approximations for polydisperse suspension viscosity and testing them against prototype experiments. On a broader level, this work provides a number of methodologies for systematic constitutive model development in complex fluids. From an engineering perspective, the results of this thesis can be used to improve upon existing numerical tools, e.g., computational fluid dynamics, to allow for accurate simulation of industrial processes such as extrusion and screen printing of thixotropic pastes, suspensions and emulsions.University of Delaware, Department of Chemical and Biomolecular EngineeringPh.D