Miscible Displacement of Non-colloidal Suspensions in Confined Channels

Abstract

Suspension flows are ubiquitous and are important to many engineering applications, including paint and coating processes, the pharmaceutical industry, and petroleum engineering. Many industrial processes involve the interaction of multiple phases inside a confined geometry, often leading to complex interfacial dynamics and instabilities. To control these interfacial featuresfor optimizing the processes, a better understanding of the underlying physics is required. This study examines the interfacial morphology and particle dynamics in the displacement of a non-colloidal suspension, comprising viscous oil and particles, by a miscible fluid inside a confined channel. The study is broadly divided into theoretical and experimental analyses. In the theoretical part, a mathematical model is developed for describing the interfacial profile of miscible displacement of a non-colloidal suspension by a pure fluid in a radially outward Hele-Shaw flow. For the case of miscible displacement, the models developed so far are either only for pure fluids or they treat the suspension as a Newtonian fluid. The particledynamics are incorporated into the defending fluid using the Suspension balance model. The governing equations in the Stokes flow limit are simplified under the lubrication approximation. Subsequently, perturbation analysis has been performed by considering the Newtonian solution as the base flow, and the next-order equations are solved to capture particle scale effects. Finite difference approximation is employed to numerically discretize the equations, and these are solved using Python codes. The goal of the theoretical part is to understand the time evolution of the interface profile h(r, t) and the local particle concentration ϕ(r, z, t). The reduced-order model provides deeper insight into the complex physics underlying the phenomenon of fluid invading suspension for the considered flow conditions. The unique approach of this model also allows for significantcomputational resource savings by circumventing the need to perform direct numerical simulations (DNS). In the experimental part of this research work, the injection of a pure fluid against a sus pension is carried out in a radial Hele Shaw cell. The invading fluid contains a fluorescent dye, while the defending suspension is prepared using suspending media of the same composition as the invading fluid, along with particles chosen to match its density and refractive index. Thesetwo fluids are miscible with each other, giving negligible interfacial tension, and the flow rates are within the Stokes flow limit, ensuring creeping flow conditions. In the first set of experiments, the initial particle concentration ϕ0 is varied between 0.05 and 0.20 at a fixed channel gap thickness b. In the second set of experiments, channel confinement ratio b/d is varied by controlling the channel gap at a fixed particle concentration ϕ0 = 0.15. A digital camera is used for imaging the flows, and subsequently, image processing tools are used for analysis. The goal of the experimental part is to understand the interface profile, referred to as h(r, t), in the r–z plane of the radial Hele-Shaw cell and the lateral interfacial patterns in the r–θ plane. An improved methodology, using fluorescent dye and index-matched particles, has been proposed for extracting the thickness of the invading oil. The interfacial profile results in thiswork do not change from smooth to blunt with the emergence of fingering patterns as opposed to the literature. This paints a rather different picture and lays a strong foundation for further investigation in this area.