Particle-induced miscible fingering

Abstract

Transport processes of fluids, particulates, or solutes occur in many fields, such as petroleum engineering, groundwater hydraulics, and wastewater treatment. Ecological and environmental concerns about the development of groundwater resources and the control of groundwater contamination require a better understanding of the transport phenomena in multiphase flows, which are mediated by the fluid-particle, particle-particle, and particle-solid matrix interactions. Viscous fingering, one of the most common instabilities associated with multiphase flows, can affect the transport efficiency of the interest phase. The proposed research here aims to study the particle-induced instability phenomena when a suspension of non-colloidal particles and viscous oil is transported inside a Hele-Shaw cell upon the injection of the same viscous oil. This research aims to uncover the fundamental physical mechanism that leads to particle-induced instability inside a Hele-Shaw cell by combining laboratory experiments with image processing and reduced mathematical modeling. This research is divided into two parts based on the most prominent parameter of our research - the aspect ratio between the gap thickness ($b$) and the diameter of the particle ($d$). First, a series of radial Hele-Shaw cell experiments are conducted to study the emergence and early-time morphology when viscous oil radially displaces the mixture of the identical oil and non-colloidal particles inside a Hele-Shaw cell with aspect ratio $b/d > 10$. Based on lubrication approximations and pure-fluid treatment of the suspension, the interfacial structure is modeled. The connection between the discontinuity in an interfacial structure spanning the gap and the lateral pattern is verified. The deviation between the theory and experiments suggests a future work of implementing the suspension balance model to account for the irreversible particle dynamics. Second, the series of miscible fingering experiments with $b/d < 2$ exhibit two novel regimes of instability: particle-level fingering and global fingering. The particle area fraction is measured and reveals the flow's rarefaction formation. A continuum model incorporating the pair-wise dipolar particle interactions is proposed to describe the suspension in a quasi-two-dimensional flow. Linear stability analysis has been conducted, revealing the experimental setup's unstable nature in the monolayer limit. The dispersion relation is obtained and qualitatively matches the experimental observation that critical wave length keeps increasing over time, and the initial suspension area fraction determines the critical wavelength increasing rate.