Manipulating Multiphase Flows using Physical or Chemical Mechanisms

Abstract

This thesis explores a variety of problems related to viscous flows in a system with multiple phases involving fluid-fluid or fluid-solid interfaces. Methods to control the flows by physical or chemical mechanisms are proposed. The thesis is divided into four main sections exploring four problems: the drainage of lubricants on liquid-infused surfaces (LIS), the drainage of a viscous gravity current into a deep porous medium, the instability of oil-in-water emulsions exposed to a salt gradient, and the maximum saturation of the invading fluid in porous media by optimal placement of the inlet and outlet.

The first section is motivated by the fact that high external shear stress causes the drainage of the lubricant and the failure of LIS. Microfluidic experiments are used to study the shear-driven failure of these surfaces, and analytical models are developed to quantify the phenomenon. In particular, the effect of the viscosity ratio of the external fluid and the lubricant is discussed. It is suggested that lubricants with lower viscosity should be used in order to prevent the shear-driven failure of LIS.

The second section discusses the problem of a fluid propagating horizontally along an infinitely-deep permeable base into another immiscible fluid with different density. Both one-dimensional and two-dimensional flow problems are solved using the lubrication approximation. In particular, the influence of capillary effects is discussed. The work highlights two impacts of the capillary effects. First, they increase the early-time leakage of the liquid into a deep porous medium that is wettable by the liquid. Second, they elongate the transition period between the early-time and late-time asymptotic behaviors.

The third section identifies a buoyancy-driven instability in oil-in-water emulsions exposed to a salt gradient. Experimental observations of a flower-like pattern of the emulsion in these systems are reported. Furthermore, numerical and analytical studies are reported to elaborate on the mechanism, the instability criteria, and the most unstable modes that determine the details of the observed patterns.

In the fourth section, the capillary-controlled immiscible two-phase flows in porous media are studied. In particular, the question - what is the maximum saturation of the invading fluid in porous media can be achieved by choosing the optimal positions of the inlet and outlet - is answered by combining invasion percolation with a hierarchical tree algorithm. The dependence of the maximum saturation under different injection pressure on the pore-size distribution is further discussed numerically using invasion percolation and a hierarchical tree algorithm and theoretically using percolation theory.