Session L26: Focus Session: Complex Fluid Flows Through Porous Media II

Clogging dynamics in microchannels

Microfluidic devices are commonly used to investigate flow through porous media. When a suspension of particles flows in a microchannel, the deposition and assembly of particles can lead to clogging. The formation of clogs dramatically alters the performance of both natural and engineered systems. Once a clog is formed, advected particles form an aggregate upstream of the clog or initial site of the blockage. The aggregate grows over time, which leads to a dramatic reduction of the flow rate in the channel. We present a model for the growth of the aggregate, which captures the results of experiments performed using a pressure-driven suspension flow in a microchannel. The characterization at the pore scale allows us to rationalize the evolution of the flow rate and the clogging cascade in multiple parallel microchannels. Our work illustrates the critical influence of clogging events on the evolution of the flow rate in model porous media. The coupled dynamics of the aggregates is key to bridge clogging at the pore scale with the macroscopic flow rate evolution in various systems from microfluidics to fracking.   

Membrane filtration with multiple fouling mechanisms

Manufacturers of membrane filters have an interest in optimizing the internal pore structure of the membrane to achieve the most efficient filtration. As filtration occurs, the membrane becomes fouled by impurities in the feed solution, and any model of filter performance must account for this. In this work, we present a simplified mathematical model, which (i) characterizes membrane internal pore structure via permeability or resistance gradients in the depth of the membrane; (ii) accounts for multiple simultaneous membrane fouling mechanisms (adsorption, blocking and cake formation); (iii) defines a measure of filter performance; and (iv) for given operating conditions, is able to predict the optimum permeability or resistance profile for the chosen performance measure.   

Modelling Connectivity and Asymmetry in Membrane Filters

In this work, we use mathematical modeling to study the influence of a membrane's internal structure on its flow properties and adsorptive fouling behavior. Layered planar membrane structures with intra-layer connections are modeled. Comparisons between non-connected and connected models are presented. Additionally, the influence of spatial, in-plane, inhomogeneities on overall performance is modeled by adding noise perturbation to homogeneous membrane structures.Membrane performance is gauged via 1) the relative comparison of total throughput and flux evolution during filtration; and 2) control of concentration of foulants at membrane pore outlets.    

Falling jet of dry granular material in water

Modeling the flow of a dry granular material entering water is crucial to optimize blending processes in the industry or for natural hazard assessment when describing the tsunami waves induced by landslides. Experimentally, we consider a dense jet of grains entering from the air into a liquid bath. After an initial transient state, a stationary front appears between dry and wet grains in the bath. The wet grains are then dispersed in the liquid. To describe the dry to wet transition, we focus on the first step of the process when the liquid invades the dense granular media, modeled as a porous material. Our approach is a first step toward the description of the interplay between dry grains and liquid.   

Precision Measurements of Pore Pressure Gradient and Solid Deformation in a Flow-Compacted Poroelastic Medium

When subjected to sufficiently high fluid pressure gradients, poroelastic media are observed to deform due to viscous drag on their solid matrix. The steady-state deformations and, by extension, fluid pressure gradients are generally nonlinear; a given segment of solid backbone needs to counterbalance both the local pressure gradient and any impinging upstream solid matrix. In order to close our theoretical understanding of these nonlocal effects, we empirically investigate the interrelation between material deformation, pore pressure gradient, and volume flux for a given pressure head. To measure these quantities, we subject a latex sponge constrained within a cylindrical cell with a rigid, permeable outlet to uniaxial flow driven by a fixed pressure head. Both the wall friction and the material properties of the sponge influence the interpretation of the experimental data; we discuss in detail our approach to mitigating and modelling these complicating effects.   

Understanding enhanced seepage through a soft porous material

Mechanical deformations driven by fluid flow through a porous solid are relevant to problems as diverse as cell and tissue mechanics, magma dynamics, and hydrology. In a soft porous medium, for sufficiently small pressure gradients, the flow-rate (seepage) obeys Darcy's law, i.e., is proportional to the pressure gradient. But at large pressure gradients, the flow-rate can be substantially higher. We use direct numerical simulations and theory to understand this phenomenon. We model the soft porous material, as a bed of soft spheres in a hexagonal lattice with random defects. The center of the spheres are held fixed. The region between the spheres is filled with a Newtonian fluid. Our DNS of this system shows that the flow-rate versus pressure gradient relationship in this model can be fit by a quartic polynomial. Next, we construct a theory in two steps. First, we perform lubrication analysis at the pore throat while using Winkler elastic foundation to model the elastic deformation of the spheres. This reveals a nonlinear relationship between pressure gradient and flow-rate across individual micro-channels. Next, we upscale this model to derive a mesoscale relationship between flow-rate and pressure gradient that reproduces the results from DNS.
  

Viscous fingering in a soft system

Viscous fingering is a classical hydrodynamic instability that occurs when an invading fluid is injected into a porous medium or Hele-Shaw cell containing a more viscous defending fluid. Viscous fingering is an undesirable feature of many industrial processes, and various strategies have been proposed for suppressing or otherwise controlling it. In a Hele-Shaw cell, for example, viscous fingering can be suppressed by replacing one of the rigid walls with a flexible membrane. The result is a complex fluid-structure interaction problem, the dominant feature of which is inflation of the flow area near the inlet (high pressure) relative to the outlet (low pressure). The resulting negative permeability gradient is ultimately responsible for suppressing the instability. Here, we constrain this problem by working in a system that is deformable but not "inflatable" - A novel Hele-Shaw cell in which one of the rigid walls is coated with soft elastomer. Our system allows for local expansion of the flow area in response to the fluid pressure, but prohibits the generation of a global permeability gradient. We show that the two-way coupling between flow and deformation is nuanced in this constrained system, such that the instability is modified but not necessarily suppressed by softness.