Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session L26: Focus Session: Complex Fluid Flows Through Porous Media II 
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Chair: Emilie Dressaire, University of California Santa Barbara Room: Georgia World Congress Center B314 
Monday, November 19, 2018 4:05PM  4:18PM 
L26.00001: Modeling and design optimization for pleated membrane filters Yixuan Sun, Pejman Sanaei, Lou Kondic, Linda J Cummings Pleated membrane filters, which offer larger surface area to volume ratios than unpleated membrane filters, are used in a wide variety of applications. The performance of the pleated filter, typically characterized by a fluxthroughput plot, however indicates that the equivalent unpleated filter provides better performance under the same pressure drop. Earlier work (Sanaei and Cummings 2016) used a highlysimplified membrane model to investigate how the pleating effect and membrane geometry impact performance. In this work, we extend this investigation, using asymptotic method to consider in detail how membrane pore morphology affects performance, and how to optimize performance through varying the pore shape within the membrane. Our optimization is designed to maximize the total throughput while simultaneously assuring adequate particle removal, which is an essential part of filtration. Within a given class of pore shapes we are able to use our newly derived model to find numerically the optimal pore shape. Our current work involves formulating our optimization as an optimal control problem, which we aim to solve to determine the optimal profile over all possible pore shapes. 
Monday, November 19, 2018 4:18PM  4:31PM 
L26.00002: Clogging dynamics in microchannels Emilie Dressaire, Katarzyna Somszor, Emmanuel Villermaux, Alban Sauret 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 pressuredriven 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. 
Monday, November 19, 2018 4:31PM  4:44PM 
L26.00003: Flow and fouling in multilayered membrane filters Daniel Fong, Pejman Sanaei, Linda J. Cummings, S. Jonathan Chapman Multilayer membrane filters, which consist of several thin porous membranes with different properties (such as pore size and void fraction) stacked on top of each other, are widely used in industrial applications to remove contaminants and undesired impurities (particles) from a solvent. It has been experimentally observed that the performance of welldesigned multilayer structured membranes are markedly better than those of equivalent homogeneous membranes. Mathematical characterization and modeling of multilayer membranes can help our understanding of how the properties of each layer affect the performance of the overall membrane stack. We present a simplified mathematical model to describe how the microscopic properties of a multilayer membrane affect the overall filter performance.

Monday, November 19, 2018 4:44PM  4:57PM 
L26.00004: Membrane filtration with multiple fouling mechanisms Pejman Sanaei, Linda J. Cummings 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. 
Monday, November 19, 2018 4:57PM  5:10PM 
L26.00005: Modelling Connectivity and Asymmetry in Membrane Filters Binan Gu, Dylan Renaud, Pejman Sanaei, Lou Kondic, Linda J Cummings 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 intralayer connections are modeled. Comparisons between nonconnected and connected models are presented. Additionally, the influence of spatial, inplane, 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. 
Monday, November 19, 2018 5:10PM  5:23PM 
L26.00006: Falling jet of dry granular material in water Alban Sauret, Guillaume Saingier, Pierre Jop 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. 
Monday, November 19, 2018 5:23PM  5:36PM 
L26.00007: Precision Measurements of Pore Pressure Gradient and Solid Deformation in a FlowCompacted Poroelastic Medium Tyler Lutz, Larry Wilen, John Scott Wettlaufer When subjected to sufficiently high fluid pressure gradients, poroelastic media are observed to deform due to viscous drag on their solid matrix. The steadystate 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. 
Monday, November 19, 2018 5:36PM  5:49PM 
L26.00008: Understanding enhanced seepage through a soft porous material Satyajit Pramanik, Luca Brandt, Dhrubaditya Mitra, Marco Edoardo Rosti 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 flowrate (seepage) obeys Darcy's law, i.e., is proportional to the pressure gradient. But at large pressure gradients, the flowrate 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 flowrate 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 flowrate across individual microchannels. Next, we upscale this model to derive a mesoscale relationship between flowrate and pressure gradient that reproduces the results from DNS. 
Monday, November 19, 2018 5:49PM  6:02PM 
L26.00009: Viscous fingering in a soft system Christopher W. MacMinn, Jian Hui Guan Viscous fingering is a classical hydrodynamic instability that occurs when an invading fluid is injected into a porous medium or HeleShaw 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 HeleShaw cell, for example, viscous fingering can be suppressed by replacing one of the rigid walls with a flexible membrane. The result is a complex fluidstructure 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 HeleShaw 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 twoway coupling between flow and deformation is nuanced in this constrained system, such that the instability is modified but not necessarily suppressed by softness. 
Monday, November 19, 2018 6:02PM  6:15PM 
L26.00010: Imbibition in plant seeds Kaare H Jensen, JeanFrancois Louf, Yi Zheng, Aradhana Kumar, Tomas Bohr, Carsten Gundlach, Jesper Harholt, Henning Friis Poulsen The mass of plant seeds varies over six orders of magnitude, and water permeation of the dry porous tissue is an essential requirement for germination. However, it is unclear if the imbibition process is similar across the full spectrum of seed sizes, or if variations in their porous structure lead to heterogeneous flow patterns. We describe imbibition in real and artificial plant seeds, using a combination of experiments and theory. In both systems, our experiments demonstrate that liquid permeates the substrate at a rate which decreases gradually over time. Tomographic imaging is used to confirm this by observation of the permeating liquid using an iodine stain. To rationalize the experimental data, we propose a model based on capillary action which predicts the temporal evolution of the radius of the wet front and the seed mass. The depth of the wetting front initially evolves as t^{1/2} in accord with the LucasWashburn law. At later times, when the sphere is almost completely filled, the front radius scales as (1 − t/t_{max})^{1/2}, where t_{max} is the time required to complete imbibition. The data obtained on both natural and artificial seeds are compared to the model. 
Monday, November 19, 2018 6:15PM  6:28PM 
L26.00011: Onset of particleinduced miscible fingering Rui Luo, Yun Chen, Sungyon Lee 
Monday, November 19, 2018 6:28PM  6:41PM 
L26.00012: Abstract Withdrawn Fluidfluid displacement in porous media using complex fluids have gained much attention recently because of a variety of industrial applications. In our previous experiments, we showed stabilization of the classical SaffmanTaylor fingering problem using a radiallyconverging passage. Here, we experimentally investigate the influence of microparticles, suspended in the displaced fluid, on viscous fingering instabilities in a converging cell. For gas displacing a suspension, our results show that the presence of the particles in the converging gradient can still result in stable displacement and hinder fingering. For a fixed gap gradient and particle concentration, we observe stable interfaces under small injection pressure, whereas unstable fingering occurs above a certain threshold. We further study the dependence of this critical injection pressure on the particle concentration for various gap gradients. These results, with additional complexity in the fluid properties, allow us to extend our understanding of the influences of complex fluids on viscousfingering instability and displacement efficiency. 
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