Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session H38: Porous Media Flow General I |
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Chair: Chris MacMinn, University of Oxford Room: 620 |
Monday, November 25, 2019 8:00AM - 8:13AM |
H38.00001: Soft porous lubrication with oriented fiber array. Zenghao Zhu, Qianhong Wu The friction mitigating property of oriented fibrous materials is widely observed in nature. In this paper, we propose a novel theoretical model to predict the lubrication performance due to the gliding motion of a planar surface over a soft porous layer made of oriented fibers. Lubrication theory for highly compressible porous media is used to predict the lifting force from the fluid phase. The theory for large deformation of flexible beam is used to predict the lifting force from the solid phase. The results are validated numerically using Abaqus. The relative contribution of the fluid lifting force to the overall lifting force, fp, is then obtained, which is used as the criteria to evaluate the lubrication performance using soft porous materials. Dimensional analysis, along with a comprehensive parametric study have been performed to reveal the dominant factors that determine the lubrication performance. The study presented herein provides valuable guidance for applying highly organized porous media to soft porous lubrication. [Preview Abstract] |
Monday, November 25, 2019 8:13AM - 8:26AM |
H38.00002: Capturing gas in soft granular media. Sungyon Lee, Jeremy Lee, Feng Xu, Christopher MacMinn Gas migration through a soft granular material involves a strong coupling between the motion of the gas and the deformation of the material. We study this process experimentally by injecting air into a quasi-2D packing of soft particles and measuring the morphology of the air as it rises due to buoyancy. We systematically increase the confining pre-stress in the packing by compressing it with a fluid-permeable piston, leading to a gradual transition in migration mechanism from fluidization to pathway opening to pore invasion. By connecting these mechanisms quantitively with macroscopic invasion, trapping, and venting, we show that the mixed-mode transitional regime enables a sharp increase in the amount of gas trapped within the packing, as well as much larger venting events. We report our experimental findings and present a simple mechanistic model to rationalize our observations. [Preview Abstract] |
Monday, November 25, 2019 8:26AM - 8:39AM |
H38.00003: Regularization of singularities at corners in two-dimensional Darcy flows Alexander Belozerov, Natalia Petrovskaya, Yulii Shikhmurzaev As can easily be shown, for flows past wedges protruding into a porous medium the standard Darcy model produces unphysically singular velocities, thus over-predicting the flow rate and making impossible to describe some flows, e.g. involving wetting fronts, where the pointwise distribution of velocity has to be modelled realistically. A seemingly obvious remedy of ‘smoothing out’ corners does not apply as, in the real life, the radius of curvature of the tips of such corners can easily be on the pore scale, i.e. zero on the Darcy scale.\\ A recent study (AIChE J. 63(2017)5207) introduces an approach to the problem where, following a suggestive physical analogy, the permeability even of a spatially uniform porous matrix with respect to a flow is, at every point, a function of the curvature of the flow streamline at this point, decreasing as the curvature increases. This preserves the Darcy model for unidirectional flows, where it has been well-tested, and regularizes 2D flows, where the flow field and the distribution of permeability now become intertwined and have to be found simultaneously.\\ The new class of models brings in a fundamentally new class of numerical problems. In the present work, we develop a method of handling such problems and highlight some outstanding issues. [Preview Abstract] |
Monday, November 25, 2019 8:39AM - 8:52AM |
H38.00004: A comprehensive experimental and analytical study of fluid flow in a thin porous layer under indentation. Qiuyun Wang, Zenghao Zhu, Qianhong Wu In this paper, we report a novel experimental and theoretical approach to examine fluid flow in a thin porous layer during an indentation process. Experimentally, a custom-designed indenter with the precisely controlled nano-positioning system is developed where the local compression of the porous layer is captured by a high-speed camera. The indenter is fully instrumented with a laser displacement sensor to measure the indentation velocity and pressure transducers to measure the pore pressure distribution. Theoretically, a consolidation theory is developed where the local relative velocity between the fluid and solid phase is considered, and the local compression-dependent permeability of the porous layer is used. Excellent agreement between the experimental results and the theoretical predictions is observed under different running conditions, verifying the validity of the theory. The study precisely captures the detailed non-uniform compression of a thin porous layer under indentation. It provides a conclusive theoretical framework in the study of fluid flow in a soft porous media, laying the foundation for the study of soft porous matter in response to indentation. [Preview Abstract] |
Monday, November 25, 2019 8:52AM - 9:05AM |
H38.00005: The hydraulic conductivity of shaped fractures with permeable walls Daihui Lu, Ivan C. Christov We derive the hydraulic conductivity $K$, i.e., the proportionally constant between the width-averaged velocity field and the pressure gradient in Darcy's law, for shaped fractures with permeable walls. As a model, we study a tapered Hele-Shaw cell, with a width gradient $dh/dx=\alpha$ in the flow direction, and porous boundaries. The permeable walls are treated using the Beavers--Joseph slip boundary condition. Using lubrication theory, we obtain $K$, accounting for geometric non-uniformity and leakage into the bounding surfaces. The approach is perturbative, giving both the leading-order term (independent of the Reynolds number $Re$) and the first correction in $Re$. Thus, our theory gives $K$ in terms of hydraulic parameters such as $Re$, geometric parameters such as the fracture's width $h(x)$ and $\alpha$, and the dimensionless slip coefficient $\phi$ at the porous walls. Previous research has not addressed the joint dependence on $Re$ and $\alpha$. Specifically, our calculations show that, quantitatively, $Re$ has a comparable effect to $\phi$ on the value of $K$, for $\alpha\ne0$. Finally, we use the open-source computational fluid dynamics software, OpenFOAM, to perform 3D direct numerical simulations to benchmark and verify our mathematical predictions. [Preview Abstract] |
Monday, November 25, 2019 9:05AM - 9:18AM |
H38.00006: Stochastic Modelling of Sieving in Membrane Filters with Complex Pore Morphology Binan Gu, Pejman Sanaei, Lou Kondic, Linda Cummings Membrane filters have been widely used in industrial applications to remove contaminants and undesired impurities from the solvent. During the filtration process the membrane internal void area becomes fouled with impurities and as a consequence the filter performance deteriorates. In addition to the internal morphology of membrane filters, fouling mechanisms contribute to the complexity of the filtration process, in deterministic or stochastic ways. So far various models have been proposed to describe the membrane structure and stochasticity of particles flow individually but very few focus on both together. In this work, we present a model, in which a membrane consists of a series of bifurcating pores, which decrease in size as the membrane is traversed and particles are removed from the feed by adsorption within pores and sieving simultaneously. We derive a probabilistic formulation of the sieving process using a continuous-time Markov chain. Lastly, we discuss how filtration efficiency depends on the characteristics of the branching structure and show the coupling between the two fouling mechanisms. [Preview Abstract] |
Monday, November 25, 2019 9:18AM - 9:31AM |
H38.00007: Upscaled models for heterogeneous reactions in porous media Matteo Icardi, Federico Municchi Although the basic understanding of the macroscopic limit of linear advection diffusion reaction equations is well understood since the early developments of porous media theory, its extension to complex flow regimes is still currently an open question, even in presence of well-separated spatial scales. This is due to the presence of non-trivial microscopic equilibrium configurations (compared to the trivial constant solution obtained by standard periodic homogenisation), or of dynamic equilibrium configurations. For example, when dealing with fast surface reactions, large microscopic gradients can develop locally. Similarly, a conservative solute in the vicinity of a concentration source (injection) undergoes a dynamic evolution of the local microscopic configuration in time and space before reaching the asymptotic self-similar profile. These are only two examples when the classical upscaling approaches fail, and effective macroscopic equations are often found either empirically or by resorting to generic random walk models. In this talk, we present some (old and) new theoretical frameworks to overcome these limitations, by computing local spectral properties (eigenvalues and eigenfunctions) of the underlying transport operators. [Preview Abstract] |
Monday, November 25, 2019 9:31AM - 9:44AM |
H38.00008: A Theoretical Model of Flow in a Pleated Filter Membrane Cartridge Daniel Fong, Pejman Sanaei A 3D model is developed for fluid flow in a cylindrical pleated membrane filter cartridge consisting of a central hollow region surrounded by annular pleated membrane within an external housing. In the region outside of the pleated filter and the hollow region, flow is described using Stokes equation, while in the pleated membrane region Darcy's law is used to model flow through the porous pleated membrane. The governing equations are reduced by exploiting the small aspect ratios of both the membrane and housing. This yields a coupled simplified system of equations for the pressures and velocities in these three regions which is solved numerically. The model is used to investigate the effect of changing various pleated membrane cartridge geometrical parameters on the filter efficiency [Preview Abstract] |
Monday, November 25, 2019 9:44AM - 9:57AM |
H38.00009: Liquid flow through paper with the consideration of swelling and intra-fiber pores Wonjung Kim, Sooyoung Chang Paper is one of the most widely used porous media for absorbing liquid, and accurate control of water imbibition in paper is crucial in developing paper-based microfluidic devices. Washburn equation is usually used to describe the dynamics of the liquid flow through the cellulose matrix of paper. However, it is well known that this equation has limitations in predicting water flow in paper. We report that swelling and intra-fiber pores that have not been considered in developing Washburn equation are mainly responsible for the limited accuracy when predicting imbibition length of water. We demonstrate that cellulose fibers have significant internal voids that absorb water. In addition, we quantify water induced swelling that leads to the expansion of inter-fiber space. We develop a hydrodynamic model of water imbibition with the consideration of intra-fiber voids and cellulose fiber swelling that well explain experimental observations. Our study provides a new insight into not only porous media flow with intra-void structure and swelling effects, but also a theoretical background to design $\mu $PADs. [Preview Abstract] |
Monday, November 25, 2019 9:57AM - 10:10AM |
H38.00010: Pressure-driven flow across a hyperelastic porous membrane. Ryungeun Song, Howard Stone, Kaare Jensen, Jinkee Lee We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate Q and the applied pressure drop $\Delta $p, in apparent disagreement with Darcy's law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nano-scale. With this model, we are able to rationalize the deviation between Darcy's law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials. [Preview Abstract] |
Monday, November 25, 2019 10:10AM - 10:23AM |
H38.00011: Nonlinear Fluid-Structure Coupling in Flow through a Deformable Porous Medium Tyler Lutz, Larry Wilen, John Wettlaufer Fluid flow through a deformable, porous matrix of solid particles is generally seen to exhibit non-Darcy behavior; viscous drag forces exerted on the solid constituents by the fluid may be communicated throughout the solid matrix, leading to a spatially inhomogeneous permeability and ultimately a nonlinear relationship between bulk pressure drop and volume flux. We present results of an experiment in three dimensions designed to provide a closure condition on the mathematical theory of large-deformation flow through a deformable porous medium. Our specific realization of uniaxial flow through a cylindrical foam is robust enough to capture the nonlinear coupling between the solid and fluid components, while the geometry is sufficiently simple to enable detailed comparisons to theoretical expectations. We focus in particular on precision measurements of the pore pressure gradient as a function of the driving pressure head; we use these measurements in combination with direct measurements of the foam deformation to determine the relationship between porosity and permeability, a crucial theoretical input parameter. This closure condition allows us to make explicit, quantitative comparisons to theoretical predictions. [Preview Abstract] |
Monday, November 25, 2019 10:23AM - 10:36AM |
H38.00012: Random Resistor Networks and Porous Media Ahmad Zareei, Shima Parsa, Ariel Amir Pore-level flow distribution in a disordered porous medium is determined through its heterogeneous micro-structure. Dissolution of solid matrix or solute retention during flow of a solution dynamically changes the micro-structure, affects the velocity distribution of pores in unpredictable ways, and further changes the bulk behavior. In order to understand the dynamics of local structural changes during polymer solution flow and its effects, we investigate random resistor networks as a model of disordered porous medium. The network of pores is modeled using connected network of pipes with a random distribution of diameters, and then the critical behavior and averaging behavior of such networks are developed. We further study the dynamics of structural changes during polymer retention process in the random resistor network, and show how this model is able to predict local process of polymer retention, micro-structural changes, flow velocity distribution of pores, and bulk properties consistent with experiments. [Preview Abstract] |
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