Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session H31: Porous Media Flows VI: Imbibition and Injection |
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Chair: Carlos H. Hidrovo, University of Texas at Austin Room: 402 |
Monday, November 25, 2013 10:30AM - 10:43AM |
H31.00001: Droplet Impact and Penetration on a Series of Capillary Tubes Saman Hosseini, Alireza Dalili, Nasser Ashgriz, Sanjeev Chandra A series of experiments were carried out in which a single droplet of water was deposited onto a substrate having a series of closely spaced parallel-holes to represent a simple porous media. At the center of the width of the 0.6''x0.5''x0.3'' poly-carbonate substrate seven through-holes each with a diameter of 300 $\mu$m and distance of 300 $\mu$m from one another were drilled in a straight line. Droplets with diameters of 3.2 and 2.0 mm were released from heights of 1, 3 and 5 cm. Using a high-speed camera the impact, spreading and capillary penetration of the droplets into the holes were videotaped. Two different penetration regimes were observed based on the impact velocity. At low droplet impact velocities, the penetration was mainly due to capillary forces, while at higher impact velocities the penetration occurred at two stages. The first stage was inertia driven, while the second stage was capillary driven penetration. The threshold velocity for liquid penetration into the holes was formulated. Inertia forces were used to describe the linear portion of penetration and the Lucas-Washburn equation was used to characterize the non-linear (capillary) part of penetration. The distance of penetration as a function of time was worked out using this equation. Droplet oscillation on the top of the parallel holes was observed as well. It was evident that the area of the penetration inside the holes played a major role in the kinetic energy dissipation and the damping of the oscillation. [Preview Abstract] |
Monday, November 25, 2013 10:43AM - 10:56AM |
H31.00002: Design of Capillary Flows with Spatially Graded Porous Films Young Soo Joung, Bruno Michel Figliuzzi, Cullen Buie We have developed a new capillary tube model, consisting of multi-layered capillary tubes oriented in the direction of flow, to predict capillary speeds on spatially graded porous films. Capillary flows through thin porous media have been widely utilized for small size liquid transport systems. However, for most media it is challenging to realize arbitrary shapes and spatially functionalized micro-structures with variable flow properties. Therefore, conventional media can only be used for capillary flows obeying Washburn's equation and the modifications thereof. Given this background, we recently developed a method called breakdown anodization (BDA) to produce highly wetting porous films. The resulting surfaces show nearly zero contact angles and fast water spreading speed. Furthermore, capillary pressure and spreading diffusivity can be expressed as functions of capillary height when customized electric fields are used in BDA. From the capillary tube model, we derived a general capillary flow equation of motion in terms of capillary pressure and spreading diffusivity. The theoretical model shows good agreement with experimental capillary flows. The study will provide novel design methodologies for paper-based microfluidic devices. [Preview Abstract] |
Monday, November 25, 2013 10:56AM - 11:09AM |
H31.00003: Phase-field modeling of two-phase flow in porous media with partial wetting Luis Cueto-Felgueroso, Ruben Juanes Current models of multiphase flow in porous media implicitly assume complete wetting, and are unable to describe non-spreading systems. This limitation has a direct impact on the ability of current theories to predict complex non-equilibrium processes in porous media, such as flow instabilities or rate-dependent displacement patterns. Here we present a continuum model of two-phase flow in porous media that can describe partially wetting systems. The model is derived within the framework of phase-field modeling. We study unstable two-dimensional flow due to viscous fingering (the instability that ensues when a less viscous fluid displaces a more viscous one in a porous medium). The displacement pattern is characterized by branching structures, with an intrinsic length scale that depends on the fluid properties, essentially viscosity and surface tension between the fluids, as well as the structure of the porous space, the wetting properties of the system, and the injection rate. Using our macroscopic model, we discuss the scaling properties of the intrinsic finger length scale. [Preview Abstract] |
Monday, November 25, 2013 11:09AM - 11:22AM |
H31.00004: Saffman-Taylor fingering with lateral injection with applications to imbibition coarsening dynamics Bertrand Lagree, Stephane Zaleski, Igor Bondino, Christophe Josserand, Stephane Popinet We report 2D simulations of Saffman-Taylor fingering motivated by the analysis of experiments on the imbibition of porous media in square slab geometries. We use a Volume-of-Fluid (VOF) method to model a two-phase Darcy flow with a sharp interface between the two fluids. The Gerris code which allows efficient parallel computations with quad-tree mesh refinement is used. It is tested for accuracy and precision using several levels of refinement and comparing to reference simulations in the literature. A fingering pattern is observed after lateral injection of a less viscous fluid into a region filled with a more viscous one. Large fractal-like clusters are observed allowing the measurements of several scaling exponents which are compared to the known Diffusion-Limited-Aggregation (DLA) and Saffman-Taylor scalings. An interesting effect is the transition from a transient cylindrical DLA pattern to a small number then a single Saffman Taylor finger. [Preview Abstract] |
Monday, November 25, 2013 11:22AM - 11:35AM |
H31.00005: Mechanics of fluid injection into a soft granular material Christopher MacMinn, Eric Dufresne, John Wettlaufer Motivated by a range of problems in geophysics and biology where fluid injection drives the mechanical deformation of a porous solid, we perform laboratory experiments in a model system. We inject fluid into a packing of soft particles and measure the dynamic, flow-driven deformation of the packing at high spatial resolution. We show that the mean deformation and relaxation of the packing, as well as the buildup and dissipation of pressure, can be described by continuum poroelastic theory. We also find, in contrast, that the granular microstructure leads to the spontaneous emergence of heterogeneous mesoscale features such as shear bands that are absent from the continuum theory. We discuss the implications of these results. [Preview Abstract] |
Monday, November 25, 2013 11:35AM - 11:48AM |
H31.00006: The usage of differential method in determining the multiphase flow transport parameters in porous media Bojan Markicevic The imbibition of wetting liquid by a porous medium starts as a single-phase flow which later transforms into a multiphase flow pattern as wetting liquid progresses into the medium. These capillary flows can be solved using the dynamic capillary network models, where the capillary pressure is calculated at the liquid free interface and progression of the flow front is found from fully resolved velocity and pressure profiles within the wetted domain. From known flow quantities, both phase permeability and capillary pressure are determined as a function of a spatial position in the flow geometry. The phase content (saturation) is also calculated from the numerical solution, and after correlations, the phase permeability and capillary pressure as a function of saturation are found. Two independent checks of this differential method are carried out: the first one being the invariance of the single-phase permeability. For region next to the fluid inlet, it is shown that the pressure gradient and the flow rate are always linearly dependent irrespective of the flow front position downstream. Secondly, the phase permeability and capillary pressure saturation functions should not change throughout the spread, irrespective of the time in which they are measured, but rather they should follow the same dependence on the saturation. The numerical results corroborate this assumption, where the invariant permeability and capillary pressure laws are predicted throughout the imbibation duration. Finally, additional properties of the porous medium can be determined including a minimum saturation of the percolation cluster within porous medium. [Preview Abstract] |
Monday, November 25, 2013 11:48AM - 12:01PM |
H31.00007: Pore-scale modeling of Capillary Penetration of Wetting Liquid into 3D Fibrous Media: A Critical Examination of Equivalent Capillary Concept Nikhil Kumar Palakurthi, Urmila Ghia, Ken Comer Capillary penetration of liquid through fibrous porous media is important in many applications such as printing, drug delivery patches, sanitary wipes, and performance fabrics. Historically, capillary transport (with a distinct liquid propagating front) in porous media is modeled using capillary-bundle theory. However, it is not clear if the capillary model (Washburn equation) describes the fluid transport in porous media accurately, as it assumes uniformity of pore sizes in the porous medium. The present work investigates the limitations of the applicability of the capillary model by studying liquid penetration through virtual fibrous media with uniform and non-uniform pore-sizes. For the non-uniform-pore fibrous medium, the effective capillary radius of the fibrous medium was estimated from the pore-size distribution curve. Liquid penetration into the 3D virtual fibrous medium at micro-scale was simulated using OpenFOAM, and the numerical results were compared with the Washburn-equation capillary-model predictions. Preliminary results show that the Washburn equation over-predicts the height rise in the early stages (purely inertial and visco-inertial stages) of capillary transport. [Preview Abstract] |
Monday, November 25, 2013 12:01PM - 12:14PM |
H31.00008: Optimization of Micropillar Arrays for Heat Pipe Applications Renee Hale, Carlos Hidrovo Demand is rising for improved thermal management solutions in areas such as electronics cooling. Heat pipes are an attractive technology, but their cooling capacity is limited by the maximum flow rate that their internal wicking structure can sustain. This capillary limit depends upon the interplay between the permeability of the internal wicking structure and the capillary forces produced by the wick pores. Micropillar arrays have recently received attention as potential wicking materials, and this project seeks to design, manufacture, test, and optimize micropillar arrays for heat pipe applications. The novelty of this work resides in the exploration of rectangular pillar arrangements where the pillar spacing is not identical in both directions. This work utilizes analytical and numerical models of fluid flow to determine array permeability. The capillary pressure is predicted by surface energy minimization techniques. Pillar dimensions are then optimized to obtain the maximum fluid flow rate through the wick. To test the wicks, a thermo-hydraulic characterization setup directly measures the mass flow rate of a working fluid through a wicking material as a function of applied heat load. The results give a clear indication of the heat capacity of each wick and provide a valuable connection between experimental results and model predictions for the fluid velocity. This work tests a range of micropillar array geometries and reports on their suitability as wicking structures for heat pipe applications. [Preview Abstract] |
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