Session G40: Porous Media Flows: Surface Wetting and Filtering

On the effect of the interface heterogeneity between porous and free flow domain

We study microscopic velocity and shear stress profiles in interfacial transition zones that separate a free Navier-Stokes flow domain and a porous Darcy flow domain using pore scale Direct Numerical Simulation (DNS) and physical experiments using Particle Image Velocimetry (PIV). We focus on the impact of the interfacial heterogeneity and the influence of the onset of sediment transport in shallow water. While both DNS and PIV measurements show that far from the interface velocity profiles are parallel and representative of creeping flow, shear stress-induced recirculating flows exist in micro-cavities of the permeable porous surface. Local velocity and shear stresses inside recirculating flows are irregular, distinct enveloping upper and lower bounds can be constructed. The upper bound corresponds to a no-slip condition at interfaces to the solid phase of the porous material. The lower bound is related to the largest micro-cavity size.~   

Velocity measurement of flow over random soft porous media

The aim of this work is to experimentally examine the flow over random soft porous media in a three-dimensional channel. Various combination of fibrous material and the morphology of the fibers were chosen to achieve void volume fraction ($\varepsilon )$ ranging from 0.4 to 0.7. Care has been taken to keep the Reynolds number low so that the flow was laminar. The channel height was constant, however the thickness of the fibrous media was varied to achieve different filling fraction. Before starting the tests in the duct with fiber arrays, a series of tests in an empty duct (i.e., without fibers) conducted to validate the experimental measurements. We also discussed the error and uncertainty sources in the experiments and described the techniques to improve their impact. We studied detailed velocity measurements of the flow over fibrous material inside a rectangular duct using a planar particle image velocimetry (PIV) technique. Using these measurements, we determined the values of the slip velocity at the interface between the fibrous media and the flow. It was found that values of the slip velocity normalized by the maximum velocity in the flow depend on solid volume fraction, pore spaces, and fraction of channel filled by the fiber layers.   

Capillary-driven, spatially-directed liquid transport on and through thin porous substrates

Thin porous substrates exhibit good wicking properties for liquid distribution. The low cost of such common substrates often makes them useful for point of care biomedical diagnostics. Isotropic and anisotropic liquid transport through porous media has been studied extensively in literature. Moreover, previous research has demonstrated spatially-directed liquid transport on textured surfaces featuring surface-tension confined track. Combining both these features, here we demonstrate and analyze capillary-driven, directional liquid transport both on the surface of, and through, a wettability-patterned, horizontal porous substrate. The vertical (through) penetration is governed by Darcy's law. The horizontal (on surface) transport is driven by the Laplace pressure gradient caused by the geometry of the meniscus on the wettability-confined track. The transport rate on the substrate is found to far exceed the liquid permeation rate through it. Consequently, the penetration resistance can be estimated using a quasi-static approach. Using a semi-analytical model, we analyze the effect of the liquid curvature on the penetration rate of a sessile drop placed on the substrate. The model accounts for the back pressure caused by the liquid on the opposing side. The transport model is validated against the experiments, and the geometry, wettability and substrate porosity parameters causing fastest transport are identified.   

Capillary rise in a textured channel

A wetting liquid can invade a textured material, for example a forest of micropillars. The driving and the viscous forces of this motion are determined by the texture parameters and the influence of shape, height and spacing of posts has been widely studied for the last decade. In this work, we build a channel with textured walls. Brought into contact with a reservoir of wetting liquid, we observe in some cases two advancing fronts. A first one ahead invading the forest of micropillars, and a second one behind filling the remaining gap. We study and model the conditions of existence and the dynamics of these two fronts as a function of the characteristics of both microstructure and gap of this elementary porous medium.   

Surface Diffusion Effect on Gas Transport in Nanoporous Materials

Polymer electrolyte fuel cells are one of the promising candidates for power sources of electric vehicles. For further improvement of their efficiency in high current density operation, a better understanding of oxygen flow inside the cells, which have micro- or nanoporous structures, is necessary. Molecular simulations such as the direct simulation of Monte Carlo (DSMC) are necessary to elucidate flow phenomena in micro- or nanostructures since the Knudsen number is close to unity. Our previous report showed that the oxygen diffusion resistance in porous structures with a characteristic pore size of \textasciitilde 100 nm calculated by DSMC agrees well with that measured experimentally. On the other hand, when it comes to the transport in structures with much smaller pore sizes, it is expected that the surface diffusion has a significant impact on gas transport because of their higher specific surface area. Here we present the calculation of gas transport in porous structures with considering surface diffusion. The numerical porous structure models utilized in our simulations are constructed from three-dimensional imaging of materials. The effect of the distance of random walk on the total diffusion resistance in the structures is discussed.   

Optimizing internal structure of membrane filters

Membrane filters are in widespread use, and manufacturers have considerable interest in improving their performance, in terms of particle retention properties, and total throughput over the filter lifetime. In this regard, it has long been known that membrane properties should not be uniform over the membrane depth; rather, membrane permeability should decrease in the direction of flow. While much research effort has been focused on investigating favorable membrane permeability gradients, this work has been largely empirical in nature. We present a simple, first-principles model for flow through and fouling of a membrane filter, accounting for permeability gradients via variable pore size. Our model accounts for two fouling modes: sieving; and particle adsorption within pores. For filtration driven by a fixed pressure drop, flux through the membrane eventually goes to zero, as fouling occurs and pores close. We address issues of filter performance as the internal pore structure is varied, by comparing the total throughput obtained with equal-resistance membranes. Within certain classes of pore profiles we are able to find the optimum pore profile that maximizes total throughput over the filter lifetime, while maintaining acceptable particle removal from the feed.   

Modeling branching pore structures in membrane filters

Membrane filters are in widespread industrial use, and mathematical models to predict their efficacy are potentially very useful, as such models can suggest design modifications to improve filter performance and lifetime. Many models have been proposed to describe particle capture by membrane filters and the associated fluid dynamics, but most such models are based on a very simple structure in which the pores of the membrane are assumed to be simple circularly-cylindrical tubes spanning the depth of the membrane. Real membranes used in applications usually have much more complex geometry, with interconnected pores which may branch and bifurcate. Pores are also typically larger on the upstream side of the membrane than on the downstream side. We present an idealized mathematical model, in which a membrane consists of a series of bifurcating pores, which decrease in size as the membrane is traversed. Feed solution is forced through the membrane by applied pressure, and particles are removed from the feed either by sieving, or by particle adsorption within pores (which shrinks them). Thus the membrane's permeability decreases as the filtration progresses, ultimately falling to zero. We discuss how filtration efficiency depends on the characteristics of the branching structure.   

Fast Simulation of Membrane Filtration by Combining Particle Retention Mechanisms and Network Models

Porous membranes are used for their particle retention capabilities in a wide range of industrial filtration processes. The underlying mechanisms for particle retention are complex and often change during the filtration process, making it hard to predict the change in permeability of the membrane during the process. Recently, stochastic network models have been shown to predict the change in permeability based on retention mechanisms, but remain computationally intensive. We show that the averaged behaviour of such a stochastic network model can efficiently be computed using a simple partial differential equation. Moreover, we also show that the geometric structure of the underlying membrane and particle-size distribution can be represented in our model, making it suitable for modelling particle retention in interconnected membranes as well. We conclude by demonstrating the particular application to microfluidic filtration, where the model can be used to efficiently compute a probability density for flux measurements based on the geometry of the pores and particles.   

Effect of adhesion on particle clogging in fiber filtration

A new multi-time step approach combining a discrete element method with computational fluid dynamics is developed to investigate the clogging phenomenon in two-fiber filtration system of micro-particles. A dimensionless adhesion parameter, Ad, is introduced to characterize clogging of particles during the filtration, while the Stokes number and the interception parameter are kept constant. The results indicate that, in the adhesion-dominated regime, clogging definitely happens at Ad$=$16 or larger, which identifies two distinct zones of unclogging and clogging. Particularly, we find a “best” clogging range of Ad$=$18 to 36 with much shorter clogging time and fewer particles penetrating through. According to the morphological characteristics of deposited particle chains, the clogging time can be further decomposed into chain growing time and bridging time. Despite the shorter bridging time under larger Ad cases, we demonstrate that the delay of clogging can be solely attributed to the increasing chain growing time. This finding highlights that the short-range van der Waals adhesion plays a crucial part during particle clogging process, and is believed to be helpful for the understanding of filtration.   

Darcy permeability of hagfish slime: an ultra-soft hydrogel

When under attack from predators, hagfish produces a large amount of slime. The slime is an exceptional hydrogel, which sets-up in fraction of a second and is known to choke the predators. A small quantity of exudate, released from specialized slime glands, mixes with a large volume of sea water (99.996{\%} w/v) and forms a mucus-like cohesive mass. The exudate has two main constituents: mucins and long intermediate filament based threads. This remarkably dilute material forms into a solid and is hypothesized to have a low hydrodynamic permeability. In this work, we present the first experimental measurements of Darcy permeability of hagfish slime. Our results explain how this ultra-soft hydrogel possesses the so-called `gill-clogging' ability. We also investigate the roles played by individual components of slime, namely, thread cells and mucins, via a concentration-dependent permeability study. Our results provide vital insights into the roles of individual components and it is evident from our observations that mucins play a vital role in significantly reducing the permeability of the fibrous network formed by threads.