Session ZC32: Porous Media Flows: Applications

Network modeling of membrane filtration with multiple fouling modes

Membrane filters are in widespread daily use, and there are commercial incentives to optimize their filtration performance (improve impurity retention while increasing lifetime, for example). We present a simple model of a membrane filter, in which the interior pore structure is represented as a randomly-generated network of cylindrical pores. Impurity-laden feed solution passes through the pore network and deposits its impurity particles via two distinct fouling mechanisms: (i) small particles are transported and attracted to pore walls, shrinking the pores; and (ii) large particles are transported by flow through the network until they reach a pore too small to transit (which is then blocked). Our study focuses on how the geometric details of the pore network (e.g. porosity, tortuosity, pore size distribution) influence filter performance. We present statistically-averaged simulations showing how filter performance changes as key design features of the pore network are changed, and in particular, how a pore size gradient in the depth of the filter may be harnessed to optimize filtration outcomes.   

On correlating topology and performance of pore networks in membrane filters

Membrane filtration is an important and ubiquitous process in industrial applications, and there is a growing body of mathematical models that capture this complex process. Previous theoretical work models the internal structure of membrane filters as a network of cylindrical pores whose radii are drawn from a uniform distribution, with fouling modeled as an adsorption process; i.e. the gradual accretion of fouling particles on the inner walls of the pores. Simulation-based approaches are used to measure membrane filter performance, using metrics such as total throughput and accumulated foulant concentration. In the present work, we investigate the correlation between the performance of these networks and their topological properties, in order to discover optimal pore topologies for membrane filter design. We use persistent homology as our principal tool for quantifying topological features, where the radii of a network's pores are represented by a collection of two-dimensional points known as a persistence diagram. The data encoded in these persistence diagrams are then statistically correlated with the performance metrics, particularly with total throughput. We also compare the performance of uniformly and log-normally distributed pore radii, since real membrane filters are believed to have pores of log-normally distributed width. Previous findings for uniformly-distributed radii, relating total throughput to membrane porosity and accumulated foulant concentration to tortuosity, respectively, are compared to new findings with log-normally distributed radii.   

Fluid-mediated forces enhance colloidal diffusion in pulsatile, "dynamic" porous materials

We study the transport phenomena of colloidal particles embedded within a moving array of obstacles that mimics a dynamic, time-varying porous material. While colloidal transport in an array of stationary obstacles ("passive" porous media) has been well studied, we lack the fundamental understanding of colloidal diffusion in a nonequilibrium porous environment. We combine Taylor dispersion theory, Brownian dynamics simulations, and optical tweezer experiments to study the transport of tracer colloidal particles in an oscillating lattice of obstacles. We discover that the dispersion of tracer particles is a non-monotonic function of oscillation frequency and exhibits a maximum that exceeds the diffusivity in the absence of obstacles. By solving the Smoluchowski (convection-diffusion) equation using a generalized dispersion framework, we demonstrate that the enhanced transport of the tracers depends critically on both the direct interparticle interactions with the obstacles and the fluid-mediated, hydrodynamic interactions generated by the moving obstacles.   

Machine Learning based prediction of pressure drop in fluid flow throughout the packed bed system with cylindrical shaped particles

A packed bed system with encapsulated PCM is extensively used in the area of thermal energy storage systems. The storage media absorbs the energy when supply of energy is excessive and release it whenever required. The fluid flows through the packed bed system to transfer the energy. The fluid flow through the packed bed system is modelled as porous media flows. The fluid flow faces resistance to flow due to obstacles because of particles filled in the packed bed. The accurate prediction of the pressure drop in fluid flow through the packed bed system is essential to the fluid flow system for the packed bed thermal energy storage system. Most of the models of pressure drop prediction through the porous media underpredict the pressure drop. The pressure drop data for the packed bed system is collected from in-house experiments and previously published experimental research work. The data is analyzed to get meaningful insights. A machine learning algorithm is applied to statistically formulate the pressure drop throughout the packed bed system. All the varying parameters like the diameter of the particles, the porosity of the packed bed, superficial velocity, density and viscosity of the fluid are taken into consideration. The developed machine learning model is tested against the unseen data. The performance of the model is tested based on R-squared statistics and root mean square error.    

Experimental Analysis of Anisotropic Porous Lattice Substrates on Pressure Gradient Induced Turbulent Separation Bubbles

We investigate the impact of anisotropic porous lattice substrates attached to a flat-plate on pressure gradient induced turbulent separation bubbles (TSB). The flow upstream of the substrate has a Reynolds number of approximately 760 based on the momentum thickness of the incoming turbulent boundary layer. The adverse pressure gradient is generated by suction, with the mean suction velocity at 45% of the free stream velocity. To examine the effects, we utilize four different substrates of High (~0.8), Medium (~0.5) and Low (~0.15) porosities. All designs have high porosities in the wall normal direction, while the porosities in the streamwise and spanwise directions are varied. These substrates span the width of the flat-plate and extend both upstream and downstream of the time-averaged separation bubble. We collect Stereoscopic Particle Image Velocimetry (SPIV) data to analyze and compare the flow characteristics in cases with and without the substrate. The SPIV measurements are taken at three different streamwise planes: the centerline plane, as well as two planes located 50 mm on either side of the centerline. Preliminary analysis of the time-averaged flow fields reveals the time-averaged flow separation is eliminated. In addition, we observe air flow jetting out from the substrate onto the surface. The SPIV results are compared with Direct Numerical Simulations (DNS) results. Overall, these findings provide valuable insights into the behavior of TSBs over anisotropic porous lattice substrates.   

Data-driven analysis and modeling of erosion networks

Channel formation and branching is widely seen in physical systems where movement of fluid though a porous structure causes the erosion of the medium. We introduce a simple model to capture this feedback mechanism in a multiphase model of flow through a frangible porous medium with dynamic permeability. We explore the model through simulations and examine how the channel morphology changes with different parameters. In addition, given a channel network, we develop a data-driven approach to predict the flow characteristics that led to the network formation.   

Edge stabilized finite element method for mass transport within and around an immersed porous media

Mass transport phenomena in immersed porous media is relevant for multiple engineering and biomedical applications. These problems can be characterized by a large spatial jump in flow, and mass transport coefficients along the interface between the free flowing and the immersed porous regions. Streamline upwind Petrov-Galerkin (SUPG) stabilized finite elements (FE) are very efficient in simulating mass transport problems at moderately high Peclet number. However, SUPG is known to still produce spurious oscillations at the location of sharp transport discontinuities without excessive mesh refinement. These oscillations ultimately pollute the solution and can be inadmissible in many applications. In problems where the immersed porous medium interface moves, adaptive mesh refinement can be computationally expensive. In this contribution, we propose the adoption of a linear edge stabilization FE technique to augment traditional SUPG stabilized FE methods to resolve instabilities at the porous medium interface. A series of model mass transport problems through porous media will be presented to evaluate the performance of the stabilization methodology. Finally, an example biological application of mass transport through a complex moving porous media will be demonstrated.   

Filtration Through Thermo-sensitive Hydrogel Membranes

Abstract

Poly(N-isopropylacrylamide) (PNIPAM) hydrogel is an attractive material because of its thermo-responsive properties. It is capable of changing its shape and wettability according to water temperature, which holds great promise for the development of advanced filter media.  In this study, PINIPAM hydrogels were specifically designed and transformed in filter membranes for applications in water filtration systems. These thermally-responsive filter membranes potentially facilitate enhanced filtration efficiency, selectivity, and the overall system performance. Here, we adopted two different procedures to form water-insoluble thermo-responsive filter media based on PINIPAM hydrogels: cross-liking and copolymerization. The PINIPAM hydrogels were electrospun, resulting in formation of thermo-responsive water-insoluble nanofiber membranes. These membranes underwent a series of comprehensive experiments to assess their performance and characteristics, including the mass loss measurements, water droplet infiltration for the wettability assessment, filtration tests, shrinkage measurements, and microscopic observations. These diverse experiments yield a thorough understanding of the PINIPAM nanofiber membranes' properties and their potential applications in water filtration systems.   

GPU-accelerated volumetric lattice Boltzmann method for pore-scale diffusion-advection in geopolymer porous structures for nuclear waste treatment

Porous materials serve as advantageous media for immobilizing radioactive ions in nuclear waste streams. To enhance absorption efficiency in nuclear waste treatment, a profound understanding of the diffusion-advection process within porous structures is imperative for designing such materials. In this study, we present the development of the volumetric lattice Boltzmann method (VLBM) to solve pore-scale diffusion-advection in geopolymer porous structures, which are generated using the phase field method (PFM) with specific pore structures. Mass transport is driven by diffusion, convection, and interface reaction. The concentration field's lattice Boltzmann equation is constructed in a manner similar to that of the velocity field. To tackle the computationally intensive nature of the coupled lattice Boltzmann equations for velocity and concentration fields, we implement GPU (Graphics Processing Unit) parallelization. We first examine the solution of pure diffusion with a point source, and favorable agreements between VLBM and PFM are observed for both velocity and concentration fields. Then, we investigate the influence of porosity, mass diffusivity, and flow rate on the diffusion by varying the pore volume fraction, diffusion coefficient, and background flow velocity. Notably, both porous material properties and fluid characteristics significantly impact this multi-physics process. Through this comprehensive parametric study, we gain insights into the kinetics of ion uptake in porous structures, facilitating the advancement of porous materials for nuclear waste treatment applications.