Session E05: Porous Media Flows: General II

Kimchi fermentation in permeable Korean earthenware Onggi

Since ancient times, Korean chefs have fermented foods such as kimchi, gochujang, and soy sauce in traditional fermentation vessels called Onggi.  Onggi are purported to provide gas permeability which facilitates the growth of lactic-acid-forming bacteria.  In this experimental study, we perform time-lapse videography and carbon dioxide measurement in various fermentation vessels, including Onggi.  Counter-intuitively, we find that the permeable wall of Onggi does not restrict the growth rate of bacteria but can limit their maximum number. The porosity thus acts as a safety valve for bacteria growth, which may have been used in preventing over-fermentation.   

Upscaling and Automation: Pushing the Boundaries of Multiscale Modeling through Symbolic Computing

Macroscopic differential equations that accurately account for microscopic phenomena can be systematically generated using rigorous upscaling methods. However, such methods are time-consuming, prone to error, and become quickly intractable for complex systems with tens or hundreds of equations. To ease these complications, we propose a method of automatic upscaling through symbolic computation. By streamlining the upscaling procedure and derivation of applicability conditions to just a few minutes, the potential for democratization and broad utilization of upscaling methods in real-world applications emerges. We demonstrate the ability of our software prototype, Symbolica, by reproducing homogenized advective-diffusive-reactive (ADR) systems from earlier studies and homogenizing a large ADR system deemed impractical for manual homogenization. Novel upscaling scenarios previously restricted by unnecessarily conservative assumptions are discovered and numerical validation of the models derived by Symbolica is provided.   

A Soft Porous Media Monolayer Experiment for Exploring Deviations from Darcy's Law

Characterizing and predicting fluid transport through soft porous media is of great importance in many contexts, including hydrogeology, various industrial settings, and biology. Fluid flow through non-deformable porous media demonstrates a linear relationship between fluid flux and pressure gradient, as described by Darcy's law. In soft porous media, material deformation can lead to a variable, nonlinear relationship between fluid flux and pressure gradients such that Darcy's law is violated. In fact, recent studies have demonstrated hysteretic behavior, in which the flux through a porous domain for a particular applied pressure drop is lower when the pressure is decreasing compared to when it is increasing. In this work, fluid is driven through a porous monolayer of hydrogel particles for a broad range of porosities, and image analysis is employed to capture both solid phase deformation and fluid velocity. We will present preliminary results aimed at quantifying the functional relationship between pressure gradients and fluid flux in a soft porous medium. We aim to characterize hysteretic behavior and use the results to build flow models for exploring interstitial fluid transport in biological systems, which often exhibit periodic oscillations in pressure.   

Small-amplitude oscillations of perforated disks

Dynamic stability of deep-water floating structures, such as off-shore wind turbines or oil and gas platforms, is essential for their optimum performance and for minimizing downtime. To this end, these structures are usually appended by submerged flat objects known as heave plates. The plates are designed to dampen unwanted environmental disturbances and, thereby, maintain the oscillations of the platforms within an acceptable range. Despite their widespread use, whether impermeable plates qualify as optimal dampers still remains an open question. To provide practical insights into this inquiry, we examine the hydrodynamic response of perforated disks, as characterized by their added mass and damping coefficients, under small-amplitude oscillations. Numerical simulations are used to solve for the flow field and to calculate the force coefficients for disks of various porosity and thickness. Our calculations reveal that permeable disks behave as their impermeable counterparts at small and intermediate values of the oscillatory Reynolds number Re_ω, with the effect of thickness being relatively insignificant. As Re_ω transitions to higher values (O(10²) and beyond), the added mass coefficient decreases monotonically with increasing the porosity, whereas the damping coefficient initially rises with the porosity, then reaches a maximum, and finally declines with further increasing the degree of perforation. In this regime, we observe modest improvements of both added mass and damping coefficients for thicker disks. Overall, our findings provide new insights into (i) the role of porosity in the dynamic response of perforated disks and (ii) the advantages offered by the porosity for performance optimizations in practical settings.   

Validation of the dusty-gas model for binary diffusion in low aspect ratio capillaries via direct simulation Monte Carlo

The dusty-gas model is an empirical formulation commonly used to describe gas flows in porous media. While experiments have validated the model for pores with high aspect ratios, i.e. pores are long compared to their radii, a validation for near-unity aspect ratios is lacking. We used direct simulation Monte Carlo as a theoretical benchmark to evaluate the accuracy of the dusty-gas model for binary diffusion in low aspect ratio capillaries. We found that the dusty-gas model deviates by less than 7% for all cases that we considered, and our results suggest that the highest errors are due to breakdown of the binary diffusivity when the diffusion length is smaller than the mean free path. We characterized the risk of incurring significant error from this breakdown according to the Knudsen number, aspect ratio, and fluid properties, concluding that the risk is generally low for air/water mixtures. Further, practical limits of fabrication and operation typically require aspect ratios greater than 1, in these cases we calculated less than 3% error. Therefore, the dusty-gas model can be seen as a suitable phenomenological model for gas transport in nanoporous structures in a wide range of applications such as heat transfer, catalysis, and water purification.   

Theoretical Study of Oscillating Squeezing Flow through a Porous Medium

In this paper, we report a theoretical study of a transient squeezing flow through a thin porous gap driven by an oscillating boundary. The process is governed by the viscous, inertial, and Darcy effects. It shows that when the squeezing depth increases, the alternating dominance of the viscous and inertial effects would increase the oscillation of the velocity profiles. The existence of the porous media effectively stabilizes the fluid field. The study presented herein, revealing the fundamental physics of an oscillating squeezing flow, has significant potential for biomedical and industrial applications, such as the cerebrospinal fluid flow under concussion and the oil film lubrication in journal bearings.   

Microscale Shear Stress Induced by Slow Flow in Fibrous Media

Tendon tissue engineering aims to grow functional tissue in vitro. One approach is to grow tendon cells on fibres that can be forced and supplied with nutrients by perfusing media. Motivated by understanding the relation between forcing and shear stress experienced by the cells, we present solutions to homogenised equations describing the interaction of slow Newtonian flow and aligned strings. Derived using multiscale asymptotics, fluid flow in the homogenised model is governed by a modified Darcy Law, coupled to string displacement via a homogenised force balance. We consider analytical solutions for the fluid flow induced by imposed oscillations of the string ends and an imposed flux. For oscillation of the string ends, we present scaling laws for the average shear stress in the limit of high and low frequency. When an inlet flux drives fluid flow, we find the average microscale shear stress for high porosity is predominantly set by parameters resulting from solution to the microscale problem obtained in the derivation of the homogenised model.   

Measurements of Turbulence Over a Streamwise Preferential Porous Medium

This study experimentally examines the possibility of the turbulent drag reduction by an orthotropic porous medium whose streamwise permeability is larger than the wall-normal permeability. We made a layered porous medium whose measured streamwise, wall-normal and spanwise permeabilities are K_xx=26.9, K_yy=1.45, and K_zz=4.26 mm², respectively. Hence, ψ_xy = 4.3 and ψ_zy = 1.7, where ψ_xy =√(K_xx/K_yy).These values satisfy the drag-reducing condition suggested by numerical studies in the literature. We carry out particle image velocimetry measurements of turbulent square duct flows over the porous medium at the bulk Reynolds numbers of 3000-15000 and examine the drag reduction probability. Although the present experiments do not show remarkable turbulence reduction over the porous medium, from the detailed analyses of the obtained data, it is confirmed that the present porous medium is suppressed at least to the same level as that of the flat smooth wall side while the near-wall flow structures are different.   

Capturing aerosol droplets with textiles

Capturing droplets from a stream with a fibrous material is a well-known and well-used process, from face masks or coalescence filters to fog collection. Using a combination of lab model experiments and measurements on a large scale in situ fog collector placed on a meteorological station, we investigate the mechanisms of droplet capture as well as the aerodynamics effects at play for different net geometries, from high porosity fog collectors to low porosity filters. In particular, both in the lab and in situ, we study the drag applied on the net and the flow deviations that may occur around the net; in addition, we characterize the capillary growth of droplets on the fibers, and the effect of this liquid distribution on the capture efficiency. Using these results, we develop a predictive theoretical model that can be used to design a robust, efficient mist collector, that we validate with lab experiments. We propose a structural design to ensure a maximized capture efficiency, and we further use this model to link the in-situ measurements of collection efficiency and drag forces with the characteristic of the fog obtained from meteorological measurements.