Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session Q23: Porous Media Flows: Mixing and Turbulence |
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Chair: Hangjie Ji, North Carolina State University Room: 231 |
Monday, November 21, 2022 1:25PM - 1:38PM |
Q23.00001: A mathematical model for wetting and drying in filter membranes Hangjie Ji, Sima Moshafi, Pejman Sanaei A filter membrane may be frequently used during its lifetime, with wetting and drying processes occurring in the porous medium for several cycles. During these cycles, the concentration distribution of molecules or contaminants and the medium morphology evolve. As a consequence, the filter performance ultimately deteriorates after several cycles. In this work, we formulate a coupled mathematical model for the wetting and drying dynamics in a porous medium occurring consecutively. Our model accounts for the porous medium internal morphology (internal structure, porosity, etc.), the contaminant deposition, and the evolution of dry/wet interfaces due to evaporation. The model provides insights to the overall porous medium evolution over cycles of wetting and drying processes and predicts the timeline to discard the filter based on its optimum performance. |
Monday, November 21, 2022 1:38PM - 1:51PM |
Q23.00002: Imbibition of Liquids through a Paper Substrate in a Controlled Environment Subhashis Patari, Pallab Sinha Mahapatra The physics of liquid spreading has become more complex when the surface is porous like paper or fabrics due to the evaporation of the liquid and swelling of the fibres. We have performed liquid imbibition experiments on paper strips in a controlled environment. The experimental results are compared to the existing analytical models that account for each effect separately. The existing models were found to be inaccurate in predicting the experimental results. We developed new analytical models by modifying existing models to predict the capillary rise of the liquid through the paper substrate accurately. Different effects, such as the barrier, evaporation, and swelling, are considered simultaneously while developing the models to mimic the exact practical situation. The modified models predict the experimental results more accurately than the existing models with a maximum prediction error of 10%. Finally, experiments with volatile (water) and non-volatile (silicon oil) liquids at various temperatures and under various relative humidity conditions are conducted to validate the analytical results. |
Monday, November 21, 2022 1:51PM - 2:04PM |
Q23.00003: Imbibition in paper channels with engineered surface grooves Bhargav Rallabandi, Sidharth Modha, Hideaki Tsutsui Paper-based microfluidic devices transport fluids by capillary imbibition and are widely used in low-cost point-of-care applications. Etching grooves onto the surface of the paper parallel to the flow is known to enhance wicking speeds, but the mechanisms and extent of speed-up are not well understood. We develop a model of vertical wicking in paper channels with etched grooves by coupling the flow in the paper matrix with that in the groove, and accounting for gravity and wettability effects. Using a lubrication-like theory for slender grooves, we show that speed up occurs due to the flow in the low-resistance groove acting as an additional source of fluid for transport in the paper matrix. At the same time, the flow in the groove is limited by its low wettability, and because driving capillary forces in the groove are counteracted by gravity. Perhaps counterintuitively, we find that the flow enhancement depends non-monotonically on the width of the groove. We also find that the addition of multiple grooves increases the flow speed but does so sub-linearly with the number of grooves. These findings are encapsulated in an analytical theory that generalizes the Lucas—Washburn wicking law to channels with etched grooves. The predictions of the theory for the wicking dynamics are shown to be in quantitative agreement with measurements of vertical imbibition in etched paper channels, and thus provide useful design guidelines for paper-based microfluidic devices. |
Monday, November 21, 2022 2:04PM - 2:17PM |
Q23.00004: Deformation-driven mixing in a soft porous medium Matilde Fiori, Satyajit Pramanik, Chris W MacMinn Soils, textiles, gels, and biological tissues are porous and very soft. In these materials, deformation and fluid flow are strongly coupled through rearrangements of the pore structure. The resulting flow fields, which are both heterogeneous and unsteady, can play a key role in the transport and mixing of solutes in practical problems such as groundwater contamination and tissue engineering. Here, we use a continuum model based on large-deformation poroelasticiy to study the impact of periodic squeezing on solute transport and mixing in a soft porous medium. Transport occurs through advection, molecular diffusion, and hydrodynamic dispersion, each of which interacts differently with the deformation. We identify the key dimensionless control parameters, explore the resulting deformation and transport regimes, and consider the implications of preliminary experimental results. |
Monday, November 21, 2022 2:17PM - 2:30PM |
Q23.00005: Dispersion effects in porous media gravity currents experiencing local drainage Saeed Sheikhi, Chunendra K Sahu, Morris R Flynn Gravity current flows in porous media are an essential component of numerous processes related to the energy sector, be these connected to resource production (e.g. heavy oil extraction), energy storage (e.g. of Η2 over seasonal timescales), or byproduct disposal (e.g. CO2 sequestration of or acid gas). Many theoretical treatments of gravity current flow invoke a sharp interface assumption and so ignore, in the case of miscible fluids, dispersive transport between the gravity current and the surrounding ambient. We derive an analytical model that takes into account transverse and longitudinal dispersion by considering the bulk and dispersed phases separately. The model in question derives from mass- and buoyancy-balance and assumes both a hydrostatic flow and a bulk phase solute concentration that matches that of the source. Dispersed fluid appears only downstream of the source and results from mixing between the bulk and ambient fluids. For given source and medium conditions, the dispersion severity is characterized by quantifying the amount of fluid (either in terms of volume or in terms of buoyancy) that appears in the dispersed phase. On this basis, we find that the volume of dispersed fluid, though typically small in the absence of gravity current drainage through an isolated fissure, can be large when such a fissure is introduced thereby providing a sink for bulk fluid. Results such as these require, as with analogue flows at much larger Re, specification of an entrainment parameter, the value of which comes from complementary COMSOL numerical simulations. Numerical output is additionally applied to verify key model predictions. |
Monday, November 21, 2022 2:30PM - 2:43PM |
Q23.00006: Flow symmetry-breaking in porous media induces opposing viscous and pressure transverse drag forces Vishal Srikanth, Andrey Kuznetsov Turbulent flow in porous media with porosity less than 80% is susceptible to macroscale symmetry-breaking depending on the solid obstacle shape and Reynolds number. Macroscale symmetry breaking introduces a unique behavior in the drag force on the solid obstacle in the transverse direction where the pressure and viscous drag forces have equal magnitude and act in opposing directions. Large Eddy Simulation of the microscale turbulent flow shows that symmetry-breaking is caused by an imbalance in the microscale pressure distribution resulting in a net macroscale pressure drag force in the transverse direction. Opposing viscous and pressure drag forces emerge in the Reynolds averaged flow due to asymmetric pressure and shear stress distributions on the solid obstacle surface. A shift in the flow stagnation point and the microscale vortices from the plane of geometric symmetry yields a resultant transverse pressure drag force. The tortuosity of the flow streamlines increases due to this shift causing high shear stress in the locations in between the stagnation point and the microscale vortices. Macroscale flow symmetry-breaking influences the turbulence length and time scales, and increases the turbulence anisotropy. |
Monday, November 21, 2022 2:43PM - 2:56PM |
Q23.00007: Scaling the irreversible mixing of carbon dioxide in brine-rich permeable media Juvenal A Letelier, Hugo Ulloa, Julio Leyrer, Jaime Ortega The supercritical CO2 injection and dissolution into deep brine aquifers allow its sequestration within geological formations. After its injection, CO2 is placed over the denser brine in an apparent gravitational stable distribution. However, mixing CO2 and brine leads to a cabbeling-like process, i.e. the resulting mixture is even denser than the pure brine. Here, we investigate the fluid dynamics of CO2 sequestration in underground brines at a laboratory scale utilising the Hele-Shaw model (Letelier et al., 2019). At this scale, the CO2-brine mixture density meets the miscible model ρ(Sω) = ρb+aSω+cSω2, with Sω the CO2 mass fraction. We performed direct numerical simulations to quantify the irreversible mixing of CO2 in brines, recovering the experimental results by Neufeld et al. (2010) and Guo et al. (2021) in porous media. More remarkably, for the Hele-Shaw model we found that the mean scalar dissipation rate, Θscalar, depends on the Rayleigh number, Ra, a novel result not predicted by previous works. The results show that the dissolved CO2 mass flux, characterised by the Sherwood number Sh, satisfies the scaling law Sh ~ Ra Θscalar within the time window between the onset of convection and the arrival of the first megaplume at the Hele-Shaw cell bottom. |
Monday, November 21, 2022 2:56PM - 3:09PM |
Q23.00008: Quantifying the effects of the Korteweg stress tensor on the CO2-brine interface mass transport in permeable media Julio Leyrer, Jaime Ortega, Hugo Ulloa, Juvenal A Letelier For the climate change solution of CO2 capture in deep geological formations, supercritical CO2 is injected in confines brine aquifers where is self allocated between the impermeable cap rock and the brine. Once it reaches this configuration, CO2 begins partially to diffuse into the brine layer. However, the mixture solution obeys a nonlinear equation of state such that the CO2-brine mixing layer becomes heavier than the brine beneath causing a cabbeling-like process that triggers fingers. The gravitational instabilities fosters the vertical transport and the dissolution of CO2 into the brine. When the diffusion rate is slow, a density gradient between CO2 and brine gives rise to a weak transient interface tension. Two miscible fluids are studied using the Hele-Shaw equations for Boussinesq fluid with the additional density dependent tensor known as the Korteweg stress. Here, we report direct numerical simulations to quantity the impact of the interface tension on the nondimensional mass flux and a novel scaling law that integrates Korteweg stress effects. The results show that the interface tensor affects the development of protoplumes by inhibiting diffusion and their coalescence the key mechanism for their grow in time. |
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