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Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.

Finger-like protrusions that form along fluid–fluid displacement fronts in porous media are often excited by hydrodynamic instability when low-viscosity fluids displace high-viscosity resident fluids. Such interfacial instabilities are undesirable in many natural and engineered displacement processes. We report a phenomenon whereby gradual and monotonic variation of pore sizes along the front path suppresses viscous fingering during immiscible displacement, that seemingly contradicts conventional expectation of enhanced instability with pore size variability. Experiments and porescale numerical simulations were combined with an analytical model for the characteristics of displacement front morphology as a function of the pore size gradient. Our results suggest that the gradual reduction of pore sizes act to restrain viscous fingering for a predictable range of flow conditions (as anticipated by gradient percolation theory). The study provides insights into ways for suppressing unwanted interfacial instabilities in porous media, and provides design principles for new engineered porous media such as exchange columns, fabric, paper, and membranes with respect to their desired immiscible displacement behavior.

Among numerous methods which have been employed to reinforce the thermal efficiency in many systems, one is the thermal radiation which is a mode of heat transfer. Another way to improve the thermal efficiency is the utilization of the porous media. The present work includes the study of micropolar flow with allowance for thermal radiation through a resistive porous medium between channel walls. The governing coupled partial differential equations representing the flow model are transmuted into ordinary ones by using the suitable dimensionless coordinates, and then, quasi-linearization is employed to solve the set of relevant coupled ODEs. Effects of physical parameters on the flow under different conditions, arose by varying the governing parameters, are scrutinized and discussed through tables and graphs. A comparison is associated with previously accomplished results and examined to be in an exceptional agreement. The culminations evidently disclose that the porosity parameter and the Reynolds number suppress the microrotation and velocity, while material parameters produce opposite effects. The thermal radiation phenomenon downturns the temperature curves and enhances the heat transfer rate on the lower wall of channel.

A theoretical and numerical study of complex sliding flows of yield-stress fluids is presented. Yield-stress fluids are known to slide over solid surfaces if the tangential stress exceeds the sliding yield stress . The sliding may occur due to various microscopic phenomena such as the formation of an infinitesimal lubrication layer of the solvent and/or elastic deformation of the suspended soft particles in the vicinity of the solid surfaces. This leads to a ‘stick–slip’ law which complicates the modelling and analysis of the hydrodynamic characteristics of the yield-stress fluid flow. In the present study, we formulate the problem of sliding flow beyond one-dimensional rheometric flows. Then, a numerical scheme based on the augmented Lagrangian method is presented to attack these kind of problems. Theoretical tools are developed for analysing the flow/no-flow limit. The whole framework is benchmarked in planar Poiseuille flow and validated against analytical solutions. Then two more complex physical problems are investigated: slippery particle sedimentation and pressure-driven sliding flow in porous media. The yield limit is addressed in detail for both flow cases. In the particle sedimentation problem, method of characteristics – slipline method – in the presence of slip is revisited from the perfectly plastic mechanics and used as a helpful tool in addressing the yield limit. Finally, flows through model and randomized porous media are studied. The randomized configuration is chosen to capture more sophisticated aspects of the yield-stress fluid flows in porous media at the yield limit – channelization.

This work reports on modelling unsteady gas flow in porous media at the macroscopic scale in the slip regime, a topic of interest in a wide range of applications. The slip effect is modelled by means of a Navier-type boundary condition. A macroscopic model is derived from the initial-boundary-value problem governing unsteady, single-phase flow of a Newtonian fluid through homogeneous porous media in the creeping, isothermal and slightly compressible slip regime. For momentum transport, the macroscopic model involves two terms. The first consists of a convolution product between the macroscopic pressure gradient and the temporal derivative of an apparent dynamic permeability tensor; the second accounts for the memory of the initial condition. Both contributions are predicted from the solution of a unique closure problem that is independent of the initial flow configuration and of the macroscopic pressure gradient. The accuracy of the model is assessed by comparisons with direct numerical simulations performed at the pore-scale, which find excellent agreement. The simulations also show that a classical heuristic model, which is the consequence of assuming a separation of time scales between the pore-scale and the macroscale, is inadequate, in general, to correctly predict the macroscopic velocity. Results from this work provide a formal clear insight about unsteady flow in porous media in the slip regime, motivating further theoretical and experimental work.

The impact of chemical reaction and activation energy plays a vital role in the analysis of fluid dynamics and its thermal properties. The application of the flow of fluid is significantly considered in nuclear reactors, automobiles, manufacturing setups, electronic appliances etc. This study explores the impacts of activation energy and chemical reaction on the magnetohydrodynamic Darcy–Forchheimer squeezed Casson fluid flow through a porous material across the horizontal channel where the two parallel plates are assumed to be in motion. By using similarity variables, partial differential equations are converted to ordinary differential equations. Numerical method is applied using MATLAB to solve the problems and acquire the data for velocity field, thermal distribution, and concentration distribution. The graphs indicate that fluid velocity and temperature increases as the plates are brought closer. In addition, there was a correlation between a rise in the Hartmann number and a decrease in the fluid's velocity because of the existence of strong Lorentz forces. The temperature and the concentration of the liquid will increase due to the Brownian motion. When the Darcy–Forchheimer and activation energy parameters are both increased, the velocity and concentration decreases.

A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids.

The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ( > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.

The magnetic field can serve as a proper controlling parameter for heat transfer and fluid flow; it can be also employed to maximize the thermodynamic efficiency in various fields. Nanofluids and porous inserts are among the conventional approaches of heat transfer enhancements. Porous media, in addition to improving the heat transfer, can enhance the pressure drop. This research presents a numerical investigation on the magnetohydrodynamics forced convection effects of Al2O3–CuO–water nanofluid inside a partitioned cylinder within a porous medium. The calculations were carried out for a broad range of governing parameters. The nanofluid flow is modeled as a two-phase flow using two-phase mixture model, and the Darcy–Brinkman–Forchheimer equation is employed to model fluid flow in porous media. Simulation was also conducted under the laminar flow regime by finite volume method. Furthermore, the thermal boundary condition of constant uniform heat flux was imposed on the cylinder walls. The average Nusselt number as well as the performance evaluation criteria (PEC) were examined for diverse Darcy numbers (0.0001 < Da < 0.1) and Hartmann numbers (0 < Ha < 40). The results indicate the significant impact of Hartmann and Darcy number enhancement on the elevation of heat transfer coefficient. Additionally, incorporation of nanoparticles to the base fluid increased the PEC in all cases. Moreover, the PEC reached to its maximum value in configurations involving permeable porous media (i.e., a medium with Da = 0.1 and Ha = 40).

The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales. It has been suggested that the cytoplasm of living cells can be described as a porous elastic meshwork bathed in an interstitial fluid. Microindentation tests now show that intracellular water redistribution plays a fundamental role in cellular rheology and that at physiologically relevant timescales cellular responses to mechanical stresses are consistent with such a poroelastic model.