Capillary hysteresis and gravity segregation in two phase flow through porous media

We study the gravity driven flow of two fluid phases in a one dimensional homogeneous porous column when history dependence of the pressure difference between the phases (capillary pressure) is taken into account. In the hyperbolic limit, solutions of such systems satisfy the Buckley-Leverett equation with a non-monotone flux function. However, solutions for the hysteretic case do not converge to the classical solutions in the hyperbolic limit in a wide range of situations. In particular, with Riemann data as initial condition, stationary shocks become possible in addition to classical components such as shocks, rarefaction waves and constant states. We derive an admissibility criterion for the stationary shocks and outline all admissible shocks. Depending on the capillary pressure functions, flux function and the Riemann data, two cases are identified a priori for which the solution consists of a stationary shock. In the first case, the shock remains at the point where the initial condition is discontinuous. In the second case, the solution is frozen in time in at least one semi-infinite half. The predictions are verified using numerical results.

Generalized IBL models for gravity-driven flow over inclined surfaces

In this investigation we propose several generalized first-order integral-boundary-layer (IBL) models to simulate the two-dimensional gravity-driven flow of a thin fluid layer down an incline. Various cases are considered and include: isothermal and non-isothermal flows, flat and wavy bottoms, porous and non-porous surfaces, constant and variable fluid properties, and Newtonian and non-Newtonian fluids. A numerical solution procedure is also proposed to solve the various model equations. Presented here are some results from our numerical experiments. To validate the generalized IBL models comparisons were made with existing results and the agreement was found to be reasonable.

Simultaneous Droplet Generation with In-Series Droplet T-Junctions Induced by Gravity-Induced Flow

Droplet microfluidics offers a wide range of applications, including high-throughput drug screening and single-cell DNA amplification. However, these platforms are often limited to single-input conditions that prevent them from analyzing multiple input parameters (e.g., combined cellular treatments) in a single experiment. Droplet multiplexing will result in higher overall throughput, lowering cost of fabrication, and cutting down the hands-on time in number of applications such as single-cell analysis. Additionally, while lab-on-a-chip fabrication costs have decreased in recent years, the syringe pumps required for generating droplets of uniform shape and size remain cost-prohibitive for researchers interested in utilizing droplet microfluidics. This work investigates the potential of simultaneously generating droplets from a series of three in-line T-junctions utilizing gravity-driven flow to produce consistent, well-defined droplets. Implementing reservoirs with equal heights produced inconsistent flow rates that increased as a function of the distance between the aqueous inlets and the oil inlet. Optimizing the three reservoir heights identified that taller reservoirs were needed for aqueous inlets closer to the oil inlet. Studying the relationship between the ratio of oil-to-water flow rates () found that increasing resulted in smaller droplets and an enhanced droplet generation rate. An ANOVA was performed on droplet diameter to confirm no significant difference in droplet size from the three different aqueous inlets. The work described here offers an alternative approach to multiplexed droplet microfluidic devices allowing for the high-throughput interrogation of three sample conditions in a single device. It also has provided an alternative method to induce droplet formation that does not require multiple syringe pumps.

Exploration of bioconvection flow of MHD thixotropic nanofluid past a vertical surface coexisting with both nanoparticles and gyrotactic microorganisms

This communication presents analysis of gravity-driven flow of a thixotropic fluid containing both nanoparticles and gyrotactic microorganisms along a vertical surface. To further describe the transport phenomenon, special cases of active and passive controls of nanoparticles are investigated. The governing partial differential equations of momentum, energy, nanoparticles concentration, and density of gyrotactic microorganisms equations are converted and parameterized into system of ordinary differential equations and the series solutions are obtained through Optimal Homotopy Analysis Method (OHAM). The related important parameters are tested and shown on the velocity, temperature, concentration and density of motile microorganisms profiles. It is observed that for both cases of active and passive control of nanoparticles, incremental values of thermophoretic parameters corresponds to decrease in the velocity distributions and augment the temperature distributions.

A Modified Beavers and Joseph Condition for Gravity-Driven Flow over Porous Layers

Gravity-driven flow through an inclined channel over a semi-infinite porous layer is considered in order to obtain a modification to the usual Beavers and Joseph slip condition that is suitable for this type of flow. Expressions for the velocity, shear stress, volumetric flow rates, and pressure distribution across the channel are obtained together with an expression for the interfacial velocity. In the absence of values for the slip parameter when the flow is over a Forchheimer porous layer, this work provides a relationship between the slip parameters of the Darcy and Forchheimer layers. Expressions for the interfacial velocities in both cases are obtained. This original work is intended to provide baseline analysis and a benchmark with which more sophisticated types of flow, over porous layers in an inclined domain can be compared.

3D Numerical Simulation of Gravity-Driven Motion of Fine-Grained Sediment Deposits in Large Reservoirs

Deposits in dam areas of large reservoirs, which are commonly composed of fine-grained sediment, are important for reservoir operation. Since the impoundment of the Three Gorges Reservoir (TGR), the sedimentation pattern in the dam area has been unexpected. An integrated dynamic model for fine-grained sediment, which consists of both sediment transport with water flow and gravity-driven fluid mud at the bottom, was proposed. The incipient motion driven by gravity in the form of fluid mud was determined by the critical slope. Shallow flow equations were simplified to simulate the gravity-driven mass transport. The gravity-driven flow model was combined with a 3D Reynolds-averaged water flow and sediment transport model. Solution routines were developed for both models, which were then used to simulate the integral movement of the fine-grained sediment. The simulated sedimentation pattern agreed well with observations in the dam area of the TGR. Most of the deposits were found at the bottom of the main channel, whereas only a few deposits remained on the bank slopes. Due to the gravity-driven flow of fluid mud, the deposits that gathered in the deep channel formed a nearly horizontal surface. By considering the gravity-driven flow, the averaged error of deposition thickness along the thalweg decreased from −13.9 to 2.2 m. This study improved our understanding of the mechanisms of fine-grained sediment transport in large reservoirs and can be used to optimize dam operations.

Experimental validation of numerical simulations of free-surface flow within casting mould cavities

PurposeThe paper targets on providing new experimental data for validation of the well-established mathematical models within the framework of the lattice Boltzmann method (LBM), which are applied to problems of casting processes in complex mould cavities.Design/methodology/approachAn experimental campaign aiming at the free-surface flow within a system of narrow channels is designed and executed under well-controlled laboratory conditions. An in-house lattice Boltzmann solver is implemented. Its algorithm is described in detail and its performance is tested thoroughly using both the newly recorded experimental data and well-known analytical benchmark tests.FindingsThe benchmark tests prove the ability of the implemented algorithm to provide a reliable solution when the surface tension effects become dominant. The convergence of the implemented method is assessed. The two new experimentally studied problems are resolved well by simulations using a coarse computational grid.Originality/valueA detailed set of original experimental data for validation of computational schemes for simulations of free-surface gravity-driven flow within a system of narrow channels is presented.

Drainage of viscous gravity currents from the edge of a porous or fractured domain with variable properties

<p>Gravity-driven flow in porous and fractured media has been extensively investigated in recent years in connection with numerous environmental and industrial applications, including seawater intrusion, oil recovery, penetration of drilling fluids into reservoirs, contaminant migration such as NAPL spreading in shallow aquifers, and carbon dioxide sequestration in subsurface formations. The propagation of such currents is typically governed by the interplay between viscous and buoyancy forces, with negligible inertial effects. For long and thin currents, the spreading can be described by similarity solutions for a variety of geometries, with topographic controls often playing a crucial role. These solutions can be extended to gravity-driven flow in vertical narrow fractures or cracks via the well-known Hele-Shaw (HS) analogy between parallel plate and porous media flow, with the aperture <em>b</em> (distance between fracture walls) squared being the analogue of permeability <em>k</em> according to <em>k</em> = <em>b</em><sup>2</sup>/12.  </p><p>Buoyancy-driven spreading in porous and fractured media is also influenced by spatial heterogeneity of medium properties; permeability, porosity, and aperture gradients affect the propagation distance and shape of gravity currents, with practical implications for remediation and storage. In this paper we are interested in the coupled effect of heterogeneity and a fixed edge draining the current at one end of a finite domain. Simultaneous permeability and porosity gradients parallel to the flow are considered: this is equivalent to a wedge-shaped fracture, as the Hele-Shaw analogy necessarily accounts for both permeability and porosity gradients.</p><p>A current of density ρ+Δρ advances horizontally in a fluid of density ρ under the sharp interface approximation, and is drained by an edge at a distance <em>x</em> = <em>L</em> from the origin; a no-flow boundary condition is considered at <em>x</em> = 0. We neglect vertical velocities for an elongated current; this implies vertical equilibrium, and in turn an hydrostatic pressure distribution within the advancing current. The final assumption is of vanishing height of the current at the draining edge after a relatively short adjustment time, favoured by the increase in permeability/porosity or aperture along the flow direction.</p><p>Under these assumptions, a semi-analytical solution is derived for the height of the current <em>h</em>(<em>x</em>, <em>t</em>) in a self-similar form, valid as a late-time approximation modelling the drainage phenomenon after the influence of the initial condition has vanished. This allows transforming the nonlinear PDE governing the flow into a nonlinear ODE amenable to a numerical solution. Knowledge of the current profile then yields the residual mass in the fracture and the drainage flowrate at the edge. A full sensitivity analysis to model parameters is performed, and the conditions required to avoid an unphysical or asymptotically invalid result are discussed. An extension to non-Newtonian rheology is then presented.</p>