The injection and in-situ generation of foam in porous media successfully control gas mobility and improve the fluids' sweep efficiency inside porous media. Mathematical models describing this problem use two phases, foamed gas and fluid, and usually have a term for foam generation and destruction. Moreover, the non-Newtonian foam behavior is frequently modeled using the Hirasaki and Lawson's formula for foamed gas viscosity. In this paper, we detail how the traveling wave analysis can be used to estimate the propagation profiles and velocity for a range of non-Newtonian foam models in porous media at constant total superficial flow velocity. We reformulate Hirasaki and Lawson's formula in an explicit form allowing us to find traveling wave solutions for the non-Newtonian Linear Kinetic model. Comparing the solution with the one for the Newtonian version, allows us to analyze qualitatively and quantitatively the rheology of the foam flow in porous media.
We report a local analysis of the flow of foams in two dimensional heterogeneous model porous media. Pressure measurements are combined with direct observation in order to determine simultaneously the effective viscosity and the fraction of trapped gas. Experiments are conducted in the low-quality regime, in a large range of capillary numbers and relative gas flow rates. The effective viscosity is very high (up to a few thousands times that of water) at low capillary numbers and rheology can be described by a decreasing power-law function of the capillary number of exponent ranging from -1 to …
This paper reports turbulent boundary layer measurements made over open-cell reticulated foams with varying pore size and thickness, but constant porosity ($ε\approx 0.97$). The foams were flush-mounted into a cutout on a flat plate. A Laser Doppler Velocimeter (LDV) was used to measure mean streamwise velocity and turbulence intensity immediately upstream of the porous section, and at multiple measurement stations along the porous substrate. The friction Reynolds number upstream of the porous section was $Re_τ\approx 1690$. For all but the thickest foam tested, the internal boundary layer was…
When using appropriate surfactants, oil and aqueous foam can be intimately mixed without the foam being destroyed. In this Letter, we show that a foam, initially free of oil, can draw an oil drop under the action of capillary forces and stretch it through the aqueous network. We focus on the suction of oil by a single horizontal foam channel, known as a Plateau border. In such confined channels, imbibition dynamics are governed by a balance between capillarity and viscosity. Yet, the scaling law for our system differs from that of classical imbibition in porous media such as aqueous foam. This…
Consider the thin-film equation $h_t + \left(h h_{yyy}\right)_y = 0$ with a zero contact angle at the free boundary, that is, at the triple junction where liquid, gas, and solid meet. Previous results on stability and well-posedness of this equation have focused on perturbations of equilibrium-stationary or self-similar profiles, the latter eventually wetting the whole surface. These solutions have their counterparts for the second-order porous-medium equation $h_t - (h^m)_{yy} = 0$, where $m > 1$ is a free parameter. Both porous-medium and thin-film equation degenerate as $h \searrow 0$, but …
Numerous studies suggest that disturbed shear, causing endothelium dysfunction, can be related to neighboring vortex structures. With this motivation, this study presents a methodology to characterize the vortex structures. Precisely, we use mapping and characterization of vortex structures' changes to relate it with the hemodynamic indicators of disturbed shear. Topological features of vortex core lines (VCLs) are used to quantify the changes in vortex structures. We use the Sujudi-Haimes algorithm to extract the VCLs from the flow simulation results. The idea of relating vortex structures wi…
We analyzed the effect of viscoelasticity on the dynamics of fluids in porous media by studying the flow of a Maxwell fluid in a circular tube, in which the flow is induced by a wave traveling on the tube wall. The present study investigates novelties brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. This problem has numerous applications in various branches of science, including stimulation of fluid flow in porous media under the effect of elastic waves. We have found that in the extreme non-Newtonian …
Tortuosity ($T$) is a parameter describing an average elongation of fluid streamlines in a porous medium as compared to free flow. In this paper several methods of calculating this quantity from lengths of individual streamlines are compared and their weak and strong features are discussed. An alternative method is proposed, which enables one to calculate $T$ directly from the fluid velocity field, without the need of determining streamlines, which greatly simplifies determination of tortuosity in complex geometries, including those found in experiments or 3D computer models. Numerical results…
