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Register a new userStagnation points control chaotic fluctuations in viscoelastic porous media flow
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Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting industrial and biological processes. Recently, Walkama textit{et al.} [Phys. Rev. Lett. textbf{124}, 164501 (2020)] have shown that geometric disorder greatly suppresses such chaotic dynamics. We demonstrate experimentally that geometric disorder textit{per se} is not the reason for this suppression, and that disorder can also promote choatic fluctuations, given a slightly modified initial condition. The results are explained by the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the initially ordered geometric configuration.
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The flow of viscoelastic fluids in porous media is encountered in many practical applications, such as in the enhanced oil recovery process or in the groundwater remediation. Once the flow rate exceeds a critical value in such flows, an elastic instability with fluctuating flow field is observed, which ultimately transits to a more chaotic and turbulence-like flow structure as the flow rate further increases. In a recent study, it has been experimentally shown that this chaotic flow behaviour of viscoelastic fluids can be suppressed by increasing the geometric disorder in a model porous media consisting of a microchannel with several micropillars placed in it. However, the present numerical study demonstrates that this is not always true. We show that it depends on the initial arrangement of the micropillars for mimicking the porous media. In particular, we find that for an initial ordered and aligned configuration of the micropillars, the introduction of geometric order actually increases the chaotic flow dynamics as opposed to that seen for an initial ordered and staggered configuration of the micropillars. We suggest that this chaotic flow behaviour actually depends on the number of the stagnation points revealed to the flow field where maximum stretching of the viscoelastic microstructure happens. Our findings and explanation are perfectly in line with that observed and provided in a more recent experimental study.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids, but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.
Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains challenging. Here we propose that the flow of liquid by capillary penetration can be accurately adjusted by tuning the geometry of porous media and develop numerical method to achieve this. Methodologies On the basis of Darcys law, a general framework is proposed to facilitate the control of capillary flow in porous systems by tailoring the geometric shape of porous structures. A numerical simulation approach based on finite element method is also employed to validate the theoretical prediction. Findings A basic capillary component with a tunable velocity gradient is designed according to the proposed framework. By using the basic component, two functional capillary elements, namely, (i) flow amplifier and (ii) flow resistor, are demonstrated. Then, multi functional fluidic devices with controllable capillary flow are realized by integrating the designed capillary elements. All the theoretical designs are validated by numerical simulations. Finally, it is shown that the proposed model can be extended to three dimensional designs of porous media
Immiscible fluid-fluid displacement in porous media is of great importance in many engineering applications, such as enhanced oil recovery, agricultural irrigation, and geologic CO2 storage. Fingering phenomena, induced by the interface instability, are commonly encountered during displacement processes and somehow detrimental since such hydrodynamic instabilities can significantly reduce displacement efficiency. In this study, we report a possible adjustment in pore geometry which aims to suppress the capillary fingering in porous media with hierarchical structures. Through pore-scale simulations and theoretical analysis, we demonstrate and quantify combined effects of wettability and hierarchical geometry on displacement patterns, showing a transition from fingering to compact mode. Our results suggest that with a higher porosity of the 2nd-order porous structure, the displacement can keep compact across a wider range of wettability conditions. Combined with our previous work on viscous fingering in such media, we can provide a complete insight into the fluid-fluid displacement control in hierarchical porous media, across a wide range of flow conditions from capillary- to viscous-dominated modes. The conclusions of this work can benefit the design of microfluidic devices, as well as tailoring porous media for better fluid displacement efficiency at the field scale.
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