Viscous Fingering Instability Research Articles

Controlling and minimizing fingering instabilities in non-Newtonian fluids

The development of the viscous fingering instability in Hele-Shaw cells has great practical and scientific importance. Recently, researchers have proposed different strategies to control the number of interfacial fingering structures, or to minimize as much as possible the amplitude of interfacial disturbances. Most existing studies address the situation in which an inviscid fluid displaces a viscous Newtonian fluid. In this work, we report on controlling and minimizing protocols considering the situation in which the displaced fluid is a non-Newtonian, power-law fluid. The necessary changes on the controlling schemes due to the shear-thinning and shear thickening nature of the displaced fluid are calculated analytically and discussed.

Interfacial elastic fingering in Hele-Shaw cells: A weakly nonlinear study

We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity.

Controlling viscous fingering in tapered Hele-Shaw cells

We present a theoretical study of a variant of the classical viscous fingering instability, which occurs when a high viscosity fluid is displaced by a low viscosity fluid in a Hele-Shaw cell. In our system, the Hele-Shaw cell is tapered in the direction of fluid displacement. We consider two tapered Hele-Shaw geometries (rectilinear and radial), which have a constant depth gradient in the flow direction. We find that the presence of a depth gradient can alter the stability of the interface offering opportunities to control and tune fingering instabilities. In particular, the stability of the interface is now determined by both the viscosity contrast of the fluids and the ratio of the depth gradient to the capillary number of the system. We also demonstrate several applications of our analysis, including the inhibition of viscous fingering by controlling the injection flow rate in a radially tapered Hele-Shaw cell.

Wavelength selection in Hele-Shaw flows: A maximum-amplitude criterion

As in most interfacial flow problems, the standard theoretical procedure to establish wavelength selection in the viscous fingering instability is to maximize the linear growth rate. However, there are important discrepancies between previous theoretical predictions and existing experimental data. In this work we perform a linear stability analysis of the radial Hele-Shaw flow system that takes into account the combined action of viscous normal stresses and wetting effects. Most importantly, we introduce an alternative selection criterion for which the selected wavelength is determined by the maximum of the interfacial perturbation amplitude. The effectiveness of such a criterion is substantiated by the significantly improved agreement between theory and experiments.

A fully-coupled upwind discontinuous Galerkin method for incompressible porous media flows: High-order computations of viscous fingering instabilities in complex geometry

A fully-coupled upwind discontinuous Galerkin method for incompressible porous media flows: High-order computations of viscous fingering instabilities in complex geometry

Computing gravity-driven viscous fingering in complex subsurface geometries: A high-order discontinuous Galerkin approach

We present a formulation of the discontinuous Galerkin method aimed for simulations of gravity-driven viscous fingering instabilities occurring in porous media flow. Specifically, we are targeting applications characterized by complex geometrical features. Viscous fingering instabilities play a very important role in carbon sequestration in brine aquifers. The proposed method has the ability to preserve high order of accuracy on completely unstructured meshes, a feature that makes it ideal for high-fidelity computations of the challenging fingering flow patterns and very complex geometries of actual reservoirs and aquifers. An extensive set of numerical computations is also included, to confirm the stability, accuracy, and robustness of the method.

Viscous fingering at ultralow interfacial tension

We experimentally study the viscous fingering instability in a fluid-fluid phase separated colloid-polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering experiments, in which the displaced fluid wets the walls. We also perform lattice Boltzmann simulations, which help to interpret the experimental observations.

Frontal stability of reactive nanoparticle transport during in situ catalytic upgrading of heavy oil

Frontal stability of reactive nanoparticle transport during in situ catalytic upgrading of heavy oil

A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media

A discontinuous Galerkin method for gravity-driven viscous fingering instabilities in porous media

Tackiness and cohesive failure of granular pastes: Mechanistic aspects

Granular pastes are dense dispersions of non-colloidal grains in a simple or a complex fluid. Typical examples are the coating, gluing or sealing mortars used in building applications. We study the rupture of a thick layer of mortar paste in a simple pulling test where the paste is confined between two flat surfaces. It is shown that, depending on the rheological properties of the paste and the plate separation velocity, two main failure modes are obtained. The first mode is the inwards shear flow of the paste with viscous fingering instabilities, similarly to what has been observed with Newtonian fluids and with non-Newtonian colloidal suspensions or polymer solutions. The second failure mode is stemming from the expansion of bubbles, similarly to what has been observed in soft adhesive polymer layers and, more recently, in highly viscous fluids. It is shown that the crossover between the two failure modes is determined by the conditions required to generate a pressure drop able to trigger the growth of pre-existing micro-bubbles smaller than the inter-granular distance.

Experimental Investigation of Viscous Fingering Instabilities in Emulsions Displacements

Experiments were conducted to analyze the viscous fingering instability that develops during the displacement of oil-in-water (O/W) emulsions. For this purpose, a horizontal rectilinear Hele-Shaw cell, which is an analogue for a homogeneous porous media, was used. Different emulsion solutions were prepared by dispersing different volume fractions of mineral oil in water using non-ionic surfactants. These emulsions were characterized systematically by examining their droplets size distribution and shear viscosity. Flow displacement experiments involved displacing the O/W emulsions by injecting water at different rates. The developments of the instability were characterized qualitatively by identifying the main mechanisms of finger development and growth. These results and the correlations between the properties of the fluids and the flow patterns were used to examine the flow dynamics and its effects on the viscous fingering instability. It was found that the development of the flow instability can be corr...

Finite element simulation of viscous fingering in miscible displacements at high mobility-ratios

Numerical simulations of viscous fingering instabilities in miscible displacements at high mobility-ratios are presented. Anisotropic dispersion and monotonic viscosity profiles are considered. The coupled set of partial differential equations is approximated by the semi-discrete SUPG stabilized finite element formulation plus a discontinuity capturing technique to improve stability around the moving sharp fronts. The pressure equation is discretized by the standard Galerkin method, and a post-processing scheme is used to improve the numerical evaluation of Darcy’s velocity. In the resulting scheme all variables (concentration, pressure and velocity) are approximated by equal order linear triangular elements. A homogeneous channel and a radial system were studied. Complex nonlinear viscous fingering mechanisms for high mobility-ratio miscible displacements were observed.

Viscous fingering of a miscible reactive A + B → C interface: a linear stability analysis

When one solution of reactant A is displacing another miscible solution of reactant B, a miscible product C can be generated in the contact zone if a simple A + B → C chemical reaction takes place. Depending on the relative effect of A, B and C on the viscosity, different viscous fingering (VF) instabilities can be observed. In this context, a linear stability analysis of this reaction–diffusion–convection problem under the quasi-steady-state approximation is performed to classify the various possible instability scenarios. To do so, we determine the criteria for an instability, obtain dispersion curves both at initial contact time using an analytical implicit solution and at later times via numerical stability analysis. Along with recovering known results for non-reactive systems where the displacement of a more viscous fluid by a less viscous one leads to a VF instability, it is found that in the presence of a chemical reaction, injecting a more viscous fluid into a less viscous fluid can also lead to instabilities. This occurs when the chemical reaction leads to the build up of non-monotonic viscosity profiles. Various instability scenarios are classified in a parameter plane spanned by Rb and Rc representing the log-mobility ratios of the viscosities of the B and C solution respectively with respect to that of the injected solution of A. A parametric study of the influence on stability of the Damköhler number and of the time elapsed after contact of the two reactive solutions is also conducted.

Unravelling carbonatite–silicate magma interaction dynamics: A case study from the Velay province (Massif Central, France)

Unravelling carbonatite–silicate magma interaction dynamics: A case study from the Velay province (Massif Central, France)

Miscible viscous fingering in microgravity

To address the issue of miscible viscous fingering instability in buoyancy free conditions, experiments have been performed under microgravity conditions in parabolic flights. A Hele-Shaw cell, two parallel plates separated by a small gap, has been used with two miscible fluids of viscosity ratio 100 (the injected fluid is the less viscous). The influence of the initial thickness of the pseudointerface between the two fluids has been studied, using flow rates large enough to prevent further mixing during displacement. The selected wavelength, measured on the observed fingering pattern, does not depend on the initial front thickness: It is around three times the gap of the cell, i.e., significantly lower than the value of five, observed on earth. However, the initial thickness does control the displacement length required for the instability to occur. Our results are in reasonable agreement with existing and new numerical simulations.

On the mechanics of rim instabilities in viscoelastic polymer thin films

Dewetting of polystyrene thin films deposited onto nonwettable silicon wafers displays unusual dynamics and various morphologies. These instability patterns have been shown to be either discrete circular holes or surface undulations, in the case of nucleated dewetting or spinodal decomposition repectively. Here, we present the existence of a new rim instability, only effective in the elasticity dominated regime, leading to the propagation of fractures into the rim. The comparison with the viscous fingering instability suggests that, in addition to dewetting dynamics, the study of elasticity and viscous-dominated rim instabilities may lead to improved understanding of the influence of viscoelasticity, slippage and friction at the film/substrate interface.

Miscible Displacements of Reactive and Anisotropic Dispersive Flows in Porous Media

The viscous fingering instability of miscible reactive–dispersive flows in a homogeneous porous media is investigated through nonlinear numerical simulations. In particular, the role of velocity-dependent transverse and longitudinal dispersions as well as the type and rate of auto-catalytic chemical reactions is analyzed. It is found that for a third-order auto-catalytic reaction, the higher the reaction rate, the more complex the finger structures. Furthermore, major differences between the flow development of third-order and second-order autocatalytic reactions are reported. In addition, the anisotropy and velocity dependence of the dispersion tensor are found to have a more profound effect on the fingering instability in the case of reactive flows than in the non-reactive ones. The qualitative characterization of the finger structures is explained by examining the flow velocity field and further quantified through an analysis of the average concentration and relative contact area.

Viscous-Fingering-Like Instability of Cell Fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two-dimensional, membrane-bound fragment containing actin filaments that polymerize at the edge and depolymerize in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of large friction, that the perturbed actin velocity and pressure fields obey the same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A remarkable feature of this instability is that it is independent of the strength of the interaction between actin filaments and myosin motors.

Experimental and Numerical Analysis of the Viscous Fingering Instability of Shear-Thinning Fluids

Miscible flow displacements in a rectilinear Hele-Shaw cell of Newtonian as well as rheologically well-characterized shear-thinning fluids are examined through experimental measurements and numerical modelling. Water is used as a displacing fluid while the displaced fluid consists of either a reference Newtonian glycerol solution or shear-thinning solutions of Alcoflood™ polymers of different molecular weights. The experimental measurements revealed that the shear-thinning behaviour of the non-Newtonian solutions resulted in more complex instability patterns and new finger structures not previously observed in the case of Newtonian displacements are identified and characterized. An analysis of the effects of the rheological behaviour of the shear-thinning fluids on instability characteristics such as the finger width and finger tip velocity is presented. Numerical simulations using a pseudo-spectral method are conducted and allowed to compare the predictions of the mathematical model based on an effective Darcy's law with the experimental measurements.

The tackiness of smectite muds. 1. The dilute regime

The tackiness of smectite muds. 1. The dilute regime