Viscous Fingering In Hele-Shaw Cell Research Articles

CFD analysis of viscous fingering in Hele-Shaw cell for air-glycerin system

In this research paper, a numerical study has been done on the viscous fingering instability for the air-glycerin system in the 2D horizontal Hele-Shaw cell. The air and glycerin are immiscible fluids and the viscosity of glycerin is too much higher than air and viscous fingering strongly depends upon the viscosity differences of fluids pairs so that the air-glycerin system is taken. In this work, an immiscible fluid–fluid displacement flow process occurs and a low viscous fluid air displaces another high viscous fluid glycerin in the rectangular Hele-Shaw cell then due to unstable displacement of glycerin by air a single finger shape instability appears at the air-glycerin interface. This phenomenon is called viscous fingering. The viscous fingering has got importance in many natural and industrial applications such as geologic carbon dioxide sequestration, oil recovery, water infiltration into the soil, mixing of fluids at low Reynolds numbers in microfluidic devices, and many more. This numerical simulation is based on the transient solver. Volume of fluid (VOF) model has been accounted for tracking of the air- glycerin interface. The Geo-reconstruct scheme has been selected for precise interface tracking. The PISO (Pressure Implicit with Splitting of Operators) scheme has been adopted because it has improved the calculation efficiency. The objectives of this paper are to track the growth of a single finger at the air-glycerin interface and calculate the displacement efficiency by image processing. We found that air displaces only 74.15% of glycerin from the entire cell. We have also shown the distribution of pressure and velocity in the entire cell domain.

Experimental study on viscous fingering in Hele-Shaw cell under acoustic impact

Viscous fingering shaped as curvature of the fluid displacement fronts are usually formed in porous media and Hele-Shaw cell when a liquid with a high viscosity is displaced by a liquid with a lower viscosity. Such interfacial instability is undesirable in many displacement processes, and mainly in oil production. We present the results of physical modeling of the displacement of viscous oil by air in Hele-Shaw cell. As a method of suppressing undesirable interphase instability, the effect of elastic vibrations on the process is proposed. The experiment was performed in stationary conditions and under acoustic action on the displacement process. In the absence of superimposed vibrations, the growth rate of viscous finger is 2.15 times higher than the speed of liquid flow at the cell border. The imposition of acoustic oscillations can both accelerate and slow down the growth rate of viscous fingers depending on their frequency. The paper discusses the peculiarities of the development of viscous fingering. The results are compared with the calculated data.

Impact of surfactant addition on non-Newtonian fluid behavior during viscous fingering in Hele-Shaw cell

We present an experimental study of viscous fingering caused by the displacement of an oil phase by non-Newtonian fluids such as Carbopol® 940 with and without surfactant (SDS) addition in a radial Hele-Shaw cell. When polymer solutions are injected, a variety of fingering patterns as a function of flow rate are observed, which differ from the classical Saffman-Taylor instability. We have shown that if the surfactant concentration locally decreases the interfacial tension, it also leads to a reduction of viscosity and hence results in an increasing impact on the capillary number. We found that surfactant-polymer solutions have wider fingers with increasing flow rates in contrast with Newtonian solutions. Our study also revealed that the relative finger width of both non-Newtonian experiments with and without the surfactant converge asymptotically to the same value. We think that this phenomenon is caused by the decrease in surfactant concentration in the vicinity of the tip as the finger is growing so that the shear-thinning features of polymer prevail at long time.

Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

Viscous fingering in a modified Hele-Shaw cell is numerically investigated. The cell allows periodic variation of depth in the lateral direction. The wavenumber n of the depth perturbation has great influence on fingering patterns. For n = 1, the fingering pattern due to the interface instability remains the same as that in the conventional Hele-Shaw cell, while the depth variation causes the steady finger to be a little narrower. For n = 2, four different fingering patterns are captured, similar to the available experimental observations in a modified Hele-Shaw cell containing a centered step-like occlusion. It is found that new fingering patterns appear as n further increases, among which, two patterns with spatial oscillation along both edges of the finger are particularly interesting. One is a symmetric oscillatory finger for n = 3, and the other is an asymmetric one for n = 4. The influence of capillary number on fingering patterns is studied for n = 3 and 4. We find that spatial oscillation of the finger nearly ceases at moderate capillary numbers and occurs again as the capillary number increases further. Meanwhile, the wide finger shifts to the narrow one. It is accompanied by a sudden decrease in the finger width which otherwise decreases continuously as the capillary number increases. The wavenumber and the amplitude of depth perturbation have little effect on the finger width.

Onset of radial viscous fingering in a Hele-Shaw cell

The onset of viscous fingering in a radial Hele-Shaw cell was analyzed by using linear theory. In the selfsimilar domain, the stability equations were derived under the normal mode analysis. The resulting stability equations were solved analytically by expanding the disturbances as a series of orthogonal functions and also numerically by employing the shooting method. It was found that the long wave mode of disturbances has a negative growth rate and the related system is always stable. For the limiting case of the infinite Peclet number, Pe→∞, the analytically obtained critical conditions are Rc=11.10/\(\sqrt {Pe} \) and nc=0.87\(\sqrt {Pe} \). For Pe≥100, these stability conditions explain the system quite well.