Experimental study of miscible viscous fingering with different effective interfacial tension

Ryuta X Suzuki,Takahiko Ban,Manoranjan Mishra,Fu Wei Quah,Yuichiro Nagatsu

doi:10.1063/5.0030152

Abstract

Viscous fingering (VF) occurs when a more viscous fluid is displaced by a less viscous one in porous media or in Hele-Shaw cells. Generally, VF can be divided into two types: immiscible VF and miscible VF. The typical immiscible finger is wider than the equivalent miscible finger because of interfacial tension. Recently, it has been pointed out that an effective interfacial tension (EIT) is present even in miscible systems when there is a steep concentration gradient of chemical species at the interface. The effects of EIT on miscible VF have so far mainly been studied numerically showing that the fingers become wider owing to EIT. Here, we perform an experimental investigation of the effects of EIT on miscible VF by establishing two solution systems that have different concentration differences but the same viscosity contrast. One is a glycerol solution with a concentration of 99 wt. % and water and has a higher water concentration difference of ∆Cw = 99 wt. %. The other is a polymer solution with a concentration of 8.5 wt. % and water and has a lower water concentration difference of ∆Cw = 8.5 wt. %. We show by direct measurement with a spinning drop tensiometer that the glycerol–water system exhibits greater EIT, and we demonstrate experimentally that typical fingers with high EIT become wider than those with low EIT. We suggest that under the experimental condition employed, the VF in the glycerol–water system with high EIT exhibits a characteristic property of immiscible VF, although it has generally been regarded as a typical representative of classical miscible VF.

Highlights

When a more viscous fluid is displaced by a less viscous one in a porous medium or in a Hele-Shaw cell, which provides a simple twodimensional model of a porous medium, the interface between the two fluids becomes hydrodynamically unstable and forms a fingerlike pattern
We find that λm,th,Gly/λm,th,HEC = 2.2, while λexp,Gly/λexp,HEC = 1.5, and these two values are quite similar. These results indicate that the difference in λexp arises from the difference in effective interfacial tension (EIT) and that the EIT must substantially affect the hydrodynamics for both the glycerol–water and HEC–water systems
By direct measurement of EIT with a spinning drop tensiometer, we have shown that the system with a larger concentration difference exhibits greater EIT

Summary

Introduction

When a more viscous fluid is displaced by a less viscous one in a porous medium or in a Hele-Shaw cell, which provides a simple twodimensional model of a porous medium, the interface between the two fluids becomes hydrodynamically unstable and forms a fingerlike pattern This phenomenon is known as Saffman–Taylor instability or viscous fingering (VF).. Miscible VF is characterized by the Péclet number Pe, defined as the ratio of the convective transport rate to diffusive transport rate, Pe = LV/D, where L is the characteristic length, V is the flow velocity, and D is the diffusivity between the displacing and displaced fluids In both types of VF, the dynamics is governed primarily by the viscosity contrast. The viscous fingers generally become thinner with increasing Ca and Pe. For the same viscosity contrast and flow rate, the fingers in immiscible systems are wider than those in miscible systems because the interfacial tension in immiscible systems can stabilize short-wavelength perturbations at the interface. Recently, control of VFs has attracted a lot of attention and several methodologies have been developed, especially for immiscible systems.

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