Viscous fingering of miscible annular ring

Abstract

Miscible viscous fingering (VF) of the annulus of a more viscous fluid radially displaced by a less viscous fluid is investigated through both numerical computations and experimental study. We aim to understand how VF with finiteness in a radial displacement different from the classical radial VF and the instability of a slice displaced rectilinearly with a uniform velocity. It is observed that the VF of a miscible annular ring is a persistent phenomenon in contrast to the transient nature of VF of a miscible slice. Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time when diffusion is the ultimate dominating force. A statistical analysis is performed for the numerical data and it is found that the second moment of the averaged profile, variance, is a non-monotonic function of time, contrary to variance in classical radial VF and rectilinear VF with one fluid sandwiched between layers of another. The minimum in the variance indicates the interaction of two fronts which is visible in terms of pressure fingers, but not the concentration fingers indicating a faster growth of pressure than the concentration growth. In addition, for existence of critical parameters for instability in terms of viscosity contrast and amount of sample, the variation of the finger length with flow rate is found to be dependent on the amount of the more viscous fluid confined in the annulus.