Scaling of the interfacial velocity in miscible viscous fingering in Hele-Shaw cell

We experimentally investigate the miscible displacement beyond the onset of formation of viscous fingers. Using high resolution imaging, we quantify the interfacial velocities during the displacement of a high-viscosity fluid by a low-viscosity fluid in a Hele-Shaw cell. Our experimental measurements reveal that the miscible viscous fingers exhibit tip-splitting following an increase in the curvature of the viscous fingers in the transverse direction to the flow. Moreover, a decrease in the local velocity of the leading edge of the viscous finger precedes the tip splitting event. Upon comparing the average velocities of the interface at different injection rates, we find that the average velocity of the fluid-fluid interface scales linearly with the inverse of injection time, which is significantly slower than the growth of a uniform circle at similar injection rates.