Experimental Measurement of Decay Length for Azimuthal Pressure Gradients in the Viscous Fingering Instability

Iconic viscous finger patterns form when a lower viscosity fluid penetrates a higher viscosity fluid within a confined geometry. Using a previously described technique [1], we experimentally measure fluid velocities as a function of radius, r, along the mid-plane of a radial Hele-Shaw cell during non-linear pattern formation after the instability onset. We find a difference in the fluid velocity between fluid flowing behind a finger protrusion and that behind the adjacent valley even far behind the interface. This velocity difference, ΔV, decays exponentially with the distance behind the interface: ΔV∝ r^-1 Exp [-(r_inner–r)/λ]. Here r_inner is the inner radius of the interface. We measure the dependence of the decay length, λ, on the length and width of the fingers and compare these measurements with prior model predictions which relate the velocity of the finger and valley interfaces to the the viscosity ratio of the fluids.

[1] Gowen S, Videbæk T, Nagel SR. Experimental Characterization of Pressure Gradients in the Viscous Fingering Instability. In: 74th Annual Meeting of the APS Division of Fluid Dynamics.; November 21–23, 2021; Phoenix, Arizona: APS; 2021. Abstract: T10.00007