Experimental Characterization of Pressure Gradients in the Viscous Fingering Instability

The viscous fingering instability occurs when a less viscous fluid is injected into a more viscous one within a confined geometry such as the thin gap between the plates of a radial Hele-Shaw cell. We determine the mid-plane velocities of our fluids in this cell using alternate injection of dyed and undyed (equal-viscosity) volumes of the inner or outer fluid. While it is apparent that the outer interface at the finger is moving much faster than the inner interface at adjacent valleys, it is observed that this velocity difference is also present significantly away from the interface within the bulk of the inner fluid. By examining velocities as a function of the distance behind the trailing interface, r_inner , we find that the difference in velocities behind a finger and its adjacent valley, △V, depends on the length of the fingers, L_finger, and decays exponentially with distance from the interface as: r*△V = △V₀ exp [-(r_inner – r)/λ]. We also find associated decay length, λ , is  proportional to L_finger. Using this technique we are able to infer an azimuthal pressure gradient.