Exploring the Influence of Wall Slip on Viscoplastic Saffman–Taylor Fingers

Viscoplastic Saffman-Taylor fingering in a Hele-Shaw cell is present when a Newtonian fluid displaces a viscoplastic fluid. Experimentally, the viscoplastic fluids typically used, such as Carbopol, suffer effective slip along the plate walls. This can dramatically alter the instability observed but is often ignored.

In this talk we describe theoretical analysis that adopts conventional Hele-Shaw approximations but is generalised to include a model for the effective slip of the fluid over smooth walls. By performing a linear stability analysis, we show that the instability is significantly reduced when slip is included. To complement the theoretical results, we show a suite of experiments conducted using aqueous suspensions of Carbopol pumped into a Hele-Shaw cell through a circular vent. Instabilities are created by first pumping a disk of Carbopol into the cell, then either pumping air into the fluid-filled cell or withdrawing the Carbopol through the vent. In both cases, the fingers forming on the retreating air-Carbopol interface are interrogated as a function of flux, gap size and the type of cell walls. In agreement with the theoretical predictions, the instability is very different for cells with either rough or smooth walls, an effect that we attribute to effective slip.