Influence of wall slip in the radial displacement of a yield strength material in a Hele–Shaw cell

Abstract

The growth of viscous fingers in the radial displacement of a yield strength material confined between the plates of a Hele–Shaw cell is investigated. The apparatus is filled with an aqueous solution of Carbopol® before air is injected to start the displacement process. In addition to striking fingering patterns, we identify unyielded residuals of the Carbopol solution arrested on the plates' surfaces with the assistance of digital mobile microscopes placed above the top plate. These unyielded residuals are subjected to slip conditions on the surface walls and appear in different forms. The experimental observations are correlated with the wall slip behavior detected in rheometric measurements, i.e., observed in the flow curve for shear rates below a critical value. This correlation provides an estimate of a critical propagating radius beyond which shear rates drop to values lower than the critical one, and the influence of wall slip becomes significant. We observe that these residuals are uniformly distributed and appear as thin films where the radii are smaller than the critical value and the wall slip is minimum. However, in locations where the radii are larger than the critical one, the residuals turn into isolated blobs of different sizes, which may propagate in a stick-slip motion radially downstream inside the air fingers. In addition, we observe that the morphology of residuals depends on the gap width between the plates, the injection rate of the invading air, the yield strength of the Carpobol solution, and the wettability conditions of the surface walls.