Saffman-Taylor Instability in Yield Stress Fluids: Theory-Experiment Comparison

The Saffman-Taylor instability for yield stress fluids appears in various situations where two solid surfaces initially separated by such a material (paint, puree, concrete, yoghurt, glue, etc.) are moved away from each other. The theoretical treatment of this instability predicts fingering with a finite wavelength at vanishing velocity, and deposited materials behind the front advance, but the validity of this theory has been only partially tested so far. Here, after reviewing the basic results in that field, we propose a new series of experiments in traction to test the ability of this basic theory to predict data. We carried out tests with different initial volumes, distances and yield stresses of materials. It appears that the validity of the proposed instability criterion cannot really be tested under such experimental conditions, but at least we show that it effectively predicts the instability when it is observed. Furthermore, in agreement with the theoretical prediction for the finger size, a master curve is obtained when plotting the finger number as a function of the yield stress times the sample volume divided by the square initial thickness, in wide ranges of these parameters. This in particular shows that this traction test could be used for the estimation of the material yield stress.