Spreading dynamics of a drop of yield-stress fluid subject to vertical oscillations

Abstract

The measurement of rheological properties from non-idealised flows is routinely used to characterise yield-stress materials. We extend the canonical slump test, which evaluates yield stress based on the spread of a large drop under gravity, by subjecting such a drop to vertical oscillation of its substrate. We test this flow configuration by direct comparison between experiments and numerical simulations of the time-dependent Cauchy equations coupled to the Saramito-Herschel-Bulkley (SHB) constitutive model. This provides a sensitive test of the SHB model near yield because the vibrated drop can releases stress exceeding the yield stress by adjusting its shape as the forcing acceleration is increased, and thus, remains close to the yield threshold for all forcing. We find that the SHB model systematically underpredicts the amplitude of the viscoelastic oscillatory response of the drop to forcing by a factor of five. However, spreading can be captured numerically by selecting a solvent viscosity that represents the appropriate post-yield rheology of the material at the expense of matching sub-yield properties. This highlights a fundamental challenge in simulating flows in which yielded and unyielded material coexist, such as those encountered in proto-rheological tests. We establish the vibrated drop as a powerful proto-rheological configuration for estimating the yield stress across drops of different rheology, size and shape, by establishing a proportional relationship between the threshold acceleration required to induce spreading relative to gravity and the yield number, the ratio of yield stress to gravitational stress acting at the centre of mass of the drop.