Buoyancy induced motion of a Newtonian drop in elastoviscoplastic materials

TL;DR

This study models the buoyancy-driven motion of a viscous drop in elastoviscoplastic materials, highlighting the importance of elastic effects for accurate prediction of phenomena like negative wake and drop shape, validated through numerical and experimental comparison.

Contribution

It introduces a numerical model incorporating elastic effects in yield-stress fluids for predicting drop dynamics, validated against experimental data and exploring entrapment conditions.

Findings

Elastic effects are crucial for accurate flow predictions.

Small drops can become entrapped due to insufficient buoyancy.

Rheological parameters significantly influence sedimentation behavior.

Abstract

We investigate theoretically the buoyancy-driven motion of a viscous drop in a yield-stress material, incorporating elastic effects represented by the Saramito-Herschel-Bulkley constitutive equation. We solve the governing equations using an open-source finite volume solver and utilizing the volume of fluid technique to accurately capture the interface between the two fluids. To validate our numerical approach, we compare our results with data from previous experimental and numerical studies. We find quantitative agreement in terms of terminal velocities and drop shapes, affirming the accuracy of our model and its numerical solution. Notably, we observe that incorporating elastic effects into the modelling of the continuous phase is essential for predicting phenomena reported in experiments, such as the inversion of the flow field behind the sedimenting drop (i.e., the negative wake) or the formation of a teardrop shape. Due to the elastoviscoplastic nature of the continuous phase, we observe that small drops remain entrapped because the buoyancy force is insufficient to fluidize the surrounding material. We investigate entrapment conditions using two different protocols, which yield different outcomes due to the interplay between capillarity and elasto-plasticity. Finally, we conduct an extensive parametric analysis to evaluate the impact of rheological parameters (yield stress, elastic modulus, and interfacial tension) on the dynamics of sedimentation.