Sedimentation of a spherical particle in a rheopectic fluid: A numerical study

In rheopectic fluids, viscosity increases with time and shear-rate as the fluid's microstructure breaks down and larger microstructural units form. The increased viscosity is expected to hinder spherical particle movement and reduce terminal velocity. However, this study's results, obtained by solving the governing equations using the finite-element method and Quemada rheological model, show that this is not always the case. In boundary-layer flow of rheopectic fluids, the shear-rate decreases due to shear-thickening behavior, which can result in lower flow-induced stress. Therefore, a higher breakdown rate is needed for the fluid's microstructure to respond more quickly to the shear-rate. The increased viscosity can then counteract the reduced shear-rate, resulting in higher flow-induced stress and a lower terminal velocity. While this behavior is observed at higher breakdown rates, the situation is different at lower breakdown rates. In this case, the microstructure's response is delayed, preventing viscosity from adjusting to the particle's motion. As a result, the reduced shear-rate leads to lower flow-induced stress and an increase in terminal velocity. This study reveals a critical breakdown rate below which terminal velocity increases with breakdown rate. Beyond this critical value, terminal velocity decreases as expected. This behavior occurs only at larger density ratios, where rapid sphere motion prevents the microstructure from adjusting, particularly at lower breakdown rates where the response is delayed. However, when the terminal velocity is made dimensionless using the fluid's timescale, accounting for the fluid's rheological response, it decreases with breakdown rate for all density ratios, aligning with intuitive expectations.