Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow - Wang, Ningning; Li, Sheng; Shi, Liang; Yuan, Xuefeng; Liu, Haihu (Journal of fluid mechanics, 2023)
The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ($Ca$), Weissenberg number ($Wi$) and solvent viscosity ratio ($β$). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$, or by increasing $Wi$ or decreasing $β$, where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $β$, and the inhibiting effect strengthens with an increase of $Ca$. Decreasing $β$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$, and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $β$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$. The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.