Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow

• Published in: Journal of fluid mechanics Vol. 963
• Main Authors: Wang, Ningning, Li, Sheng, Shi, Liang, Yuan, Xuefeng, Liu, Haihu
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 16.05.2023
• Subjects: Breakup; Colour; Constitutive equations; Constitutive relationships; Couette flow; Deformation; Deformation effects; Droplets; Elasticity; Enhanced oil recovery; Flow velocity; Investigations; JFM Papers; Polymers; Solvents; Steady state; Viscoelasticity; Viscosity; Viscosity ratio; Wettability; multiphase flow; contact lines; viscoelasticity
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2023.340

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 ($\beta$). 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 $\beta$, 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 $\beta$, and the inhibiting effect strengthens with an increase of $Ca$. Decreasing $\beta$ 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 $\beta$ 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.