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

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, Ar 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.