Abstract:

This paper focuses on the coalescence dynamics of two Newtonian droplets within the viscoelastic fluid under simple shear flow. A two-dimensional (2D) lattice Boltzmann (LB) method is adopted. It integrates the phase field theory to solve the hydrodynamic governing equations for multiphase systems and a lattice advection-diffusion solver to account for the elastic stress tensor. The validity of the numerical method is benchmarked against the analytical solutions and experimental and numerical results for the single-phase Oldroyd-B Poiseuille flow, single droplet deformation under simple shear flow, and effects of two droplets on the liquid film. With the method, the effects of the Deborah number (De), solvent viscosity ratio (β), and capillary number (C_a) on the shear-induced dynamics of double droplets are systematically examined. The results reveal two distinct droplet behaviors, i.e., coalescence and non-coalescence. For constant De, the droplet deformation increases monotonically with C_a. The force and energy analyses show that De affects the deformation and coalescence time by modulating the elastic stresses at the droplet’s two poles. For varying β, only non-coalescence is observed; increasing β suppresses the deformation and migration by reducing the elastic forces and first normal stress difference. In addition, regardless of De, droplets typically coalesce at low C_a and remain separated at high C_a.

Key words: viscoelastic fluid, droplet coalescence, shear flow, lattice Boltzmann (LB) method