Numerical simulation of breakup and detachment of an axially stretching Newtonian liquid bridge with a moving contact line phase field method

Abstract

The extensional, breakup and detachment dynamics of an axially stretching Newtonian liquid bridge are investigated numerically with a dynamic domain multiphase incompressible flow solver. The multiphase flow solver employs a Cahn–Hilliard phase field model to describe the evolution of the diffuse interface separating the liquid bridge fluid from the surrounding medium. The governing axisymmetric Navier–Stokes and Cahn–Hilliard phase field equations are discretized on a continuously expanding domain, the boundaries of which coincide with the planar solid surfaces containing the liquid bridge. The entire formulation, including the fast pressure correction for high density ratios and the semi-implicit discretization that overcomes the numerical stiffness of the fourth-order spatial operators, is performed on a fixed simplified computational domain using time-dependent transformation. Simulations reveal that the dynamic domain interface capturing technique effectively captures the deformation dynamics of the stretching liquid bridge, including the capillary wave formation, necking and interface evolution post breakup and detachment. It is found that the liquid bridge detachment is strongly influenced by the contact angle prescribed at the stationary and moving solid surfaces. At relatively small pulling speeds, the entire liquid is found to preferentially adhere to the less hydrophobic surface. When the prescribed contact angles are equal, however, the liquid bridge undergoes complete detachment so that no liquid resides either on the stationary or on the moving solid surface.