Numerical Investigation of Boundary Conditions for Moving Contact Line Problems

When boundary conditions arising from the usual hydrodynamic assumptions are applied, analyses of dynamic wetting processes lead to a well-known nonintegrable stress singularity at the dynamic contact line, necessitating new ways to model this problem. In this paper, numerical simulations for a set of representative problems are used to explore the possibility of providing material boundary conditions for predictive models of inertialess moving contact line processes. The calculations reveal that up to Capillary number Ca=0.15, the velocity along an arc of radius 10Li (Li is an inner, microscopic length scale! from the dynamic contact line is independent of the macroscopic length scale a for a.103Li , and compares well to the leading order analytical ‘‘modulated-wedge’’ flow field [R. G. Cox, J. Fluid Mech. 168, 169 (1986)] for Capillary number Ca,0.1. Systematic deviations between the numerical and analytical velocity field occur for 0.1168, 169 (1986)] is used as a boundary condition along an arc of radius R=10-2a from the dynamic contact line, agree well with those using two inner slip models for Ca\u3c0.1, with a breakdown at higher Ca. Computations in a cylindrical geometry reveal the role of azimuthal curvature effects on velocity profiles in this vicinity of dynamic contact lines. These calculations show that over an appropriate range of Ca, the velocity field and the meniscus slope in a geometry-independent region can potentially serve as material boundary conditions for models of processes containing dynamic contact lines

Nonsingular boundary integral method for deformable drops in viscous flows

A three-dimensional boundary integral method for deformable drops in viscous flows at low Reynolds numbers is presented. The method is based on a new nonsingular contour-integral representation of the single and double layers of the free-space Green's function. The contour integration overcomes the main difficulty with boundary-integral calculations: the singularities of the kernels. It also improves the accuracy of the calculations as well as the numerical stability. A new element of the presented method is also a higher-order interface approximation, which improves the accuracy of the interface-to-interface distance calculations and in this way makes simulations of polydispersed foam dynamics possible. Moreover, a multiple time-step integration scheme, which improves the numerical stability and thus the performance of the method, is introduced. To demonstrate the advantages of the method presented here, a number of challenging flow problems is considered: drop deformation and breakup at high viscosity ratios for zero and finite surface tension; drop-to-drop interaction in close approach, including film formation and its drainage; and formation of a foam drop and its deformation in simple shear flow, including all structural and dynamic elements of polydispersed foams