Contact line dynamics in binary lattice Boltzmann simulations

Abstract

We show that, when a single relaxation time lattice Boltzmann algorithm is used to solve the hydrodynamic equations of a binary fluid for which the two components have different viscosities, strong spurious velocities in the steady state lead to incorrect results for the equilibrium contact angle. We identify the origins of these spurious currents and demonstrate how the results can be greatly improved by using a lattice Boltzmann method based on a multiple-relaxation-time algorithm. By considering capillary filling we describe the dependence of the advancing contact angle on the interface velocity.

Multiphase lattice Boltzmann simulations for porous media applications

“…Pooley et al [133] identified that the strong spurious velocities in the steady state lead to an incorrect equilibrium contact angle for binary fluids with different viscosities. The key to reducing spurious velocities lies in the formulation of treating the interfacial tension force [134].…”

Microfluidics of imbibition in random porous media

“…We use the binary free energy lattice Boltzmann model, first developed by Swift et al [22] and later extended by Briant et al [15] and Pooley et al [16]. The binary free energy lattice Boltzmann model includes two particle distribution functions, f i (r,t) and g i (r,t), where r denotes the position in the lattice and i is the lattice direction.…”

“…(35) for C 0 , we have the value for the order parameter at the wall node, which is inserted to Eqs. (16) and (17) to obtain the equilibrium distribution functions. Such a value of C 0 is considered to be a "target" value for the equilibrium.…”

“…The dynamics is governed by the continuity equation, the Navier-Stokes equations, and the convection-diffusion equation [15,16]:…”

“…For this purpose we set up a model structure that consists of a network of interconnected capillaries. We use a lattice Boltzmann method for binary fluids [15,16] together with a wetting boundary condition [17][18][19] to solve the dynamic equations for this two-phase microfluidic problem.…”