Capillary spreading of a droplet in the partially wetting regime using a diffuse-interface model

Abstract

The spreading of a liquid droplet on a smooth solid surface in the partially wetting regime is studied using a diffuse-interface model based on the Cahn--Hilliard theory. The model is extended to include non-90$^{\circ}$ contact angles. The diffuse-interface model considers the ambient fluid displaced by the droplet while spreading as a liquid. The governing equations of the model for the axisymmetric case are solved numerically using a finite-spectral-element method. The viscosity of the ambient fluid is found to affect the time scale of spreading, but the general spreading behaviour remains unchanged. The wettability expressed in terms of the equilibrium contact angle is seen to influence the spreading kinetics from the early stages of spreading. The results show agreement with the experimental data reported in the literature.

Dynamics of Fattening and Thinning 2D Sessile Droplets

“…Refs. [36][37][38][39]. In this approach, a locally conserved field, denoted as φ, plays the role of an order parameter by taking two equilibrium limiting values +φ e and −φ e that represent the liquid and air phases, respectively.…”

Multiphase lattice Boltzmann simulations for porous media applications

“…Note that the cubic boundary condition has been widely used to simulate two-phase flows with moving contact lines [145][146][147][148]. It was demonstrated numerically that such a boundary condition can eliminate the spurious variation of the order parameter at solid boundaries, thereby facilitating the better capturing of the correct physics than its lower-order counterparts (e.g.…”

3D phase-field simulations of interfacial dynamics in Newtonian and viscoelastic fluids

“…The most important physics here is the motion of the contact line, which presents a well-known stress singularity that is conventionally removed by assuming ad hoc conditions such as Navier slip or numerical slip [49,50]. In recent years, the diffuse-interface model has emerged as a promising alternative that offers a more rational approach to this issue [33,[51][52][53].…”

“…For example, Zosel [54] measured the spreading of drops of polymer solutions on a partially wetting substrate. Khatavkar et al [52] simulated the capillary spreading of Newtonian droplets using the diffuse interface method in 2D axisymmetric geometry, and compared the numerical results with Zosel's experiment. For comparison,…”