Triple-line kinetics for solid films

Abstract

We present a derivation of the triple-line kinetic boundary conditions for a solid film in contact with a solid substrate for both nonconserved (evaporation-condensation) and conserved (surface diffusion) dynamics. The result is obtained via a matched asymptotic expansion from a mesoscopic model with a thickness-dependent wetting potential (or disjoining pressure) and mobility. In the nonconserved case, we obtain a single boundary condition, which relates the triple-line velocity with the deviation of the contact angle from its equilibrium value. In the conserved case, two kinetic boundary conditions are needed. They relate the velocity and mass flux at the triple line to the contact angle deviation and discontinuity of the chemical potential. These linear relations are described by three kinetic coefficients. The conditions under which the kinetic coefficients remain finite are obtained. We find, for example, that some kinetic coefficients diverge within the conserved model in the presence of van der Waals interaction.

Disjoining-pressure-induced acceleration of mass shedding in solid-state dewetting

“…(2) is not the only possible model which extends the definition of the wetting potential to finite slopes. Indeed, while some authors have used an approach similar to ours to study wetting statics and dynamics at finite slopes [26,27,[32][33][34][35][36], other options are possible as reported, e.g., in Ref. [37], where the finite-slope wetting term is chosen as dx w(h) instead of ds w(h).…”

“…(5) by ∂ x h, and integrating, one obtains the Young-Dupré equation (4), as discussed for example in Refs. [25,26].…”

“…In the following, we assume for the sake of simplicity that m is a constant independent of h. Some discussion of the case where m depends on h can be found in Ref. [26]. All one-dimensional simulations in this paper are based on the numerical solution of the finite-slope model Eq.…”

“…Thin film models with a contact angle as a boundary condition at the triple line and without influence of the wetting potential on the film away from the triple line are recovered from models with a wetting potential in the limit where the range of the wetting potential vanishes (see, e.g., Ref. [26]). Models with a wetting potential have already been used to study hole opening [27] in anisotropic solid films, and Ostwald ripening of nanoislands [28], or to derive effective nonequilibrium kinetic boundary conditions at the triple line of macroscopic films [26].…”

“…[26]). Models with a wetting potential have already been used to study hole opening [27] in anisotropic solid films, and Ostwald ripening of nanoislands [28], or to derive effective nonequilibrium kinetic boundary conditions at the triple line of macroscopic films [26].…”