Drop spreading on heterogeneous substrates via Monte Carlo simulations

Abstract

We study the dynamics of liquid drops in the partial wetting regime first on pure surfaces and then on heterogeneous substrates. We model the spreading of a drop by a 3-dimensional Ising model (3D IM). The initial nonequilibrium configuration is a parallelepiped of occupied sites with appropriately chosen boundary conditions from which we let the system evolve towards its equilibrium state via a particle-conserving dynamics. We find that the time behaviors of the base radius R1 (t) and the cosine of the contact angle cos theta; (t) are well described by exponential decay functions with relaxation times tau(r) and tau(cos theta;) correspondingly. Thus it follows that the molecular kinetic theory gives a valid description of the initial stage of drop spreading in the partial wetting regime for times smaller than both relaxation times tau(r) and tau(cos theta;) . Also, our MC results for the 3D IM with regularly distributed single-site impurities at low temperatures and low surface fields are compatible with Cassie's and Israelachvili's equations, the description of the data with Israelachvili's equation being slightly better. At high temperatures and high surface fields there is a deviation from the purely linear behavior of the cosine of the contact angle on the concentration known as Cassie's law for chemically heterogeneous surfaces.