Partial wetting boundary conditions on micro-structure surface for Lattice Boltzmann method

•Partial wetting boundary conditions on micro-structure surface for LBM is proposed.•Liquid droplet on micro pillar surface investigated is at the Cassie-Baxter state.•Enhanced hydrophobicity of the structure surface is predicted correctly.•Measured and predicted apparent contact angles show slight pillar height dependent.

Three-dimensional liquid droplet resting on the square pillar-structure surface is simulated by a lattice Boltzmann model combined with partial wetting boundary condition. Simulations are applied to two geometric setups at the Cassie-Baxter state. Different discretization schemes to calculate the wall order parameter gradient on the faces, edges and corner of the pillar are investigated to examine their influences on the capability to predict the enhanced hydrophobicity on the droplet. Discretization of wall derivatives along the edge and corner of the pillar, which accounts for the wall normal direction, produces results closer to the measured values. In strong contrast, the enhanced hydrophobicity is underpredicted if the wall normal derivative is not discretized correctly. Both predictions and measured values indicate that pillar height shows slight dependence on apparent contact angles. Also, apparent contact angle of Cassie-Baxter theory is pillar height independent and it also overpredicts the hydrophobicity. This can be attributed partly to the present investigated structure, which is close to the threshold surface roughness.