Oriented ordering parameters for free energy lattice Boltzmann methods using the bounce-back boundary condition

We evaluate the Lattice-Boltzmann model that combines the free energy approach for multiphase flow with the bounce-back boundary condition. This method requires a virtual ordering parameter to be assigned to the wall nodes. Existing literature has assigned a single ordering parameter for the entire wall node, but this is too coarse to give accurate simulations since it allows for a spurious interaction of different phases through the wall nodes. The consequences are illustrated by examining rough and hydrophobic surfaces where contact angles can be predicted using the Cassie–Baxter equation. It is found that the single value approach gives a large systemic error in the measured contact angles. Considerable improvement can be obtained by assigning different values of the ordering parameter to each side of the wall node.