Abstract
In the non-ideal gas lattice Boltzmann equation (LBE), the intermolecular forces between solid and fluid can be represented by the inclusion of the wall free energy in the expression of the total free energy. We derived and investigated three types of polynomial (linear, quadratic, and cubic) wall free energy based boundary conditions for the non-ideal gas LBE method. Static cases with a liquid drop sitting on solid surfaces are examined. All the proposed boundary conditions are able to predict the equilibrium states very well in the range of moderate contact angles by incorporating the potential form of the intermolecular forces and the bounce-back rule that guarantees mass conservation. Simulations with different boundary conditions are carried out and the results are compared concerning the accuracy as well as the applicability of different polynomial boundary conditions.
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