Delta-comb potential in modeling three-phase contact line (TPCL) on periodically patterned surfaces

This work is a study of wetting of small water droplets on smooth glass surfaces with periodic patterns in the form of imprinted net with hydrophilic cells and hydrophobic bars. Microcover slides consisted of soda lime glass were used. The imprinted images of the net were with cell sizes in the range 40-200 μm, which corresponds to a quite narrow scope of hydrophilic surface fractions f(1)(30-36%) due to the relative increase in the size of the hydrophobic bars. The receding contact angles θ(R) of small water droplets, positioned on the patterned surfaces, were measured. The experiment showed significantly lower receding contact angles as compared to the theoretical expectations by the Cassie formula, which accounts for the contribution to the contact angle of the surface fraction of the imprinted hydrophobic/hydrophilic net. For this reason, we developed new theory accounting for the periodicity of the surface and the contribution of the three-phase contact line on the contact angle. This new theory considered delta-comb potential energy Δ(x,y) of the surface, effective line tension κ, and the lattice parameter a. The restriction of theory was discussed as well. It was pointed out that the theory is not valid for very small and very large lattice parameters.