Dynamics of liquid bridges between patterned surfaces

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates consisting of alternating hydrophilic and hydrophobic stripes, using a multicomponent pseudopotential lattice Boltzmann method. This extends our earlier work where the substrates were uniformly hydrophilic or hydrophobic. In steady-state conditions, we calculate the following, as functions of pattern wavelength and the liquid bridge contact angles at the hydrophilic and hydrophobic regions: (i) the velocity fields of moving bridges, in particular their (time-averaged) terminal velocities; (ii) the deformation of moving bridges, as measured by the deviation of bridge contact angles from their equilibrium values; (iii) the minimum applied force necessary to mobilise a bridge, and the minimum applied force that breaks a moving bridge. In addition, we found that a bridge moving between patterned substrates cannot be mapped onto a bridge moving between uniform substrates endowed with some effective contact angle, even in the limit of very small pattern wavelength compared to bridge width.