| Micro-patterned solid surfaces exhibit a plethora of apparent wetting states ranging from super-hydrophobicity to super-hydrophilicity. Understanding the mechanisms of transitions between the different stable or metastable wetting states is of critical importance since it is related to the design of surfaces with fully controllable wettability. Wetting transitions are induced by surpassing certain energy barriers set by saddles in the free energy landscape corresponding to unstable wetting states, not observable in experiments, however tractable only computationally by applying suitable numerical techniques. Thus, it is essential to apply system-level tasks, such as bifurcation and stability analysis, which enable the computation of entire solution families both stable and unstable. A mesoscopic lattice Boltzmann (LB) model is employed for the simulation of wetting transitions on model structured surfaces, utilizing its efficiency to deal with flows around solid micron scale obstacles of increased geometric complexity, and to incorporate non trivial microscopic effects (e.g., disjoining pressure). We demonstrate the application of a time-stepper based computational framework, which exploits short bursts of appropriately initialized LB simulations to perform systems level analysis, and track entire solution branches corresponding to stable and unstable steady states. On one hand the computation of wetting transitions energy barriers is enabled, on the other hand, stability analysis provide the directions, along which a targeted actuation could trigger a desired transition, efficiently in terms of strength and energy demand. Here, we report the dependence of the energy barriers on various geometric features of a patterned surface as well as the effect of various perturbations on the wetting and de-wetting transitions. |
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