We implemented three-dimensional numerical simulations with an incompressible, laminar flow model to capture the evolution of the liquid-air interface during the coalescence of two identical liquid droplets (R0) resting on a superomniphobic surface. Similar to previous studies (2, 3, 5, 7, 39, 40), we used smooth surfaces (with perfectly smooth wall boundary conditions), with known contact angles [i.e., Embedded Image; see table S1], to define the superomniphobic surfaces in our numerical simulations. Since the experimentally measured contact angle hysteresis is low (i.e., Δθ* < 10°; see table S1) on our superomniphobic surfaces, in our numerical simulations, we ignored contact angle hysteresis at the superomniphobic ridge and at the lower boundary of the computational domain (i.e., z = 0; see section S2) representing the flat superomniphobic surfaces. The two droplets were initially situated with overlapping diffuse interfaces that led to the onset of coalescence (3, 5, 7). Because of the symmetry in the x and y directions, only half of a coalescing droplet was simulated in a computational domain of 6R0 × 6R0 × 10R0 (see section S2) (3, 5, 7). Symmetric boundary conditions were used at the planes x = 0 and y = 0 (5, 7). We solved the governing equations (equation of continuity and momentum equation) with ANSYS Fluent using a pressure-based solver (7). The geometric reconstruction scheme was used in the volume of fluid model to represent the liquid-air interface, with a piecewise-linear approach. Further, we used the continuum surface force method, with surface tension as the source term in the momentum equation. The momentum equation was discretized using the second-order upwind scheme (7). We used the SIMPLE (semi implicit-explicit) algorithm for pressure-velocity coupling, and fluid properties were updated from the pressures using the PISO (pressure implicit with splitting of operators) algorithm (7). A mesh with >40 cells per radius was used within the droplet (7). Further, local mesh refinement was performed close to the ridge, the lower boundary of the computational domain (i.e., z → 0), and the symmetry planes (i.e., x → 0 and y → 0) to mitigate the influence of high gradients (see section S2). A mesh-independence check was performed to confirm that the numerical results were virtually insensitive to further mesh refinement. A variable time-step scheme was used in all cases to ensure Courant-Friedrich-Levy number < 0.8 in each time step. Iterations at each time step were terminated when the convergence criteria of all equations was smaller than 10−6.

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