Multifaceted design optimization for superomniphobic surfaces

Abstract

Superomniphobic textures are at the frontier of surface design for vast arrays of applications. Despite recent substantial advances in fabrication methods for reentrant and doubly reentrant microstructures, design optimization remains a major challenge. We overcome this in two stages. First, we develop readily generalizable computational methods to systematically survey three key wetting properties: contact angle hysteresis, critical pressure, and minimum energy wetting barrier. For each, we uncover multiple competing mechanisms, leading to the development of quantitative models and correction of inaccurate assumptions in prevailing models. Second, we combine these analyses simultaneously, demonstrating the power of this strategy by optimizing structures that are designed to overcome challenges in two emerging applications: membrane distillation and digital microfluidics. As the wetting properties are antagonistically coupled, this multifaceted approach is essential for optimal design. When large surveys are impractical, we show that genetic algorithms enable efficient optimization, offering speedups of up to 10,000 times.

Fig. 1. Simulation surface configuration.

Illustration of the 3D simulation repeat unit (left), with 2D cross section showing labeled structural parameters (right).

Fig. 2. Quantification and mechanisms leading to the CAH for reentrant and doubly reentrant geometries at zero applied pressure.

(A) (i) CAH dependence on both the area fraction F_r and total cap height D_r. Symbols indicate the depinning mechanism upon receding, with purple diamonds indicating a hybrid mechanism. (ii and iii) Comparison of the bridge-, edge-, and lip-depinning receding models (solid lines, color-coded) against the simulated θ_r (data points); examples shown with varying F_r at fixed D_r = 0.05 and 0.35. The ±1° error bars in the simulation data are too small to be seen. (B) 3D visualization of the advancing liquid-vapor interface (shown in blue); the advancing direction is indicated by a black arrow. Black and red lines indicate the center and edge 2D cross sections that are also presented (right). (C) (i to iv) Visualizations of the major four receding mechanisms. The receding direction is indicated by black arrows.

Fig. 3. Critical pressure analysis for reentrant and doubly reentrant geometries.

(A) Contour plots of ΔP_c variation with F_r and H_r for reentrant (i) and doubly reentrant (ii) geometries. Data points mark the critical height at which the failure mechanism switches from Base Failure (BF) to Depinned Cap Failure (DCF) or Pinned Cap Failure (PCF), and error bars indicate the uncertainty in this height due to the diffuse interface width. Solid and dashed white lines show the critical height based on the capillary model and 2D model, respectively. (B) Model fits to ΔP_c of the Cap Failure mechanisms at H_r = 0.25 for reentrant (i) and doubly reentrant (ii) geometries. (C to E) The three failure mechanisms shown in 3D, with associated diagonal cross sections. Critical pressure liquid morphologies are shown in blue, the vapor phase is shown in white, and the interface is indicated with a black solid line. Red regions show how the unstable meniscus evolves upon increasing ΔP above ΔP_c. (D and E) Under-cap views, highlighting the shapes of the contact lines at the critical pressure. (F) Details of the 3D horizontal (3DD) and 3D diagonal (3DH) capillary bridge models used, showing the inner and outer circumferences (blue) against the system configuration. The 3D illustration compares the simulated liquid-vapor interface (light blue) to the horizontal capillary model (dark blue).

Fig. 4. Reentrant and doubly reentrant transition state analysis.

(A to C) 3D visualizations of the transition states of each transition pathway (liquid-vapor interfaces shown in blue) with associated diagonal cross sections (liquid-vapor interface outlined in black). (C) Under-cap views show the three CC transition state morphologies. (D) 3D contour plots showing the energy barrier ΔE_r of the lowest energy transition mechanism for the reentrant geometries. Each surface is a surface of constant ΔE_r. The dividing surface between different transition mechanisms is shown in black. Impossible geometries with pillar widths A_r wider than the cap width W_r are shaded in dark gray. Geometries approaching this limit and requiring infeasibly large computational domains are shaded in light gray. (E) 3D contour plots showing the energy barrier ΔE_r of the lowest energy transition mechanism for the doubly reentrant geometries.

Fig. 5. Simultaneous optimization of the three wetting properties for membrane distillation and digital microfluidics applications.

(A) (i) 3D contour plot of the membrane distillation scoring function at fixed H_r = 0.3, A_r = 0.05, and t_r = 0.05. Each surface is a surface of constant score. (ii) A 2D slice of the 3D contour plot at the optimal L_r = 0.17. Square data points show the initial (white), second (light gray), fifth (dark gray), and final (black) generations of the genetic algorithm, projected onto the 2D plane. (B) Scoring function for the digital microfluidics application, projected onto the H_r = 0.3 plane at fixed B = 100 μm, also showing the successive generations of the genetic algorithm population.