(95d) Simulating Contact Angle Hysteresis Using Pseudo-Line Tensions in a Continuum Fluid Dynamics Approach

Contact angle hysteresis (CAH) is defined as the difference between the advancing and receding contact angles of a liquid droplet, which is immersed in a gas environment (normally the air), advancing or receding on a solid substrate. In general, CAH is understood to be mainly caused by the topological roughness, defects, and/or chemical heterogeneity of the substrate. A specific study by Dufour et al. (Soft Matter, 2011) of water-ethanol mixtures on micro-patterned substrates reveals that at different conditions of surface tensions and micro-patterns: (1) the advancing contact angle does not change much; however, (2) the receding contact angle largely varies because the receding mode is greatly affected by the formation process of the micro capillary bridges connecting the nearby micro-structures. More experimental results in the literature indicate that the advancing and receding processes are not the reverse of each other, but are quite different events that correspond to totally different activation energies.

Simulating the dynamics of CAH is of interest in numerous chemical engineering processes in industry, especially when the liquid-gas-solid contact line is influential. The challenge of modeling CAH in continuum simulations mainly lies in the multi-scale boundary conditions at the contact line. Previously, the authors have developed a dynamic slip boundary model composed based on the Navier-Stokes (N-S) equation, and studied CAH on micro-patterned, hybrid surfaces. In this study, pseudo-line tensions are used in the slip boundary model to model CAH. A pair of pseudo-line tensions in the receding and advancing states are utilized to represent the contact line interactions with a substrate, which is caused by the topological and/or chemical heterogeneity.

A water droplet sitting on a horizontal or inclined Teflon substrate, whose volume is 4—30 μL, has been studied both experimentally and numerically. Using pseudo-line tensions, our simulation model predicts consistent hysteresis at four different droplet volumes compared to experiments. The critical roll-off angles captured in simulations also match well with experiments. Moreover, our numerical approach demonstrates its capability of simulating and visualizing the three-dimensional details of droplet contours and flow patterns for droplets interacting with solids of plain, micro-patterned, or hierarchical features. Note that the current study establishes the numerical methodology of modeling hierarchical surfaces in continuum simulations: (1) micro-structures are modeled in the meshes (which is the base structure), and (2) nano-structures and/or atomic heterogeneity are captured using pseudo-line tensions (which can be considered as an experimentally validated sub-grid model). The modeling of the former has been validated in our previous study, while the latter is validated in this study, both through extensive comparisons with experiments. We are now able to model realistic and accurate contact line dynamics of liquid droplets interacting with hierarchical structures.