Non-dimensional numerical study of droplet impacting on heterogeneous hydrophilicity/hydrophobicity surface

- A general analysis was performed for drop impacting on heterogeneous surface.
- Two modes of drop breakup and the superposition principle were found.
- Three regimes of drop patterns and transition boundaries were given.
- Effect of hydrophilic size, We and Oh on the drop dynamics were analyzed.

Heterogeneous hydrophilicity/hydrophobicity surface involves many applications such as dropwise condensation, but droplet dynamics on such surface is not well understood. Here, droplet impacting on heterogeneous surface was described by non-dimensional conservation equations. The volume of fluid (VOF) method tracked the gas-liquid interface. A set of parameters such as impacting velocity, drop size etc. were combined to form three key non-dimensional parameters of We, Oh and βi (size ratio of hydrophilic dot to drop). Numerical simulations agreed with impacting outcomes on uniformly hydrophilic or hydrophobic surface in references. For drop dynamics on heterogeneous surface, the regime maps containing complete-drop, single-drop-pinching-off and multi-drops-pinching-off were demonstrated over a wide range of We = 1-100, Oh = 0.001-1 and βi = 0.5-10. The increased βi enlarges the complete drop regime. The single-drop-pinching-off mode involves combined wall adhesion and surface tension induced short wave mechanism, while the multi-drops-pinching-off mode is caused by the propagation and interference of capillary waves from both ends of an elongated liquid column. The superposition principle was found for the first time: drop patterns include an adhesion part on the wall, similar to that on a hydrophilic surface, plus a rebounding part, similar to that on a super-hydrophobic surface. Spreading diameters are increased by βi at smaller We and moderate or larger βi, but they are not influenced by hydrophilic dot sizes at large We, under which inertia force thoroughly suppress effects of surface tension and wall adhesion. The present findings of this paper are helpful to design hydrophilic/hydrophobic surface and ensure droplet completeness during the impacting process.

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