Dynamic wetting and spreading and the role of topography

Abstract

The spreading of a droplet of a liquid on a smooth solid surface is often described by the Hoffman-de Gennes law, which relates the edge speed, v e , to the dynamic and equilibrium contact angles θ and θ e by v e ∝θ(θ 2 -θ e 2 ). When the liquid wets the surface completely and the equilibrium contact angle vanishes, the edge speed is proportional to the cube of the dynamic contact angle. When the droplets are non-volatile this law gives rise to simple power laws with time for the contact angle and other parameters in both the capillary and gravity dominated regimes. On a textured surface the equilibrium state of a droplet is strongly modified due to the amplification of the surface chemistry induced tendencies by the topography. The most common example is the conversion of hydrophobicity into superhydrophobicity. However, when the surface chemistry favors partial wetting, topography can result in a droplet spreading completely. A further, frequently over-looked consequence of topography is that the rate at which an out-of-equilibrium droplet spreads should also be modified. In this report, we review ideas related to the idea of topography induced wetting and consider how this may relate to dynamic wetting and the rate of droplet spreading. We consider the effect of the Wenzel and Cassie-Baxter equations on the driving forces and discuss how these may modify power-laws for spreading. We relate the ideas to both the hydrodynamic viscous dissipation model and the molecular-kinetic theory of spreading. This suggests roughness and solid surface fraction modified Hoffman-de Gennes laws relating the edge speed to the dynamic and equilibrium contact angle. We also consider the spreading of small droplets and stripes of non-volatile liquids in the capillary regime and large droplets in the gravity regime. In the case of small non-volatile droplets spreading completely, a roughness modified Tanner's law giving the dependence of dynamic contact angle on time is presented. We review existing data for the spreading of small droplets of polydimethylsiloxane oil on surfaces decorated with micro-posts. On these surfaces, the initial droplet spreads with an approximately constant volume and the edge speed-dynamic contact angle relationship follows a power law v e ∝θ p . As the surface texture becomes stronger the exponent from p=3 towards p=1 in agreement with a Wenzel roughness driven spreading and a roughness modified Hoffman-de Genne's power law. Finally, we suggest that when a droplet spreads to a final partial wetting state on a rough surface, it approaches its Wenzel equilibrium contact angle in an exponential manner with a time constant dependent on roughness.

Influence of the coating method on the formation of superhydrophobic silicone–urea surfaces modified with fumed silica nanoparticles

“…They are irregularly distributed on the leaf surface with distances between each other ranging from 10 to 100 m. The cones also displayed nanometer sized hairy features, which are reported to be critical in achieving superhydrophobic surfaces with low contact angle hysteresis [11][12][13][14][15][16][17]. Some of the pioneering work in the field was performed by McCarthy and co-workers [8,9,[11][12][13][14][46][47][48][49][50][51][52][53][54][55][56][57][58] and other groups [4,10,[15][16][17]28,41,[59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74], which ...…”

Dynamic polygonal spreading of a droplet on a lyophilic pillar-arrayed surface

“…[19,20] The scaling laws for the dynamic contact angles and spreading radius are modified. [1,21] Moreover, the shape of a droplet may spread into polygonal bilayer structure, instead of a simple spherical cap. CONTACT ya-Pu Zhao yzhao@imech.ac.cn supplemental data for this article can be accessed here.…”

Wetting failure of hydrophilic surfaces promoted by surface roughness

“…With further experimental and theoretical studies of the contact line dynamics on ideally smooth surfaces13141516171819, the influences of roughness on dynamic wetting have been explored recently, e.g., hemi-wicking of superhydrophilic spreading2021, coating limits on rough surfaces56, pinning potential by defects22, and topographically driven spreading232425. However, most present studies only consider one certain aspect such as superwetting limit2022232425, superhydrophobic limit26, and low capillary number limit2022232425. Clarke5 and Benkreira6 carried on experiments to determine how the roughness modifies the wetting failure systematically outside of those limits; however, no explanation was provided to describe when and how the roughness effects occur on an arbitrary hydrophilic surface.…”