Dynamic wetting and spreading and the role of topography

Abstract

The spreading of a droplet of a liquid on a smooth solid surface is oftendescribed by the Hoffman–de Gennes law, which relates the edge speed,ve, to the dynamic and equilibrium contact anglesθ andθe through . 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. Whenthe droplets are non-volatile this law gives rise to simple power laws with timefor the contact angle and other parameters in both the capillary and gravitydominated regimes. On a textured surface, the equilibrium state of a dropletis strongly modified due to the amplification of the surface chemistry inducedtendencies by the topography. The most common example is the conversion ofhydrophobicity into superhydrophobicity. However, when the surface chemistry favorspartial wetting, topography can result in a droplet spreading completely. A further,frequently overlooked consequence of topography is that the rate at which anout-of-equilibrium droplet spreads should also be modified. In this report, we review ideasrelated to the idea of topography induced wetting and consider how this may relateto dynamic wetting and the rate of droplet spreading. We consider the effectof the Wenzel and Cassie–Baxter equations on the driving forces and discusshow these may modify power laws for spreading. We relate the ideas to both thehydrodynamic viscous dissipation model and the molecular-kinetic theory of spreading.This suggests roughness and solid surface fraction modified Hoffman–de Genneslaws relating the edge speed to the dynamic and equilibrium contact angle. Wealso consider the spreading of small droplets and stripes of non-volatile liquidsin the capillary regime and large droplets in the gravity regime. In the case ofsmall non-volatile droplets spreading completely, a roughness modified Tanner’slaw giving the dependence of dynamic contact angle on time is presented. Wereview existing data for the spreading of small droplets of polydimethylsiloxane oilon surfaces decorated with micro-posts. On these surfaces, the initial dropletspreads with an approximately constant volume and the edge speed–dynamiccontact angle relationship follows a power law . As the surface texture becomes stronger the exponent goes fromp = 3 towardsp = 1 in agreement with a Wenzel roughness driven spreading and a roughness modifiedHoffman–de Gennes power law. Finally, we suggest that when a droplet spreads to a finalpartial wetting state on a rough surface, it approaches its Wenzel equilibrium contactangle in an exponential manner with a time constant dependent on roughness.