In the other extreme, Liu et al 10 studied droplet impact on a superhydrophobic structured surface patterned by posts in the 0.1вЂ…mm range, that in themselves have a superhydrophic coating. Based on controlled experiments on hydrophilic surfaces structured with circular pillars, Xiao and Wang 29 formulated models for how the speed at which the liquid invades the microstructure (wicking) is affected by the microscopic geometry. In a recent study, Yuan and Zhao 28 undertook experiments with silicone oil spreading on silicon substrates with pillars between 10 and 20 micrometers in size and made illustrative molecular dynamics simulations, showing that for the completely wetting case the liquid may be pulled ahead through the forest of pillars, in front of the visible contact line. Cazabat and Stuart 27 undertook experiments on spreading of perfectly-wetting silicone oils on glass surfaces that had been roughened to various degrees and found that the presence of roughness could enhance spreading. One way to quantify the contact-line energy dissipation rate coefficient Ој f is to implement it into the boundary condition of Cahn-Hilliard Navier-Stokes (CHNS) simulations and find the value that makes the simulated spreading match that of corresponding experiments 25, 26.Дespite the progress in understanding the dynamic wetting on flat surfaces, investigations of truly dynamic spreading on rough surfaces are infrequent. Where U denotes the local speed of the contact-line. This phenomenological parameter is defined such that the energy dissipation rate w associated with molecular processes at the contact line, per unit length of contact line, is The local non-hydrodynamic energy dissipation due to events on the molecular scale can be effectively described in terms of the contact line friction parameter 22 Ој f, which has the same units as dynamic viscosity. In Molecular Kinetic Theory (MKT) 23, 24, wetting is described in terms of transition of molecules from one adsorption site to another with kinetic energy overcoming an activation barrier. Interestingly, the inertial scaling properly describes the dependence of spreading rate on the droplet size/wettability of the surface 19 although the exponent of the power law r ~ ( t/П„) О± is no longer 1/2 but decreases with increasing equilibrium contact angle.ДЄnother branch of analysis discusses the resistance in terms of non-hydrodynamic energy dissipation at the contact line 22, 23, 24, 25, 26. For a completely wetting case (Оё ~ 0В°) the spreading radius was shown to follow r ~ ( t/П„) 1/2, which can be derived by using the inertial time scale ( ПЃR 3Оі) 1/2 in analogy to droplet coalescence 18, where ПЃ is the liquid density.

Recently however it was found that wetting on smooth surfaces at the initial stage is much faster than Tanner's law predicts 18, 19, 20, 21. Tanner's law 17 assumes that viscous dissipation is the dominant source of resistance and uses a capillary time scale to derive a power-law time dependence between the spreading radius r and time t of r ~ ( t/П„) 1/10, where the capillary time is given by П„ = ОјR/Оі with Ој, R and Оі the viscosity, droplet radius and surface tension, respectively. The key issue is to identify the primary physical effect that resists the wetting. Thus there is recent growing interest in studying dynamic wetting on rough surfaces, supporting the development of emerging technologies such as ink-jet printing of electronics 4, 5, 6, 7, boiling enhancement 8, droplet repulsion 9, 10, material patterning and design 11, 12, 13, 14, 15 and adhesion 16. Understanding of wetting on a rough surface is important because even a macroscopically flat surface has microscale roughness. The rate of dynamic spreading of a liquid on a rough surface, whether during adhesion of a Gecko's feet to a surface 1, the self-cleaning of a Lotus leaf during rainfall 2 or the splashing of an object falling into liquid 3, depends on the degree of surface roughness.

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