Revisited Cassie's law to incorporate microstructural capillary effects

The equilibrium contact angle and the receding contact angle of water droplets suspended on surfaces comprising arrays of equidistant, uniformly sized square micropillars has been measured with goniometry. Surfaces with distinct pillar size and spacing were fabricated via photolithography and deep reactive-ion etching prior to hydrophobization via the molecular vapor deposition of perflourodecyltrichlorosilane (FDTS). The surfaces exhibited superhydrophobic properties and the measured equilibrium contact angle was compared with the prediction of the Cassie equation based on the measured contact angle on a flat FDTS surface and the surface morphology. A poor agreement between the experimental data and the data predicted by the Cassie equation was found when the spacing between structures was less than the width of the pillars. For more closely spaced structures, the deviation between the measured and predicted values increased. In this roughness region, the measured angle is unchanged by the spacing but the receding angle continues to be dependent on the surface structure. A microscopic examination of the interface between the surface and the droplet revealed that the liquid-gas portion of the contact line was distorted at the pillar edges. The extent of the distortion could not be accurately quantified but it was shown that if the capillary region was assumed to be semicircular and extending half of the width of a pillar in to the liquid-gas region of the contact line, that the contact angle could be predicted well. Moreover, a good prediction of the experimental data of a prior study of droplets on closely spaced circular polydimethylsiloxane micropillar arrays is presented.