Dependence of the contact line roughness exponent on the contact angle on substrates with dilute mesa defects:...

We compute the roughness exponent of the averaged contact line width of a liquid on heterogeneous substrates with randomly distributed dilute defects in statics. We study the case of circular "mesa"-type defects placed on homogeneous base. The shape of the liquid meniscus and the contact line are obtained numerically, using the full capillary model when a vertical solid plate, partially dipped in a tank of liquid, is slowly withdrawing from the liquid. The obtained results imply that the contact line roughness exponent depends on the contact angle [Formula: see text], which the liquid meniscus forms with the solid homogeneous base. The roughness exponent grows when [Formula: see text] decreases, and it changes from 0.5 at [Formula: see text] to 0.67 at [Formula: see text]. A wide range of contact angles ([Formula: see text]-[Formula: see text]) is present, where the roughness exponent is practically constant, equal to previously obtained experimental results on the magnitude of the roughness exponent and its dependence on [Formula: see text].