The spreading of a liquid on a rough solid surface

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Abstract
The equilibrium configurations of a liquid spreading on a rough solid surface are derived by making expansions in terms of the characteristic slope ε of the surface roughness, which is assumed to be very small. It is also assumed that the microscopic contact angle is a constant and that the liquid–air interface is planar at large distances from the contact line. Expressions for the value of the macroscopic contact angle and a discussion of the existence of contact-angle hysteresis and of stick-jump behaviour of the contact line are given for (i) surfaces with parallel grooves, (ii) surfaces with periodicity in two perpendicular directions and (iii) general non-period surfaces.

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