Contact angle at the first-order transition in sequential wetting

Sequential wetting, i.e., a sequence of two wetting transitions, in which the first one consists of a discontinuous jump from a microscopically thin to a mesoscopically thick film, followed by a divergence of the thickness of this film as the second, critical transition temperature is approached, has been observed experimentally for alkanes of medium chain length on (salt) water. The contact angle at the critical wetting transition is, naturally, zero—the first-order transition, however, can, in principle, occur at any value of the contact angle. For the specific system of pentane on water, this contact angle has been found to be very small due to the large film thickness of the mesoscopic film. Using the phenomenological model introduced by Ispolatov and Widom, we investigate the relations among film thickness, contact angle, and the discontinuity of the derivative of the latter with respect to temperature at the first-order transition. In particular, we study the asymptotic behavior as the two transition temperatures are made to approach each other within the proposed phenomenological model.