Straight contact lines on a soft solid

Using a Stokes like approach of incompressible elasticity, I calculated the distortions induced by a straight contact line on a elastic substrate having a non-zero surface tension. The response is very similar to that of Shanahan and de Gennes, except that the short scale divergence of the Log profile is regularized by the elastocapillary length built upon shear modulus and substrate surface tension, and replaced by a Neumann balance of surface tensions. This method is extended to treat a substrate surface tension that differs in the dry and wetted regions, i.e. a contact angle that differs from 90 degrees, with the example of a infinite rivulet composed of two contact lines connected by a curved, cylindrical, liquid interface. The perhaps most surprising result is that the local slope of the substrate, very near contact line, is nearly inversely proportional to the substrate surface tension, each ``side'' (``dry'' or ``wet'') of the contact line being very close to support one half of the applied vertical force. This result has surprising implications for the approximate treatment of wetting hysteresis on substrates having both plastic and elastic properties, that seem to be ruled at small scales only by surface tension effects