Contact Angles on a Soft Solid: From Young's Law to Neumann's Law
Abstract
The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young’s relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles differently from those predicted by Neumann’s law, which applies when the drop is floating on another liquid. Here, we derive an elastocapillary model for contact angles on a soft solid by coupling a meanfield model for the molecular interactions to elasticity. We demonstrate that the limit of a vanishing elastic modulus yields Neumann’s law or a variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit to the soft limit appears when the length scale defined by the ratio of surface tension to elastic modulus γ/E reaches the range of molecular interactions.
 Publication:

Physical Review Letters
 Pub Date:
 December 2012
 DOI:
 10.1103/PhysRevLett.109.236101
 arXiv:
 arXiv:1205.2883
 Bibcode:
 2012PhRvL.109w6101M
 Keywords:

 68.03.Cd;
 Surface tension and related phenomena;
 Physics  Fluid Dynamics
 EPrint:
 doi:10.1103/PhysRevLett.109.236101