The influence of droplet size on line tension
  Within the effective interfacial Hamiltonian approach we evaluate the excess line free energy associated with cylinder-shaped droplets sessile on a stripe-like chemical inhomogeneity of a planar substrate. In the case of short-range intermolecular forces the droplet morphology and the corresponding expression for the line tension - which includes the inhomogeneity finite width effects - are derived and discussed as functions of temperature and increasing width. The width-dependent contributions to the line tension change their structure at the stripe wetting temperature T_W1: for T<T_W1 they decay exponentially while for T>T_W1 the decay is algebraic. In addition, a geometric construction of the corresponding contact angle is carried out and its implications are discussed. 
Pawel Jakubczyk Marek Napiorkowski