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Liquid droplet spreading with line tension effect

For a macroscopic liquid droplet, we applied the fluid mechanics to predict its dynamic spreading where the energies associated with volume are dominant (e.g. Shikhmurzaev 1997 J. Fluid Mech. 334 211). When the droplet size is reduced to the sub-millimetre level, the surface energy becomes the dominant factor. If the droplet size is further reduced to the micrometre or sub-micrometre level, the line tension should be included in our theoretical formulation for predicting droplet spreading. In the present paper, we extend the non-equilibrium thermodynamics (Gao et al 2000 Acta Mater. 48 863–74) to describe the micrometre or nanometre size droplet spreading on a solid substrate with the line tension effect. Discussion of the stable and unstable equilibrium states is made based on the thermodynamic force expression.