Anisotropy of local stress tensor leads to line tension

Line tension of three-phase contact lines is an important physical quantity in understanding many physical processes such as heterogeneous nucleation, soft lithography and behaviours in biomembrane, such as budding, fission and fusion. Although the concept of line tension was proposed as the excess free energy in three-phase coexistence regions a century ago, its microscopic origin is subtle and achieves long-term concerns. In this paper, we correlate line tension with anisotropy of diagonal components of stress tensor and give a general formula of line tension. By performing molecular dynamic simulations, we illustrate the formula proposed in Lennard-Jones gas/liquid/liquid and gas/liquid/solid systems, and find that the spatial distribution of line tension can be well revealed when the local distribution of stress tensor is considered.