To express the capillary stress in the diffuse interface method, there are two different formulations in the literature: one formulation is proportional to the density and the other is to the density gradient. Confusingly, these two apparently different formulations both have been widely used for the same purpose without much attention in the difference. In the present study, we theoretically show that only the latter represents the capillary stress and the former represents the stress due to the non-equilibrium irreversible process in the fluid. The formulations are analyzed not only for the one-component fluid but also for the multi-component fluid. In the prediction of the incompressible flow of one-component fluids, the two formulations turn out to give the identical velocity field, but not the pressure field even in this case.
A diffuse-interface theory of active nematic interfaces: transport mechanisms and modal structure
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院理论与计算物理中心）；Departamento de Física, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院物理系）；International Institute for Sustainability with Knotted Chiral Meta Matter, Hiroshima University（广岛大学螺旋手性超物质可持续发展国际研究所）
Universal behavior in diffuse charge dynamics with patterned electrodes
Center for Computation and Theory of Soft Materials, Robert R. McCormick School of Engineering and Applied Science, Northwestern University（西北大学麦考密克工程与应用科学学院软物质计算与理论中心）；Department of Materials Science & Engineering, Northwestern University（西北大学材料科学与工程系）；Department of Physics and Astronomy, Northwestern University（西北大学物理与天文学系）
