Evaluating the radius dependency of surface tension in nano-droplets by a diffuse-interface lattice Boltzmann

In this paper, the dependency of surface tension and droplet radius is investigated by determination of pressure jump across the interface of a nano-scale droplet. For this goal, a gas liquid system consists of a nano-droplet and surrounding vapour is modelled using a diffuse interface, free energy lattice Boltzmann method. The density and pressure distribution inside and outside the droplet can be obtained from LBM. Consequently, the surface tension is calculated by Laplace equation. Surface tension is found initially for carbon dioxide and then the results are extended for different materials and conditions. Interface thickness can be calculated as a function of material properties and conditions. The results show that, when the ratio of droplet radius to interface thickness (R* = R / h) is greater than 8.0, the surface tension is not a function of radius and it will be equal to the flat surface tension (constant regime). But if this ratio be less than 6.0, the surface tension decreases with radius in a linear pattern (linear regime). It is also shown that for a wide range of properties and conditions the quantitative behaviour of surface tension relative to droplet radius is the same.