The Tolmen length in the model that takes into account the wedging energy of the surface layer of the droplet

Аuthors

Shcherbakov M. E.^*, Kalaydin E. N.^**, Shcherbakov E. A.

Kuban State University, Krasnodar, Russia

*e-mail: latiner@mail.ru
**e-mail: kalaidin@econ.kubsu.ru

Abstract

In B. V. Deryagin's model, which takes into account the interphase transition from liquid to gas, a molecular / wedging layer of thickness h_m is formed in the surface layer of the droplet, compensating for gas adsorption into the surface layer of the liquid. For this model, the droplet equilibrium condition is defined, which includes both the average and Gaussian curvature of the Gibbs surface; droplets, for determining which it is necessary to take into account the energy of formation of the wedging layer and its elastic energy, will be called small droplets.; For the first time, the relationship between the Tolmen length and the thickness of the wedging layer, characterizing the degree of gas adsorption into a liquid, is determined; the Tolmen length for droplets with a small radius of curvature is specified. Within the framework of the integral approach, the dependence of the cosine of the wetting angle of a small droplet on the radius of the sticking spot is obtained from the equality to zero of the first variation of the functional of the total energy of the droplet in a model that takes into account the wedging energy.; A comparison of calculations of the wetting angle of a small droplet for various models that take into account the surface layer confirms the conclusion that the wetting angle decreases non-linearly as the droplet size decreases. The relationship between the spreading of a small droplet and the size of the droplet is obtained. The smaller the drop, the greater the degree of spreading. For droplets in zero gravity and droplets smaller than 10 nm, the pressure difference does not depend on the position of the point inside the droplet and is equal to the Lagrange multiplier of the variational problem for the functional of the total energy of the droplet, which includes terms corresponding to the wedging energy of the surface layer and its elastic energy.

Keywords:

functional of the total energy of the droplet, wedging energy, Deryagin model, Willmore functional, droplet equilibrium condition, droplet wetting angle, nanodrip, ranking of the total energy of the droplet, Tolman length, dependence of the coefficient of surface tension on the droplet size, small droplet, spreading droplet, Lagrange multiplier, Gibbs surface, surface layer, elastic energy, droplet in zero gravity, the Young–Laplace formula

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