Determination of surface tension based on thermocapillary motion

Abstract

Relevance. Research the properties of oil-in-water emulsions, in particular their dispersed composition, viscosity, and surface tension, is of great importance for optimizing production processes and improving product quality in various industries, including food, pharmaceutical, cosmetic, and petroleum. In a previous work, the authors identified the dependence of the natural frequency of oscillations of an oil-in-water emulsion spherical droplet on its radius, density, and surface tension. However, the issue of estimating this last parameter has not been resolved, since existing methods have several disadvantages. The derivation of an analytical expression for assessing the surface tension of the dispersed phase of an oil-in-water emulsion will allow for more accurate determination of emulsion properties and the development of new effective methods for studying them. Aim. To obtain an analytical expression for assessing the surface tension and viscosity of the dispersed phase of an oil-in-water emulsion based on thermo-capillary phenomena and the use of surfactants. Object. Water-in-oil emulsion Methods. To obtain analytical expressions, the hydrodynamic partial differential equations are transformed into ordinary differential equations with boundary conditions. In the stationary case, the hydrodynamic equations are converted into the Laplace equation, for which the method of separation of variables is used to find a solution. Results. The authors were able to derive an estimated formula for the propagation velocity of the emulsion surface layer. This formula allows determining the temperature coefficient of surface tension. The authors also succeeded in reducing hydrodynamic equations to ordinary differential equations with boundary conditions. An analytical formula was obtained that allows estimating the viscosity of the emulsion. The article derives a formula that makes it possible to estimate surface tension through wave front velocity using a surfactant on the emulsion surface.