Investigation of the Methane Nucleation Growth Process in the Linear Approximation
This paper considers a linear problem of growing a single methane nucleus in water, which is initially in thermodynamic and force equilibrium with a liquid. It shows that as a result of the action of Laplace forces on the surface of the embryo, its state is unstable. To solve this problem, the basic differential equations describing the growth dynamics of the embryo in methane-saturated water were linearized. From the solution of the system of linearized equations, a unified characteristic equation was obtained in which such factors as the growth of the embryo as radial inertia, diffusion and viscosity of water were taken into account. The quantitative characteristic of the embryo growth in the work is the growth rate, which shows the time during which the amplitude of perturbations of the embryo increases by a factor of e. Based on the results of the study, we can conclude that the main role in the embryo growth (and, obviously, of any gas one) is the diffusion effect. The input parameter in the diffusion effect - Ostwald’s number, showing the amount of soluble methane per unit volume of liquid, showed that, depending on the volume of soluble methane in water, the growth rate of the embryo is different. This fact makes it possible to control the boiling process of a gas-saturated liquid.