Investigation of the Methane Nucleation Growth Process in the Linear Approximation

About the authors:

Victor V. Koledin, Cand. Sci. (Phys.-Math.), Associate Professor, Department of Humanities and Science Disciplines, South Ural State University Branch (Nizhnevartovsk); vikoled@mail.ru

Ivan S. Melnik, Undergraduate Student, Building program, Industrial and Civil Construction specialization, South Ural State University Branch (Nizhnevartovsk); melnik_chess_genius@mail.ru

Anastasia A. Yakovleva, Undergraduate Student, Instrument Making program, Information and Measuring Equipment and Technologies in the Oil Industry specialization, South Ural State University Branch (Nizhnevartovsk); nastyaya15@mail.ru

Abstract:

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.

References:

1. Vargaftik N. B. 1972. Spravochnik po teplofizicheskim svoystvam gazov i zhidkostey [Reference Book on Thermophysical Properties of Gases and Liquids]. Moscow: Nauka.
2. Davydov M. N. 2012. “Osobennosti nukleatsii i rosta gazovogo puzyr'ka v magme” [Peculiarities of Nucleation and Growth of a Gas Bubble in a Magma]. PMTF, vol. 53, no 3, pp. 20-29.
3. Koledin V. V. 2013. “Razvitie neustoychivosti parovykh, gazovykh i parogazovykh puzyr'kov v peregretoy zhidkosti” [The Development of Instability of Vapor, Gas and Vapor-Gas Bubbles in a Superheated Liquid]. Cand. Sci. (Phys.-Math.) diss. Ufa: Bashkir State University.
4. Kuchma A. E, Gore G. Yu., Kuni F. M. 2008. “Statsionarnyy rost gazovogo puzyr'ka v sil'no peresyshchennom rastvore gaza v zhidkosti” [Stationary Growth of a Gas Bubble in a Strongly Supersaturated Solution of a Gas in a Liquid]. Nauchnoye priborostroenie, vol. 18, no 4, pp. 124-128.
5. Namiot A. Yu. 1981. Rastvorimost' gaza v vode [Solubility of Gas in Water]. Moscow: Nedra.
6. Nigmatulin R. I. 1987. Dinamika mnogofaznykh sred [Dynamics of Multiphase Media], part 1. Moscow: Nauka.
7. Popov V. N., Cherepanov A. N. 1986. O dinamike povedeniya zarodysha gazovogo puzyr'ka v geterofaznykh sredakh [On the Dynamics of the Behavior of the Embryo of a Gas Bubble in Heterophase Media]. PMTF, vol. 53, no 4, pp. 68-76.
8. Chernov A. A., Pilnik A. A. 2013. “Osobennosti rosta gazovykh puzyr'kov v vysokovyazkom gazonasyshchennom rasplave” [Peculiarities of the Growth Of Gas Bubbles in a High-Viscosity Gas-Saturated Melt]. Modern science: Researches, Ideas, Results, Technologies, vol. 1 (12), pp. 446-451. Dnepropetrovsk: Triakon.
9. Shagapov V. Sh. 1986. “Ob ustoychivosti puzyr'kovykh parozhidkostnykh sred” [On the Stability of Bubbly Vapor-Liquid Media]. PMM, vol. 50, no 3, pp. 516-524.