{"title":"Simulation of Substrate Cooling during Evaporation of Pure Vapor from the Surface of a Thin Liquid Film and Droplets","authors":"A. L. Kupershtokh, D. A. Medvedev, A. V. Alyanov","doi":"10.1134/S1990478923030110","DOIUrl":null,"url":null,"abstract":"<p> A numerical study of the process of cooling a substrate under the conditions of\nevaporation of pure vapor from the surface of a liquid film and droplets was carried out. The\nlattice Boltzmann method was used for modeling such a two-phase system taking into account the\nthermal conductivity of the substance and the evaporation. We used the van der Waals equation\nof state describing the liquid–vapor phase transition. A new method is proposed for setting the\nboundary conditions on a flat surface for modeling the contact wetting angles in the lattice\nBoltzmann method. The latent heat of phase transition is taken into account. It is shown that the\nprocess depends on the film thickness and the rate of vapor removal from the film surface. The\ncases of forced outflow of vapor, as well as the method of vapor condensation on a cooled\ncondenser are considered. It is shown that the heat flux from the substrate increases sharply in\nthe vicinity of the droplet contact lines. A comparison is made of the heat fluxes during the\nevaporation of the film and droplets on substrates with different wettabilities.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"582 - 591"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A numerical study of the process of cooling a substrate under the conditions of
evaporation of pure vapor from the surface of a liquid film and droplets was carried out. The
lattice Boltzmann method was used for modeling such a two-phase system taking into account the
thermal conductivity of the substance and the evaporation. We used the van der Waals equation
of state describing the liquid–vapor phase transition. A new method is proposed for setting the
boundary conditions on a flat surface for modeling the contact wetting angles in the lattice
Boltzmann method. The latent heat of phase transition is taken into account. It is shown that the
process depends on the film thickness and the rate of vapor removal from the film surface. The
cases of forced outflow of vapor, as well as the method of vapor condensation on a cooled
condenser are considered. It is shown that the heat flux from the substrate increases sharply in
the vicinity of the droplet contact lines. A comparison is made of the heat fluxes during the
evaporation of the film and droplets on substrates with different wettabilities.
期刊介绍:
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.