Skip to main content
Log in

Interfacial Balance Equations for Diffusion Evaporation and Exact Solution for Weightless Drop

  • Original Research
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

Introducing of additional terms into the balance equations to specify the conditions at the interface allows to study physical phenomena in the diffusion evaporation (condensation) of the liquid into the neutral gas. We have taken into account the vapour dynamic effects on evaporating liquid, as well as the waste of energy on deformation of the boundary, changing of the interfacial temperature (the interface has an internal energy and therefore heat capacity), to overcome the surface tension etc. This paper presents the balance conditions at the interface with the diffusion evaporation of the liquid into the neutral gas, for the case when the vapour is considered as an impurity in the gas phase. The analysis of the dimensionless criteria is carried out. The areas of parameters for which the effect of some physical factors take a place have been defined. The exact solution of the diffusion evaporation for a spherical drop at zero gravity conditions has been constructed. The explicit expression for the interfacial temperature and evaporation rate were derived. Solution for evaporation rate coincides with the solution obtained by Maxwell (1890).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ajaev, V.S.: Spreading of thin volatile liquid droplets on uniformly heated surfaces. J. Fluid Mech. 528, 279–296 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Andreev, V.K., Gaponenko, Y.A., Goncharova, O.N., Pukhnachov, V.V.: Modern Mathematical Models of Convection. Fizmatlit, Moscow (2008, in Russian)

    Google Scholar 

  • Bashkirov, A.G.: Nonequilibrium statistical mechanics of heterogeneous systems. I. Transport phenomena at an interface and the problem of boundary conditions. Theor. Math. Phys. 43(3), 542–552 (1980)

    Article  MathSciNet  Google Scholar 

  • Brutin, D., Zhu, Z.Q., Rahli, O., Xie, J.C., Liu, Q.S., Tadrist, L.: Sessile drop in microgravity: creation, contact angle and interface. Microgravity Sci. Technol. 21(Suppl), 67–76 (2009)

    Article  Google Scholar 

  • Das, S., Ward, C.A.: Surface thermal capacity and its effects on the boundary conditions at fluid-fluid interfaces. Phys. Rev. E 75, 065303(R) (2007)

    Article  Google Scholar 

  • David, S., Sefiane, K., Tadrist, L.: Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops. Colloids Surf., A Physicochem. Eng. Asp. 298(is.1–2), 108–114 (2007)

    Article  Google Scholar 

  • Gatapova, E.Y., Kabov, O.A.: Shear-driven flows of locally heated liquid films. Int. J. Heat Mass Transfer 51(19–20), 4797–4810 (2008). doi:10.1016/j.ijheatmasstransfer.2008.02.038

    Article  MATH  Google Scholar 

  • Haut, B., Colinet, P.: Surface-tension-driven instability of a liquid layer evaporating into an inert gas. J. Colloid Interface Sci. 285, 296–305 (2005)

    Article  Google Scholar 

  • Iorio, C.S., Goncharova, O.N., Kabov, O.A.: Study of evaporative convection in an open cavity under shear stress flow. Microgravity Sci. Technol. 21(Suppl. 1), S313–S319 (2009)

    Article  Google Scholar 

  • Ji, Y., Liu, Q.S., Liu, R.: The coupling of evaporation and thermocapillary convection in a liquid layer with mass and heat exchanging interface. Chin. Phys. Lett. 25(2) (2008)

  • Klentzman, J., Ajaev, V.S.: The effect of evaporation on fingering instabilities. Phys. Fluids 21, 122101 (2009)

    Article  Google Scholar 

  • Kryukov, A.P., Levashov, V.Y., Shishkova, I.N.: Evaporation in mixture of vapor and gas mixture. Int. J. Heat Mass Transfer 52(23–24), 5585–5590 (2009)

    Article  MATH  Google Scholar 

  • Lamb, H.: Hydrodynamics, Sixth Edn. Cambridge University Press (1932, Dover Publications (paperback))

  • Levich, V.G.: Physico Chemical Hydrodynamics. Prentice-Hall, Englewood Cliffs (1962)

    Google Scholar 

  • Liu, R., Liu, Q.S.: The convective instabilities in a liquid-vapor system with a non-equilibrium evaporation interface. Microgravity Sci. Technol. 21(Suppl 1), S233–S240 (2009)

    Article  Google Scholar 

  • Maxwell, J.K.: Collected scientific papers. Cambridge 11, 625 (1890)

    Google Scholar 

  • Mollaret, R., Sefiane, K., Christy, J.R.E., Veyret, D.: Experimental and numerical investigation of the evaporation into air of a drop on a heated surface. Chem. Eng. Res. Des. 82(4), 471–480 (2004)

    Article  Google Scholar 

  • Napolitano, L.G.: Thermodynamics and dynamics of pure interfaces. Acta Astronaut. 5, 655–670 (1978)

    Article  MATH  Google Scholar 

  • Napolitano, L.G.: Thermodynamics and dynamics of surface phases. Acta Astronaut. 6(9), 1093–1112 (1979)

    Article  MATH  Google Scholar 

  • Nepomnyashchy, A.A., Simanovskii, I.B.: The influence of gravity on the dynamics of non-isothermic ultra-thin two-layer films. Microgravity Sci. Technol. 21(Suppl. 1), S261–S269 (2009)

    Article  Google Scholar 

  • Nigmatulin, R.I.: Dynamics of Multiphase Media, vol. 1, 2. Hemisphere, N.Y. (1990)

  • Pukhnachov, V.V.: Viscous Fluid Flow with Free Boundaries. Novosibirsk State University, Novosibirsk (1989, in Russian)

    Google Scholar 

  • Sazhin, S.S.: Advanced models of fuel droplet heating and evaporation. Pror. Energy Combust. Sci. 32, 162–214 (2006)

    Article  Google Scholar 

  • Shikhmurzaev, Y.D.:Capillary Flows with Forming Interfaces. Taylor & Francis (2007)

  • Ward, C.A., Duan, F.: Turbulent transition of thermocapillary flow induced by water evaporation. Phys. Rev. 69(5), 056308 (2004)

    Google Scholar 

  • Zhu, Z-Q., Liu, Q-S., Xie, J-C.: Experimental study on the combined evaporation effect and thermocapillary convection in a thin liquid layer. Microgravity Sci. Technol. 21(Suppl 1), S241–S246 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maria V. Bartashevich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuznetsov, V.V., Bartashevich, M.V. & Kabov, O.A. Interfacial Balance Equations for Diffusion Evaporation and Exact Solution for Weightless Drop. Microgravity Sci. Technol. 24, 17–31 (2012). https://doi.org/10.1007/s12217-011-9285-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12217-011-9285-2

Keywords

Navigation