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Evaporation of a liquid film in a microchannel under the action of a co-current dry gas flow


A joint motion of thin liquid film and dry gas in a microchannel is investigated numerically at different values of initial concentration of the liquid vapor in the gas phase, taking into account the evaporation process. Major factors affecting the temperature distribution in the liquid and gas phases are as follows: transfer of heat by liquid and gas flows, heat loses due to evaporation, diffusion and heat transfer. The velocity and temperature fields in the liquid and gas phases, as well as the vapor concentration in the gas, were calculated. It has been established that in the zone of entry of flows into the channel near the interface, thermal and concentration boundary layers are formed, whose properties differ from the classical ones. Comparisons of the numerical results for the case of the dry gas and for the case of equilibrium concentration of vapor in the gas have been carried out. It is shown that use of dry gas enhances the heat dissipation from the heater. It is found out that not only intense evaporation occurs near the heating areas, but also in both cases vapor condensation takes place below the heater in streamwise direction.

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dimensionless number (\( g\ \cos\ \alpha\ {H}_0^2/{U}^2l \))

b :

heat transfer coefficient, W/(m2 K)

c p :

specific heat of the liquid, J/(kg K)


inverse Froude number (g sin α H0/U2)

C :

mass fraction of moisture in the gas phase

C* (T):

mass fraction of moisture in the gas phase corresponding to the pressure of the saturated vapor at the temperature T

C1 (t):

mass fraction of moisture in the gas phase at the channel entry point of the flow

D :

diffusion coefficient, m2/s


dimensionless number (\( f\ {H}_0^2/{\mu}_0U \))

f :

the gas pressure gradient in the longitudinal direction, kg/(m2s2)

F, G :

Functions for intermediate calculations

\( \overrightarrow{g} \) :

gravitational acceleration vector, m/s2

h :

dimensionless film thickness

H :

local film thickness, m

H С :

channel height, m

H 0 :

film thickness at the initial moment

I :

identity tensor

k 1 , k 2 , k 3 :

3 dimensionless coefficients

K :

curvature of the interface, 1/m

l :

characteristic scale of streamwise length, m


Evaporation number (λDρg/κ[T])


Marangoni number (\( {\sigma}_T\left[T\right]{H}_0^2/U\ l{\mu}_0 \))


modified Prandtl number (cpμ0H0/)

\( \overrightarrow{n} \) :

normal unit vector

p :

pressure, N/m2

P :

stress tensors

q :

heat flux released on the heater, W/m2

Q :

flow rate of the liquid per unit film width, m2/s


modified diffusion Peclet number (\( Dl/{H}_0^2U \))


Reynolds number (ρQ/μ)

Ω n :

heating area, m2

Sg :

modified Schmidt number, (μ0gH0/g)

T :

temperature, °C


characteristic scale of the temperature, K

U :

characteristic scale of the liquid velocity, m/s

\( \overrightarrow{v} \) :

velocity vector

u, v, w :

velocity components, m/s

V n :

velocity of the interface in the direction of normal unit vector, m/s

W :

rate of strain tensor

x, y, z :

Cartesian coordinates, m

α :

plate inclination angle, °

ε :

the film aspect ratio estimated time of the calculation process, dimensionless

γ, φ, Ψ :

Functions for intermediate calculations

κ :

thermal conductivity, W/(m K)

λ :

latent heat of vaporization, J/kg

ξ, η :

dimensionless coordinates in the vertical direction in phases

μ :

liquid dynamic viscosity, kg/(m s)

θ :

dimensionless temperature of the liquid

ρ :

liquid density, kg/m3

σ :

surface tension, N/m

ω :

ratio of the channel height to the initial film thickness


initial parameters of the flow (at T = T0)


gas phase

x, y, z, t, ξ :

derivatives on x, y, z, t and ξ


modified velocity components


dimensionless variables


  1. Bekezhanova, V.B., Goncharova, O.N.: Problems of evaporative convection (review). Fluid Dyn. 53(1), S69–S102 (2018a)

    MathSciNet  MATH  Article  Google Scholar 

  2. Bekezhanova, V.B., Goncharova, O.N.: Modeling of three dimensional thermocapillary flows with evaporation at the interface based on the solutions of a special type of the convection equations. Appl. Math. Modell. 62, 145–162 (2018b)

    MathSciNet  MATH  Article  Google Scholar 

  3. Eugene Stanley, H.: Introduction to Phase Transitions and Critical Phenomena, p. 308. Oxford University Press, New York (1971)

    Google Scholar 

  4. Fei, L., Ikebukuro, K., Katsuta, T., Kaneko, T., Ueno, I., Pettit, D.R.: Effect of static deformation on basic flow patterns in thermocapillary-driven free liquid film. Microgravity Sci. Technol. 29, 29–36 (2017)

    Article  Google Scholar 

  5. Gatapova, E.Y., Kabov, O.A., Kuznetsov, V.V., Legros, J.-C.: Evaporating shear-driven liquid film flow in minichannel with local heat source. J. Eng. Thermophys. 13(2), 179–197 (2005a)

    Google Scholar 

  6. Gatapova, E.Ya., Kuznetsov, V.V., Kabov, O.A., Legros, J.-C.: Annular liquid film flow under local heating in microchannels. Third International Conference on Microchannels and Minichannels, June 13–15, 2005, Toronto, Canada, publication on CD-ROM by ASME, ISBN: 0-7918-3758-0, pp. 1–7 (2005b)

  7. Hirokawaa, T., Murozono, M., Kabov, O., Ohta, H.: Experiments on heat transfer characteristics of shear-driven liquid film in co-current gas flow. Front. Heat Mass Transf. 5(17), 1–8 (2014)

    Google Scholar 

  8. Houshmand, F., Peles, Y.: Convective heat transfer to shear-driven liquid film flow in a microchannel. Int. J. Heat Mass Transf. 64, 42–52 (2013)

    Article  Google Scholar 

  9. Kabov, O.A., Legros, J.C., Marchuk, I.V., Scheid, B.: Deformation of free surface in a moving locally-heated thin liquid layer. Fluid Dyn. 36(3), 521–528 (2001)

    MATH  Article  Google Scholar 

  10. Kabov, O.A., Legros, J.C., Kuznetsov, V.V.: Heat transfer and film dynamics in shear-driven liquid films cooling system of microelectronic equipment. Proceedings of the Second International Conference on Microchannels and Minichannels (ICMM2004), ASME, Rochester Institute of Technology, Rochester, NY, 687–694 (2004)

  11. Kabov, O.A., Kabova Yu, O., Kuznetsov, V.V.: Evaporation of a nonisothermal liquid film in a microchannel with co-current gas flow. Doklady Phys. 57(10), 405–410 (2012)

    Article  Google Scholar 

  12. Kabova Yu, O., Kuznetsov, V.V., Kabov, O.A.: Effect of temperature dependence of physical properties of fluid on flow and evaporation of film with concurrent gas flow in a microchannel. Doklady Phy. 60(6), 259–262 (2015)

    Article  Google Scholar 

  13. Kabova, Y.O., Kuznetsov, V.V., Kabov, O.A.: Gravity effect on the locally heated liquid film driven by gas flow in an inclined minichannels. Microgravity Sci. Technol. 20, 187–192 (2008)

    Article  Google Scholar 

  14. Kabova, Y., Kuznetsov, V.V., Kabov, O., Gambaryan-Roisman, T., Stephan, P.: Evaporation of a thin viscous liquid film sheared by gas in a microchannel. Int. J. Heat Mass Transf. 68, 527–541 (2014)

    Article  Google Scholar 

  15. Kikoin, I.K. (Ed.): Academician: Tables of Physical Units. Handbook, Atomizdat, Moscow, p. 1008 (1976)

  16. Li, P., Chen, Z., Shi, J.: Numerical study on the effects of gravity and surface tension on condensation process in square minichannel. Microgravity Sci. Technol. 30, 19–24 (2018)

    Article  Google Scholar 

  17. LyulinYu, V., Spesivtsev, S.E., Marchuk, I.V., Kabov, O.A.: Investigation of disruption dynamics of the horizontal liquid layer with spot heating from the substrate side. Tech. Phys. Lett. 41(11), 1034–1037 (2015)

    Article  Google Scholar 

  18. Mahajan, R., Chin, C., Chrysler, G.: Cooling a Microprocessor chip. Proc. IEEE94. 8, 1476–1485 (2006)

    Article  Google Scholar 

  19. Nikolskii, V.P. (Ed.), Chemist Directory, 2nd edn. Chemistry, vol. 1, p. 1072 (1966)

  20. Schlichting, H.: Grenzschicht-Theorie, p. 873. G. Braun, Karlsruhe (1951)

    MATH  Google Scholar 

  21. Sri-Jayantha, S.M., McVicker, G., Bernstein, K., Knickerbocker, J.U.: Thermomechanical modeling of 3D electronic packages. IBM J. Res. Dev. 52(6), 623–634 (2008)

    Article  Google Scholar 

  22. Wang, Z.R., Zhang, X.B., Wen, S.Z., Huang, Z.C., Mo, D.C., Qi, X.M., He, Z.H.: Experimental investigation of the effect of gravity on heat transfer and instability in parallel mini-channel heat exchanger. Microgravity Sci. Technol. 30, 831–838 (2018)

    Article  Google Scholar 

  23. Wertgeim, I.I.: Numerical study of nonlinear structures of locally excited marangoni convection in the long-wave approximation. Microgravity Sci. Technol. 30, 129–142 (2018)

    Article  Google Scholar 

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Correspondence to V. V. Kuznetsov.

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This article belongs to the Topical Collection: Thirty Years of Microgravity Research - A Topical Collection Dedicated to J. C. Legros

Guest Editor: Valentina Shevtsova

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The paper uses functions that specify the viscosity μ(T) and surface tension σ(T). To construct them, the following experimental data were used (Kikoin 1976; Nikolskii 1966), summarized in Tables 2 and 3:

Table 2 Surface tension values
Table 3 Liquid viscosity values

The values of the properties from Tables 2 and 3 were approximated by functions μ = μ0(1 + μT(T − T0) + μTT(T − T0)2)−1, σ = σ0 − σT(T − T0) − σTT(T − T0)2, in which the values of constants σ0, σT, σTT and μ0, μT, μTT are set in Table 1. On Figs. 10 and 11 a comparison of the actual values of these properties and calculations using the above formulas is given.

Fig. 11

Temperature dependence on fluid viscosity. Triangles specify tabular values, a line is the calculation by an approximation formula

Fig. 10

The dependence of surface tension on temperature. Triangles specify tabular values, a line is the calculation by an approximation formula

From Fig. 11, 12 it is seen that the approximation of the properties of the liquid according to the proposed formulas is quite accurate.

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Kuznetsov, V.V., Fominykh, E.Y. Evaporation of a liquid film in a microchannel under the action of a co-current dry gas flow. Microgravity Sci. Technol. 32, 245–258 (2020).

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  • Shear-driven liquid film
  • Local heating
  • Thermocapillarity
  • Microgravity
  • Long-wave theory