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Study of the thermocapillary effect on a wavy falling film using a fiber optical thickness probe

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Abstract

The wave flow of a water film down a vertical plate with a 150×150 mm heater has been experimentally studied. The effect of the heat flux on the film flow leads to the formation of periodically flowing rivulets and thin film between them due to the action of thermocapillary forces in spanwise direction. The local film thickness between rivulets is measured by means of a noncontact fiber optical probe. As the heat flux grows, the average film thickness continuously decreases but upon reaching about 50% of the initial thickness, the film spontaneously breaks down. It is found that the decrease of the wave amplitude between rivulets is caused by the reduction of the local Reynolds number and is in a qualitative agreement with the laws of the hydrodynamics for the isothermal case. That is, no appreciable effect of streamwise thermocapillary forces on the wave amplitudes is detected. The experimental results are in good agreement with recently published data obtained by the capacitance method.

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Abbreviations

c :

Wave phase velocity (m/s)

c p :

Thermal capacity of liquid (J/kg K)

d :

Distance between thermocouples centers (m)

Fi:

Film number (Kapitsa number), = σ3 ρ /gμ4, dimensionless

h :

Liquid film thickness (m)

h 0 :

Initial liquid film thickness (m)

h ave :

Time-averaged film thickness (m)

h max :

Film thickness in the wave crest (m)

h res :

Thickness of residual layer (m)

k :

Dimensionless wave number, =2π h 0/Λ

L :

Heater length (m)

l ν :

Scale of viscosity-gravitational interaction, =(ν2 /g) 1/3 (m)

l σ :

Scale of capillary-gravitational interaction, =(σ /ρ g)1/2 (m)

p :

Probability density, dimensionless

q :

Average heat flux, = Q/L 2 (W/m2)

q loc :

Local heat flux (W/m2)

Q :

Electrical power dissipated on the heater (W)

q idp :

Heat flux corresponding to initial dry spot appearance (W/m2)

r :

Distance from the end of the probe to the film surface (m)

r 0 :

Distance from the end of the probe to the substrate (m)

r sm :

Distance from the end of the probe to the smooth film (m)

r def :

Distance from the end of the probe to the deformed film (m)

Re:

Reynolds number, =Γ/μ, dimensionless

Reloc :

Local Reynolds number, dimensionless

T 0 :

Initial temperature of the film (°C)

T F,loc :

Local bulk temperature of the film (°C)

ΔT h :

Temperature drop across the stainless steel plate, measured by thermocouples (K)

V :

Output signal from the amplifier (V)

x :

Abscissa of the graph, dimensionless

X t :

Distance from the upper edge of the heater (m)

y :

Ordinate of the graph, dimensionless

Γ:

Specific liquid flow rate (kg/ms)

δφ :

Error in determining h due to the inclination of the film surface with respect to the substrate (m)

λ ss :

Thermal conductivity of stainless steel (W/mK)

Λ:

Wavelength (m)

μ:

Liquid dynamic viscosity (kg/ms)

ν:

Liquid kinematics viscosity (m2/s)

ρ:

Liquid density (kg/m3)

σ:

Liquid surface tension (N/m)

φ:

Inclination angle of the film surface with respect to the substrate (°)

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Acknowledgements

The authors gratefully acknowledge the support of this work by INTAS (YSF 03-55-1791) and by the Human Capital Foundation.

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Authors and Affiliations

  1. Institute of Thermophysics SB RAS, Lavrentiev Ave. 1, Novosibirsk, 630090, Russia

    D. V. Zaitsev & O. A. Kabov

  2. Microgravity Research Center of the Free University of Brussels, Av. Roosevelt 50, 1050, Brussels, Belgium

    O. A. Kabov

Authors
  1. D. V. Zaitsev
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  2. O. A. Kabov
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Correspondence to D. V. Zaitsev.

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Zaitsev, D.V., Kabov, O.A. Study of the thermocapillary effect on a wavy falling film using a fiber optical thickness probe. Exp Fluids 39, 712–721 (2005). https://doi.org/10.1007/s00348-005-0003-y

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  • DOI: https://doi.org/10.1007/s00348-005-0003-y

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