Abstract
Thermocapillary rupture of a film under conditions of turbulent undulatory flow is associated with the buildup of wave motion on its surface. Here an approximate solution to the problem and criterial relations are obtained for determining the limits of stable film flow.
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Abbreviations
- Γmin, kg/m·sec:
-
minimum irrigation intensity at which no film rupture occurs
- Γ1, kg/m· sec:
-
irrigation intensity at which the first dry spot appears
- q, W/m2 :
-
thermal flux density
- ϑ D, °C:
-
temperature at the rupture section
- x, m:
-
space coordinate along the warm surface in the direction of flow
- y, m:
-
coordinate in the direction normal to the warm surface
- δo, m:
-
mean thickness of the film between large waves
- δc, m:
-
thickness of the continuous layer
- δcr, m:
-
critical film thickness
- αo=α/δo andl o=l o/δo :
-
dimensionless initial amplitude and length of a wave
- ω, sec−1 :
-
recurrence frequency of large waves
- tcr, sec:
-
time till thermocapillary rupture of a film
- tp, sec:
-
time of penetration of a thermal perturbation through the film thickness
- u, m/sec:
-
velocity of thermocapillary flow of the liquid
- λ, W/m·°C:
-
thermal conductivity
- cp, kJ/kg·°C:
-
specific heat
- ρ, kg/m:
-
linear density
- μ, N·sec/m2 :
-
dynamic viscosity
- a, m2/sec:
-
thermal diffusivity
- σ, N/m:
-
surface tension
- τ, N/m2 :
-
tangential stress at the film surface
- L, m:
-
length of the warm pipe segment
- Lo, m:
-
distance from the inlet to the section where wave motion at the film surface occurs
- ¯w, m/sec:
-
mean velocity of downward flow of liquid in the film
- δ, m:
-
mean thickness of the laminar layer
- g, m2/sec:
-
free-fall acceleration due to gravity
Literature cited
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B. G. Ganchev and V. M. Kozlov, “Velocities in a downward flowing liquid film under conditions of developed wave motion,” Tr. Mosk. Vyssh. Tekh. Uchil., No. 207, Issue 2, 52–61 (1975).
Yu. I. Snigirev, “Exact solution to the equation of heat conduction at a given thermal flux,” Tr. Tsentr. Aerogidrodin. Inst. Issue 944 (1966).
B. E. Anshus and E. Ruckenstein, “The appearance of dry patches on a wetted wall,” J. Colloid Interface Sci.,5, No. 1, 12–22 (1975).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 581–591, October, 1980.
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Ganchev, B.G., Bokov, A.E. Thermocapillary stability during gravity flow of a liquid film. Journal of Engineering Physics 39, 1035–1042 (1980). https://doi.org/10.1007/BF00822129
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DOI: https://doi.org/10.1007/BF00822129