Confined thermo-capillary flows in a double free-surface film with small Marangoni Numbers

Author(s):  
B. Messmer ◽  
T. Lemee ◽  
K. Ikebukuro ◽  
I. Ueno ◽  
R. Narayanan
1974 ◽  
Vol 75 (2) ◽  
pp. 283-294 ◽  
Author(s):  
D. Porter ◽  
B. D. Dore

AbstractThe mass transport velocity field is determined for surface waves which propagate from a region with a clean free surface into a region beneath an inextensible surface film. The waves are assumed to be incident normally on the edge of the film. Determination of this velocity field requires the investigation of a mixed boundary value problem for the bi-harmonic equation, the solution of which is obtained using the Wiener–Hopf technique. Streamlines for the mean motion of the fluid particles are thus obtained. It is found that considerable vertical displacement of fluid is possible due to the presence of the surface film.


2017 ◽  
Vol 72 (4) ◽  
pp. 796-800 ◽  
Author(s):  
Koji Kusumi ◽  
Tomoaki Kunugi ◽  
Takehiko Yokomine ◽  
Zensaku Kawara ◽  
Egemen Kolemen ◽  
...  

Author(s):  
Kseniia A. BORODINA

Studying the processes occurring in liquid films under thermal influence allows improving a variety of technological systems, since a thin layer aids in providing a high intensity of heat and mass transfer and a significant surface of phase contact with a minimum liquid consumption. Many Russian and international works wrote about theoretical and experimental studies of film flows, though paid insufficient attention to the study of the behavior of films of a binary homogeneous solution. This article studies the behavior of a thin liquid film containing a volatile component during local heating of a solid horizontal substrate. The presented calculations were performed for an aqueous solution of isopropanol. The author describes the formation of a specific surface shape, which is formed with a sufficient increase in the substrate temperature and the initial film thickness — the so-called “liquid drop”, separated from the main volume of the liquid by a thin extended layer, which is explained by the sequential occurrence of thermal and concentration-capillary flows. The results show a significant influence of the Laplace pressure jump on the character of the entire process. In addition, the cooling of the substrate leads to multidirectional flows, but in the opposite directions. The analysis of the functions of the temperature of the film free surface, the volatile component concentration in the solution, and the vapor density over the free surface at different times is carried out. The velocity field in liquid and gas during the evolution of thermocapillary and concentration-capillary flows is illustrated.


PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2100043-2100044
Author(s):  
D. Tseluiko ◽  
M. G. Blyth ◽  
D. T. Papageorgiou ◽  
J.-M. Vanden-Broeck

The damping of surface waves in closed basins appears to be due to ( a ) viscous dissipation at the boundary of the surrounding basin, ( b ) viscous dissipation at the surface in consequence of surface contamination, and ( c ) capillary hysteresis associated with the meniscus surrounding the free surface. Boundary layer approximations are invoked in the treatment of ( a ) and ( b ) to reproduce and extend results that have been obtained previously by more cumbersome procedures. The surface film is assumed to act as a linear, viscoelastic surface and may be either insoluble or soluble; however, the relaxation time for the equilibrium of soluble films is neglected relative to the period of the free-surface oscillations. Capillary hysteresis is analysed on the hypothesis that both the advance and recession of a meniscus are opposed by constant forces that depend only on the material properties of the three-phase interface. The theoretical results for the logarithmic decrements of gravity waves in circular and rectangular cylinders are compared with the decay rates observed by Case & Parkinson and by Keulegan, which typically exceeded the theoretical value based on wall damping alone by factors of between two and three. It is concluded that both surface films and capillary hysteresis can account for, and are likely to have contributed to, these observed discrepancies. The theoretical effect of a surface film on wind-generated gravity waves is examined briefly and is found to be consistent with the observation that the addition of detergent to water can increase the minimum wind speed (required to produce waves) by one order of magnitude.


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