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가열되는 수평면에 위치한 얇은 액막의 불안정성 해석
An Analysis of Instabilities of Horizontal Thin Liquid Films Heated from Below
HWAHAK KONGHAK, April 1998, 36(2), 280-286(7), NONE
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Abstract
본 연구에서는 밑에서 등온 가열되는 수평판 위에 놓여 있는 얇은 액막의 안정성을 이론적으로 조사하였다. 윗면은 공기와 접하고 있는 자유 경계면으로 이를 통해 열이 방출되며 또한 굴곡이 가능하다. 장파에 대하여 액막의 안정성을 연구하였으며 초기 액막의 두께를 수 nm에서 수 mm에 이르기까지 변화시켜 가며 조사하였다. 윤활유동 근사 아래 선형 안정성 이론을 적용하여 이론을 전개하였고 액막이 비적심 특성을 보이는 물 또는 에탄올로 이루어진 경우에 적용하여 보았다. 그 결과 액막의 두께가 매우 얇은 경우에는 분자간의 인력 때문에 교란의 크기가 성장을 하여 액막이 불안정해지지만 어느 크기 이상의 두께를 갖는 액막은 장파형태의 교란으로부터 안정해짐을 알 수 있었다.
In this study a thin liquid film on the horizontal plane is considered. It is heated isothermally from the lower rigid boundary and its upper deformable, free interface is open to the air. Through the interface the heat flows upward. The hydrodynamic instabilities of liquid films are analyzed theoretically when the long-wave type disturbances are introduced. This analysis is performed for non-wetting systems with varying the film depth from the order of nm to that of mm. The disturbance equations are obtained by applying the linear stability theory under the lubrication approximation and the result is applied to a liquid film of water or ethanol. When the film depth is very small, it is shown that the liquid film is unstable owing to the intermolecular forces. But when the depth of a liquid film is above a certain value, the liquid film becomes stable against long wave instabilities due to gravity forces.
Keywords
References
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Goussis DA, Kelly RE, Int. J. Heat Mass Transf., 33(10), 2237 (1990)
Pearson JRA, J. Fluid Mech., 4, 489 (1958)
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Miller CA, Neogi P, "Interfacial Phenomena," Marcel Dekker, New York (1985)
