Skip to main content
    • Aa
    • Aa

On the instabilities of vertical falling liquid films in the presence of surface-active solute

  • Wei Ji (a1) and Fredrik Setterwall (a1)

A linear-stability analysis is performed on a vertical falling film with a surface-active solute. It is assumed in the present model that the surfactant is soluble and volatile. In addition to the surface wave mode and the ‘wall wave’ mode which originate from the gravity-driven flow of the falling film itself, a new mode of instability related to the Marangoni effect induced by surface tension gradients is found for low Reynolds numbers and for moderate- or short-wavelength disturbances. The new mode is thought to be analogous to the thermocapillary instability examined first by Pearson (1958). The Marangoni instability of large-wavelength disturbances, revealed by Goussis & Kelly (1990) in a study of a liquid layer heated from below, may be completely suppressed in the present system by the effect of surface-excess concentration of the surfactant. The influence of the desorption of the solute and of its adsorption at the gas-liquid interface is determined for both the surface wave mode and the new wave mode. Desorption of the surfactant is shown to be responsible for the Marangoni instability of the new mode.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

Benjamin, T. B.1957Wave formation in laminar flow down an inclined plane. J. Fluid Mech.2, 554.

Brian, P. L. T.1971Effect of Gibbs adsorption on Marangoni instability. AIChE J.17, 765.

Brian, P. L. T. & Ross, J. R.1972The effect of Gibbs adsorption on Marangoni instability in penetration mass transfer. AIChE J.18, 582.

Castillo, J. L. & Velarde, M. G.1985Marangoni convection in liquid films with a deformable open surface. J. Colloid Interface Sci.108, 264.

Goussis, D. A. & Kelly, R. E.1990On the thermocapillary instabilities in a liquid layer heated from below. Intl J. Heat Mass Transfer33, 2237.

Ho, K. & Chang, H.1988On nonlinear doubly-diffusive Marangoni instability. AIChE J.34, 705.

Ji, W., Bjurström, H. & Setterwall, F.1993A study of the mechanism for the effect of heat transfer additives in an absorption system. J. Colloid Interface Sci.160, 127140.

Lin, S. P.1970Stabilizing effects of surface-active agents on a film flow. AIChE J.16, 375.

Lin, S. P.1975Stability of liquid flow down a heated inclined plane. Lett. Heat Mass Transfer2, 361.

Mctaggart, C. L.1983Convection driven by concentration- and temperature-dependent surface tension. J. Fluid Mech.134, 301.

Pérez-Garcia, C. & Carneiro, G.1991Linear stability analysis of Bénard-Marangoni convection in fluids with a deformable free surface. Phys. Fluids A 3, 292.

Scriven, L. E. & Sternling, C. V.1964On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech.19, 321.

Whitaker, S.1964Effect of surface active agents on the stability of falling liquid films. Indust. Engng Chem. Fundam. Q.3, 132.

Whitaker, S. & Jones, L. O.1966Stability of falling liquid films. Effect of interface and interfacial mass transport. AIChE J.12, 421.

Yao, W., Bjurström, H. & Setterwall, F.1991Surface tension of lithium bromide solutions with heat-transfer additives. J. Chem. Engng Data36, 96.

Yih, C. S.1963Stability of liquid flow down an inclined plane. Phys. Fluids6, 321.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *