The effect of surfactants on the flow characteristics of falling liquid films

Abstract

Experimental values of the wave length and wave velocity have been obtained far dilute sohtions of valeric and hexanoic acid for a vertical fulling liquid film. The wave length was unaffected by the surfactants for Reynolds numbers in the range 5 to 100; however, the wave velocity was decreased for increased surface concentrations of the two acids. This is in direct contradiction to previous theoretical work, and the explanation for the anomaly is that the free surface velocity is greatly retarded by the adsorption of the surface active agents.In an effort to determine the extent of this retardation, an approximate form of the diffusion equation and the equations of motion were solved subject to boundary conditions describing the effect of the adsorbed surfactant on the surface stress. The results indicate that the entrance length can be increased several orders of magnitude by the addition of small amounts of surfactant.The flow characteristics of falling liquid films have been a subject of interest in connection with gas absorption studies (9, 17, 24, 27) primarily because the falling film appears to provide a reasonably well defined interfacial area and contact time. Knowledge of the nature of the flow of thin liquid films is also of importance in analyzing heat transfer rates for ablating space vehicles ( 3 1 ) , in the design of cooling systems for high temperature turbine blades (15), and in the analysis of mass transfer rates in certain desalinization processes ( 6 ) .By itself, the falling liquid film provides a reasonable experimental tool for studying the effect of surface active agents on bulk fluid motion. In addition to the wave length and wave velocity, one can also observe the location (measured from the top of the film) of the first visible waves as a function of Reynolds number, and the rate of approach of the surface velocity to the value predicted for uniform flow.In order to test recent mathematical studies (1, 4, 28, 29) of the stability of vertical falling liquid films, an experimental study of the wave length and wave velocity was planned. In a sense, the experimental study was unsuccessful for the data were obtained under conditions which did not allow the direct comparison of theory and experiment; however, some interesting characteristics of the flow were observed and analyzed, and it seems appropriate to report the results at this time.

The primary instability of falling films in the presence of soluble surfactants

“…Finally, figure 9(d) presents the wave velocity of the marginally unstable mode at neutral stability as a function of the wavenumber and for different amounts of surfactant. In agreement with previous experimental and theoretical studies (Strobel & Whitaker 1969;Cerro & Whitaker 1971), we find that the addition of surfactant decreases the wave velocity, and more so the higher the wavenumber. It is also notable that the variation with M tot is strictly monotonic, reaching an asymptotic limit for high surfactant concentrations.…”

“…The theoretical results by Whitaker (1964) also suggested that the wave velocity should increase with increasing elasticity of the interface. However, the experimental work of Strobel & Whitaker (1969) indicated that the free-surface velocity actually decreases for increased surfactant concentration and this was later confirmed experimentally and theoretically by Cerro & Whitaker (1971). The latter work also noted that surface velocity depends strongly on the surface elasticity and is only mildly affected by surfactant diffusivity and interfacial mass transport.…”

Impact of droplets on inclined flowing liquid films

“…Since then, the flow in falling liquid films has been studied extensively through experimental measurements [10,45], low-dimensional modelling [46,47], and full numerical simulations [48]. The effects of many factors that influence the flow in falling films have been investigated, such as the effects of thermocapillarity [49], electric fields [50,51], and surfactants [52,53]. Different processes that may be involved in falling films have also been studied, such as heat transfer [54], mass transfer [55], chemical reactions [56], and phase change [57].…”

Surface boundary conditions for small amplitude waves on a falling liquid film

“…This result for the critical Reynolds number associated with insoluble surfactants has also been presented by Benjamin (1964) and by Anshus and Acrivos (1967). It was used originally by Strobel and Whitaker (1969) to estimate surface elasticities from wave inception line data, and more recently by Cerro and Whitaker (1971).…”