Initiation of Motion in a Fluid with a Free Surface of Small Area

Abstract

It is generally assumed that the surface of a Newtonian fluid begins to move at any arbitrarily small shear stress. However, specially designed experiments show that under real conditions the fluid flow can be initiated by a particular (threshold) stress, whose value increases rapidly with decreasing surface area of the fluid. At subthreshold shear stresses generated by the surface forces or volumetric flows, the fluid surface remains immovable. Such a behavior of the surface is explained by the existence of an adsorption layer formed by the uncontrolled surface-active impurities contained in the fluid. The composition and amount of impurities absorbed by the surface are dependent on the degree of purification of the fluid and its surface tension value. The most accurate theoretical description of the behavior of a Newtonian fluid in the presence of the adsorption layer can be obtained by introducing a free surface showing the Bingham properties.In this study, we performed a series of experiments in order to analyze the peculiarities of the fluid flow developed under such conditions. As an example, we investigated the appearance of the oscillatory mode of the solutal convection near a stationary bubble. In the experiments, the bubble was placed in a horizontal channel of small cross-section filled with an aqueous solution of a surfactant with non-uniform concentration. As a surfactant, we used several monoatomic alcohols, which made it possible to investigate the influence of their physicochemical characteristics, such as their surface activity and solubility in water. These characteristics affected the frequency of occurrence of the capillary convection near the bubble, convection intensity, the ratio of predominance of the capillary to buoyancy flow times, duration of the oscillatory mode, the threshold stress value, and the relevant critical Marangoni number.