Spontaneous non-linear surface tension oscillations in the presence of a spread surfactant monolayer at the air/water interface

Abstract

The phenomena accompanying the dissolution of a surfactant droplet under the water/air interface covered by a spread monolayer are studied experimentally and theoretically. It is shown that the variation of the initial surface coverage changes the way of the system evolution. With respect to the character of changes of the interfacial tension with time one can distinguish between three different regimes which replace each other by increase of the initial surface coverage: (i) single oscillation followed by a long period of the monotonous decrease of the surface tension after which repeated non-linear oscillations develop spontaneously; (ii) repeated non-linear oscillations of the surface tension (without period of the monotonous decrease); (iii) monotonous decrease of the surface tension without any oscillation. The hydrodynamics of the observed regimes are discussed.

Introduction

Spontaneous non-linear oscillations of the surface tension or electric potential arising at a liquid/liquid interface in the systems with a solute transfer, which are far from equilibrium, attract the scientific interest during the last decades. Studying these phenomena is important for understanding of fundamental problems, such as, the processes of self-organization in the systems far from equilibrium, the influence of various physico-chemical factors on mechanisms of the instability onset and the development in the non-linear region, the possibilities to control the behaviour of the systems far from equilibrium, the relation of processes in artificial systems to rhythmic processes in living organisms. Non-linear oscillations occurring at liquid interfaces are also of great practical significance, for example, for the stability of foams and emulsions. It was proposed to use such oscillations in testing systems for drugs and foods. So far, the phenomenon of spontaneous non-linear oscillations was observed in three different types of systems:

• Transfer of ionic solutes, one of them is a surfactant, through the interface between two immiscible phases (oil and water). The condition necessary for the appearance of oscillations is that each of the ionic solutes is dissolved in the phase in which it is less soluble [1], [2], [3], [4], [5], [6], [7] (for instance, the aqueous solution of octadecyltrimethylammonium chloride and the solution of potassium iodide in nitrobenzene).

• Transfer of an ionic surfactant from one aqueous phase to another one through an oil membrane (nitrobenzene, octanol, etc.). Oscillations of the electric potential appear on one of the oil/water interfaces depending on the experimental conditions, particularly on the composition of the oil and water phases [8], [9], [10], [11], [12], [13], [14].

• Transfer of a non-ionic or ionic surfactant from a point source in the liquid bulk (for instance, from a small surfactant droplet) to the air/liquid [15], [16], [17], [18] or liquid/liquid [19], [20] interface.

Although these systems differ essentially from each other, in all of them the oscillations appear only by surfactant transfer and are accompanied by convective motion in the liquid. Furthermore, for all these systems the development and characteristics of the oscillations depend essentially on the system geometry, namely, on the interfacial area and on the presence of a lateral wall [7], [11], [18]. For example, auto-oscillations of the surface tension by dissolution of a surfactant droplet under the air/water interface (system (iii)) was observed predominantly in a certain range of the ratio of the container diameter to the immersion depth of the droplet (aspect ratio) [18]. Analogously, oscillation of the surface tension and wave motion were detected in system (i) only by using of small diameter glass containers [7]. Thus, it can be supposed that the hydrodynamics underlying the oscillations in all these systems should have many in common, and the elucidation of mechanisms leading to the appearance of oscillation in one of the considered system can be helpful for the understanding the behaviour of the other systems.

Despite of rather large amount of experimental works in this area, a generally accepted mechanism for the oscillations in systems (i) and (ii) is not developed so far because of complicity of coupled hydrodynamics and the chemical and electrochemical processes. System (iii) is much simpler from chemical point of view and, therefore, its comprehensive study can give a key for understanding the behaviour of the more complicated systems (i) and (ii). The evolution of a system with a surfactant droplet dissolving under the air/water interface can be described in the frame of a hydrodynamic model, taking into account the adsorption/desorption processes at the interface [21], [22], [23]. Analytical consideration remains still too complicated owing to the strong non-linearity of the phenomenon. Nevertheless the numerical simulation of the model on basis of the first principles (non-linear, non-steady state Navier–Stokes equation, continuity equation and convective diffusion equation with appropriate boundary conditions) allows the understanding of the main features of the oscillations mechanism. It was shown [21], [22], [23], that auto-oscillations of the surface tension, which develop by dissolution of a surfactant droplet under the air/water interface, are the result of Marangoni instability periodically arising and fading in the system. The major cause for fading of the instability is the interaction of the longitudinal concentration wave with the container wall.

In the present paper we proceed with studying the surface tension auto-oscillations. Experimental studies have shown that the system with the surfactant droplet dissolving under the water/air interface can reach the final equilibrium state in different ways over an oscillatory or quasi-stationary regime [16], [18]. Understanding of the auto-oscillation mechanism allows us the regime control of the droplet dissolution. The switching between the oscillatory and quasi-stationary regime can be controlled by change of the container aspect ratio. An increase of the aspect ratio has established the quasi-stationary regime, whereas a decrease of the aspect ratio led to the appearance of the oscillatory regime [18].

In this work we propose to control the regime of droplet dissolution and the characteristics of non-linear oscillation by spreading of an insoluble surfactant monolayer at the water/air interface. We focus on the nature of the system evolution by the variation of the initial surface coverage. The experimental results obtained by increase of the initial surface coverage should be discussed on the basis of a simple theoretical model.