Marangoni-instabilities and dissipative structures

From the thermodynamical point of view the formation of dissipative structures is entropy driven as intensively explained by Prigogine Glansdorf (1971). The criteria for surface instabilities due to mass transfer across a liquid interface were evaluated by Stemling Scriven (1959). The typical Marangoni instability starts on surfactant concentration or temperature differences between two phases. Surface tension differences along the surface are 

A classical form of dissipative structures are the so-called first order or higher order roll-cells. Fig. 3C.1 shows the stream lines of a first order roll-cell stimulated by mass transfer (Linde 1978). A magnified section of this picture is given in Fig. 1.19. First Schlieren -optical observations of hydrodynamically caused structure formation during mass transfer across a liquid/liquid interface were published by Linde (1959) and Linde Kretzschmar (1962). 

19 describes the same structure as alignment of small particles along the trajectories of a first order roll-cell in a vertically oriented capillary gap. The curvature of the liquid meniscus controls the capillary pressure differences. 

A schematic of an instability caused by temperature gradients between the two phases resulting in surface tension gradient along the interface is shown in Fig. 3C.2. A small initial disturbance like interfacial convection from R to S will be amplified by additional mass transport at higher temperature, because this leads to y y j on condition dy / dT 0. 

Schematic of instability caused by the temperature gradient of a sink, a) temperature gradients, b) sceme of initial interfacial convection 

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