Roll-cell, first order

Shaping the gain-frequency curve of the control OA requires knowing the value of feedback resistor Rf (Fig. 7.1) and an estimate of the cell roll-off frequency fs. First-order approximations for the stabilizing elements are... 

Fig. 1.19. Stream lines of first order roll-cells during transfer of SDS across the iso-amylol/water interface ...

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). 

Fig 1.19 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. 

Example of autowaves of first-order roll-cells of Marangoni instability (left pictures) and of BZR (right pictures), a) concentric rings, b) spirals, according to Linde and co-workers... 

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