Electro-kinetic oscillations

Another point has to be noted in this connection. Electro-kinetic oscillations are observed in the case of both types of membranes. Thus, it follows that bistability is not a necessary condition for oscillation to occur. The former phenomenon corresponds to a situation where A4> varies with change in I when AP is fixed or zero and AC is fixed. 

Dynamic instability at solid-liquid interface 11.2.1. Electro-kinetic oscillators... 

First attempt in formulation theory of electro-kinetic oscillations was reported by Teorell [6]. Alternative theories were first suggested by Kobatake and Fujita [20, 21] and subsequently by Mears and Page [8]. The former belong to the class of macroscopic theory, while the latter are concerned with the microscopic details of the phenomena. 

In the former case, we had considered electro-osmotic-driven oscillations at fixed value of current while AP was allowed to vary, on account of which membrane resistance could vary. An interesting case of electro-kinetic oscillations also occurs when AP is fixed, and the resistance varies due to progressive thickness of the emulsion on the membrane surface and the oscillations occur around the steady state corresponding to / = 0. Such electric potential oscillations, in a number of cases using DOPH-doped membranes have been reported [16, 19]. Chaotic oscillations in membrane oscillator have been reported and analysed from the angle of non-linear dynamics. 

Steady-state thermodynamics in the linear range provides a good glimpse of the non-equilibrium region close to equilibrium. The utility of steady-state thermodynamics is illustrated in the case of electro-kinetic phenomena in Parts Two and Three in the regions more and more distant from equilibrium (non-linear steady state, bistability, oscillations, pattern formation) including complexity and complex phenomena. 

Since electro-kinetic systems can be maintained in the far-from-equilibrium region to any desired extent by controlling the variables, they constitute a very good system for the study of dynamic instability from experimental angle. A brief discussion of bistability and oscillations in electro-kinetic phenomena from an experimental point of view is given below. 

Fast detection of the electro-acoustic impedance is a condition for successful kinetic studies. Soares [64] introduced a circuit to measure both resonant frequency and damping resistance R, though not as fast as simple active oscillator methods mainly used for resonant frequency measurement. Most active circuits operate in the series frequency a>s although some oscillators are designed to operate in the parallel frequency wp , which is slightly higher and very susceptible to the value of Ca. 

Growth kinetics data obey the simple empirical equation d = cf" for point cathode and circular anode system d is the radius of the circular envelope grown in time t, and m and log c are the slope and intercept, respectively. Scanned pictures of electro-deposits are characterized in terms of fractal dimension by box counting method. Cathode potential changes with time were also monitored during electro-deposition and dissolution processes. Next amplitude plots indicated that the oscillations were periodic in the binary system while for pure Pb and Zn, it was like random noise. Das et al. [47] developed patterns from pure copper sulphate and zinc sulphate solutions as shown in Fig. 13.21... 

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