Teorell oscillator

Preliminaries. This entire chapter is devoted to one physical phenomenon—electro-osmotic (Teorell) oscillations. As opposed to phenomena discussed in previous chapters, electro-convection will be of importance here in its interaction with electro-diffusion. 

Electro-osmotic oscillation (first observed by Teorell [1]—[4] in a laboratory set-up devised to mimic nerve excitation) may likely represent a common source of oscillations in various natural or synthetic electrokinetic systems such as solid microporous filters, synthetic ion-exchange membranes or their biological counterparts. The original experimental set-up, which contained all essential elements to look for when the electro-osmotic oscillations are suspected in a natural system, is schematically as follows. 

Generalized local Darcy s model of Teorell s oscillations (PDEs) [12]. In this section we formulate and study a local analogue of Teorell s model discussed previously. The main difference between the model to be discussed and the original one is the replacement of the ad hoc resistance relaxation equation (6.1.5) or (6.2.5) by a set of one-dimensional Nernst-Planck equations for locally electro-neutral convective electro-diffusion of ions across the filter (membrane). This filter is viewed as a homogenized aqueous porous medium, lacking any fixed charge and characterized... 

K. R. Page and P. Meares, Factors controlling the frequency and amplitude of the Teorell oscillator, Faraday Symp. Chem. Soc., 9 (1974), pp. 166-173. 

T. Erneux and I. Rubinstein, Hopf bifurcation in a local model of Teorell oscillations, to appear. 

The system investigated by Teorell consists of two vessels containing electrolytes at different concentrations and in contact with each other via a sintered glass membrane (Figure 6). Normally, the liquid columns in the two vessels are different, so that there is a hydrostatic head drop across the membrane, p. In one of the vessels the surface area may be small, and then the passage of liquid from one vessel to another causes the pressure drop, p, to vary, as it does in the case of self-oscillations. Otherwise p remains fixed, and it will be assumed to be so below in our discussion of the excitation impulse. The flow of liquid through the membrane is caused not only by the head drop p, but also by the electroosmosis that can be initiated by applying a potential difference to the membrane with the help of an electrode pair. 

The pioneering experiments in this area are due to Teorell [6]. In this setup, aqueous solutions of electrolytes of different concentrations were kept in the two compartments (NaCl, KCl, LiCl) separated by the membrane, and a current of fixed magnitude was passed. Synchronous oscillations in electric potentials, resistance and pressure differences were observed. Teorell observed that (i) there exists a threshold value of current density below which one obtains highly damped or moderately damped oscillations, (ii) in the undamped case the oscillations go on for hours and start to die away when current becomes too low or Ag/AgCl electrodes gets exhausted, (iii) oscillations are... 

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. 

Using these assumptions, it has been shown [6, 13] that van der Pol type equation can be deduced. Theoretical formulations of Teorell as well as that of Kobatake and Fujita have been compared, and it has been shown [13-15] that both involve certain assumptions but both yield van der Pol type equation. It also turns out that there is no relationship between bistability and oscillations. The validity of the two-variable model has been further examined by comparing the experimental results with computer simulation based on the use of experimentally determined parameters [14], which did not yield satisfactory results. 

Further modifications in the theory have been made, which also lead to van der Pol type equation. Computer simulation yields satisfactory results [23]. In the case of coupling of the two forces and /, two types of steady states can occur when = 0 or when / = 0. In the case of Teorell oscillator as depicted in Fig. 11.1, the steady state corresponds to the first situation. In order to keep the system far from equilibrium and have oscillations, AC has to be sufficiently large, of the order of 0.1 M. The magnitude of streaming current is quite low as compared to ohmic current. Since... 

The glass frit in the Teorell oscillator can be replaced by nanoporous Alter membranes [33-35], or even capillary electrophoresis tubes [36]. By these means, important parameters such as salt and hydraulic permeability, salt concentration, pore width, and fixed charge relevant to electro-osmotic flow (which may in turn depend on pH) can be varied systematically. 

Changes in membrane resistance and electro-osmotic properties as salt redistributes play a critical role in the Teorell oscillator, so the membrane is an active player in the oscillation mechanism. Changes in membrane permeabihties to various species (including solvent and current carriers) also play a role in most of the nonen2ymatic oscillators discussed. We also showed that the membrane can act simply to limit transport into and out of a reactor, with the membrane s own properties remaining constant - the PFK system is exemplary of this limit Here, the membrane s selectivity to different reactants contributes to oscillatory behavior. In the discussion of the hydrogel-enzyme system in the next section, the membrane and enzyme behaviors are seen to be mutually coupled, and the most significant transitions occur inside the membrane. 

A teorell oscillator with flne pore membranes. Biophys. J., 36, 93-107. 

Bala, K., Kumar, K., Saha, S.K., and Sristava, R.C. (2004) Single-capillary teorell oscillator-studies with nonelectrolytes. J. Colloid Interface Sci., 273,... 

The teorell membrane oscillator as a mechano-electric transducer. J. Memh. Bid., 11, 197-216. 

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