Nonlinear Dynamics of Membrane Processes: Bistability and Oscillations in Electrokinetic Phenomena

Abstract

Bistability and oscillations have been studied for a C 1 |membrane| C 2 system, where C 1 and C 2 represent the concentrations of dilute and concentrated solutions of NaCl/KCl. In this context (i) hydrodynamic permeability, (ii) electroosmotic permeability, (iii) streaming current, and (iv) diffusion current (current due to concentration difference on the two sides of the membrane) have been measured to test the assumptions of existing theories. Bistability data do not support the existing theories. The ratio of the slopes does not correspond to C 1/ C 2 as predicted by the theory of Kobatake et al. A semiempirical correlation has been proposed for the interpretation of data. Data on electrokinetic oscillations in (i) a Pyrex membrane-aqueous electrolyte system and (ii) a Millipore filter-aqueous electrolyte system have been reported in order to test certain features of the existing theories. The results show that the time period depends on the geometrical factors describing the system and is independent of the current strength, which is in conformity with the theory of Teorell et al. as well as that of Meares et al. It has been shown that previous theory also leads to an equation of the Van der Pol type. An attempt has been made to examine the correlation between bistability and oscillations. It is found that bistability can occur when electroosmotic permeability is a function of potential difference and conductance is a function of volume flux. On the other hand, oscillations can occur when conductance is a function of volume flux, provided certain dynamic conditions are satisfied.