Hydrodynamic instabilities in membrane systems with current loading, Fourier analysis

The article presents the results of current measurements in membrane systems with bacterial cellulose membranes, located in horizontal plane, for various initial quotients of NaCl concentrations on the membrane. The obtained time-current characteristics indicate a stable formation of concentration boundary layers near the membrane for the configuration with a solution of lower concentration and lower density above the membrane (A). In turn, for the configuration with a higher concentration and higher density solution above the membrane (B) and a sufficiently large initial concentration quotient on the membrane, greater than 50, current pulsations are observed over time, resulting from hydrodynamic instabilities occurring in the vicinity of the membrane. The increase of initial concentration quotient on the membrane in configuration B causes an increase in the frequency of current pulsations and a change in their amplitudes over time. Furthermore, significant differences were observed between the types of the temporal changes in membrane currents in both configurations, and these differences persisted even 24 hours after turning off mechanical stirring of solutions. To analyze the hydrodynamic instabilities in configuration B of the membrane system, Fourier analysis was used both in the range of observed pulsations of the measured currents (from 50 to 250 min) and in the twenty-minute intervals with the intervals centered at 20, 100, 150, 200 and 290 min). As the analysis shows in all tested time ranges, the average signal power of currents in the frequency range from 0.05 to 1 min-1, depends non-linearly on the initial concentration quotient on the membrane, showing a maximum for the concentration quotient on the membrane equal to 2500.