Hydrodynamic instabilities in membrane systems with current loading, Fourier analysis

Abstract

Time-current characteristics for membrane systems with bacterial cellulose membranes located in horizontal plane and with NaCl solutions, 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 above the membrane (B) and a sufficiently large initial concentration quotient on the membrane (( C h / C l ) o ) current pulsations are observed over time, resulting from hydrodynamic instabilities occurring in the vicinity of the membrane. The increase of ( C h / C l ) o in configuration B causes an increase in the frequency of current pulsations and a change in their amplitudes. Furthermore, significant differences were observed between the types of the temporal changes in membrane currents in both configurations. The currents measured in steady states after 24 hours show differences between A and B configurations for ( C h / C l ) o  > 500. Fast Fourier Transform (FFT) used to analyze the hydrodynamic instabilities in the range of observed pulsations of the measured currents shows that 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 ( C h / C l ) o equal to 2500. In turn, the Short Time Fourier Transform (STFT) applied to the current signal as well as to the current difference signal (time lag equal to 1 min.) showed better resolution of the hydrodynamic instability analysis for the current difference signal. The increase of ( C h / C l ) o in the membrane system causes a gradual increase in STFT amplitudes towards longer times and higher frequencies. In turn, significant activity of hydrodynamic instabilities was observed in the first 50 min of current measurements for ( C h / C l ) o  > 2500, followed by suppression of these instabilities.