We used the method of measuring potential difference between two Ag|AgCl electrodes immersed directly into electrolyte solution with lower concentration and at different distances from membrane. The bacterial cellulose membrane was placed in horizontal plane in the membrane system with configurations with higher NaCl concentration and density under (A) and over the membrane (B). In both configurations at the initial moment the voltage between electrodes amounted to zero. After turning off mechanical stirring of solutions, in configuration A we observed the monotonic increase and next stabilization of voltage while in configuration B after short time dependent on the initial quotient of NaCl concentrations on the membrane we observed appearance of pulsations of measured voltage and gradual decrease of mean voltage over time. Smooth changes of voltage are connected with diffusional reconstruction of Concentration Boundary Layers (CBLs) while fast increase and subsequent pulsations of voltage are connected with the appearance of hydrodynamic instabilities (gravitational convection) near membrane imposed on diffusive reconstruction of thin layer. The time needed for the appearance of hydrodynamic instabilities in CBL depended nonlinearly on the initial ratio of electrolyte concentrations on the membrane.