The time-dependent development of electric double-layers in saline solutions

We have studied the time-dependent development of electric double-layers (ionic sheaths) in saline solutions by simultaneously solving the sodium and chlorine Ion continuity equations Coupled with Poisson's equation in one dimension. The study of the effects of time-varying electric fields in Solution is relevant to the possible health effect of radio-frequency electric fields on cells in the human body and to assessing the potential Of using external electric fields to orient proteins for attachment to surfaces for biosensing applications. Our calculations, for applied voltages of 10-175 mV between the electrode and the solution, predict time scales of similar to 0.1-110 mu s for the formation of double-layers in solutions of concentration between 0.001 and 1.0 M. We develop an empirical equation that can predict the double-layer formation time to within 10% over this wide parameter range. The method has been validated by comparing the solutions obtained, once the program has run to a steady state, with the standard non-linear Poisson-Boltzmann equations. Excellent agreement is found with the Gouy-Chapman solution of the non-linear Poisson-Boltzmann equation. Thus the method is not restricted in accuracy and applicability as is the case for the linear Poisson-Boltzmann equation. The method can also provide solutions for cases where there are orders of magnitude changes in the ion densities; this has not been the case for previous Studies where small perturbation analysis has been employed. The method developed here can readily be extended to two and three dimensions using time-splitting methods.