Transient fluctuation-induced forces in driven electrolytes after an electric field quench

Abstract

Understanding how electrolyte solutions behave out of thermal equilibrium is a long-standing endeavor in many areas of chemistry and biology. Although mean-field theories are widely used to model the dynamics of electrolytes, it is also important to characterize the effects of fluctuations in these systems. We have recently shown that the dynamics of the ions in a strong electrolyte that is driven by an external electric field can generate long-ranged correlations manifestly different from the equilibrium screened correlations; in the nonequilibrium steady state, these correlations give rise to a novel long-range fluctuation-induced force (FIF). Here, we extend the Langevin analysis of the FIF by considering the dynamics of a strong electrolyte after it is quenched from thermal equilibrium by a constant electric field. We show that the asymptotic long-distance limit of both of the charge and density correlation functions is long-ranged and generally diffusive in time. These correlations give rise to long-ranged FIFs acting on uncharged confining plates with long-time regimes that are governed by slow power-law temporal decays toward the steady-state value of the force amplitude; at early times, the temporal variations of the FIF are non-monotonic with possible sign changes in some parameter regimes. These findings show that nonequilibrium fluctuations have nontrivial implications on the dynamics of objects immersed in a driven electrolyte, and they could be useful for exploring new ways of controlling long-distance forces in charged solutions.