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We investigate active electrolytes within the mean-field level ofdescription. The focus is on how the double-layer structure of passive,thermalized charges is affected by active dynamics of all constituting ions.One feature of active dynamics is that particles adhere to hard-surfaces,regardless of chemical properties of a surface and specifically in completeabsence of any chemipsorption or physisorption. To carry out the mean-fieldanalysis of the system that is out of equilibrium, we develop the "mean-fieldsimulation" technique, where the simulated system consists of charged parallelsheets moving on a line and obeying active dynamics, with the interactionstrength rescaled by the number of sheets. The mean-field limit becomes exactin the limit of an infinite number of movable sheets.

Mean-field theory of active electrolytes: dynamic adsorption and overscreening