My question about electrochemistry is best phrase via an exercise in "Intermolecular and surface forces" by Israelachvili (although this is not my homework problem!): When an electric field is applied across an electrolyte solution containing charged particles they are seen to move parallel or antiparallel to the field depending on the sign of their charge. Now, since almost all of the potential drop must occur across the double layer at each electrode surface, there can be no electric field within the conducting electrolyte solution and hence no force on the charged colloidal particles. Why, then, do the particles move? When two electrodes applying an electric field across a membrane, is the potential drop across the electrolyte solution the same as that I have applied? I understand that the situation above applies only to charged electrodes without electron transfer. Suppose electron transfer takes place on one or both electrodes, would the potential drop across the electrolyte the same as what I applied? Are there any electric double layers in this case. Thanks.