Reciprocal relations in electroacoustics

In a colloidal suspension, one can generate sound waves by the application of an alternating electric field (Electrokinetic Sonic Amplitude, i.e., ESA). Another phenomenon is electrophoresis (Electrophoretic Mobility, i.e., EM) where a colloidal particle moves relative to the solvent in an electric field. Vice versa one can generate electric fields or electric currents by sound waves (Colloid Vibration Potential/Current, i.e., CVP/CVI). In 1988 and 1990, O'Brien [J. Fluid Mech. 190, 71-86 (1988) and O'Brien, J. Fluid Mech. 212, 81-93 (1990)] derived a reciprocal relation between the proportionality coefficients of the EM and CVI phenomena. In this paper, we will generalize his proof by constructing the relevant entropy production from which the linear force-flux relations follow. General relations are derived for electrolyte solutions, of which colloidal suspensions are a particular case. The relations between CVI, CVP, EM, and ESA are discussed. O'Brien's reciprocal relation then follows as an Onsager relation. The relation is valid for any applied electric field frequency, particle surface charge and particle concentration (even in the presence of particle-particle interactions) provided the system is isotropic.