Colloid vibration potential and ion vibration potential in a dilute suspension of spherical colloidal particles

A general electroacoustic theory is presented for the macroscopic electric field in a dilute suspension of spherical colloidal particles in an electrolyte solution, which consists of the colloid vibration potential (CVP) and the ion vibration potential (IVP), induced by an oscillating pressure gradient field due to an applied sound wave. This is a unified theory that unites previous theories for CVP and those for IVP. Approximate analytic expressions are derived for CVP and IVP. The obtained IVP expression agrees with Debye's formula that is corrected by taking into account the force acting on the electrolyte ions as a result of the pressure gradient in the sound wave. The obtained CVP expression is correct to the first order of the particle zeta potential and applicable for arbitrary kappaalpha, where kappa is the Debye-Hückel parameter and alpha is the particle radius. It is found that an Onsager relation holds between CVP and dynamic electrophoretic mobility. It is also shown that the CVP from particles with very small kappaalpha approaches IVP; that is, in the limit of very small kappaalpha a particle behaves like an ion.