Use of a network simulation method for the determination of the response of a colloidal suspension to a constant electric field

A network simulation method, based on the theory of network thermodynamics, is applied in this work to the description of the structure of the double layer around a spherical colloidal particle, in the presence of an external ly applied constant electric field. It is demonstrated that the system of d ifferential equations governing the phenomena involved is formally equivale nt to that of:a properly designed electric circuit, obtained as a series of subcircuits corresponding to each of the volume elements into which the sy stem is divided. A simulation program is then used to solve the circuit in order to obtain the quantities of interest. The methodology is first applie d to the calculation of the electrophoretic mobility of a spherical colloid al particle, and of the de conductivity of a dilute suspension of spheres. The results are compared to the predictions of O' Brien and White's classic al theories, and an excellent agreement is found in all cases checked. We e mphasize that the network technique not only avoids the knowledge of sophis ticated numerical integration methods but also allows one to readily obtain the profiles of any physical variable of interest (potential, ionic concen trations, fluid velocity, for instance) at all points of the double layer. The polarization of the latter under the action of the applied external fie ld is easily described in terms of the dependence of the variables with the distance to the particle's surface. The power of the method is illustrated by the calculation of ion concentrations, and potential and velocity profi les in the presence of the external electric field.