A rectangular micro-electrophoresis cell is commonly used for measuring the zeta-potential of mineral particles in suspension. It is thus important to analyze the electro-osmotic circulation of the dispersion liquid in the cell for determing the electrophoretic velocities of suspended solids.
A theoretical calculation of this circulation was presented by Smoluchowski (1921) and Komagata (1933). According to their theories, the velocity of liquid changes with depth such that the velocity distribution may be represented by a symmetrical parabola in the cell. However, we have obtained results which conflict with their theories. In our experiments, the velocity distribution curve is represented by a parabola which is asymmetric with respect to the center line of the cell. A similar phenomenon had been suggested by Lane and White (1937) based on the Iatter's theory which seemingly was incomplete. By using methods of measuring electrophoretic velocities based on the above three theories, serious errors are obvious.
We are thus proposing a unified theory for determining the electrophoretic velocity of mineral particles in a rectangular cell (equation (31)). The equations of Smoluchowski, Komagata and White are derivable from our theory as special cases. By our theory, we propose an improved method of determining the precise electrophoretic velocity of mineral particles (equation (41)) based solely on the coefficients of the velocity distribution curve which is represented by an asymmetrical parabola (equation (38)). In our experiments, this method gives satisfactory results.