Sedimentation velocity and potential in a dilute suspension of charged spherical colloidal particles

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Abstract
General expressions for the sedimentation velocity and potential in a dilute suspension of charged spherical rigid particles in an electrolyte solution have been derived in terms of the flow of the liquid and the electrochemical potential of the electrolyte ions. Exact numerical results for the sedimentation velocity and potential are displayed as functions of the ζ potential and κa(where κ is the Debye–Hückel parameter and a is the particle radius). The results were obtained by using a computer program similar to that developed by O'Brien and White for the calculation of the electrophoretic mobility of spherical particles. Approximate analytic expressions for small ζ and those for large κa have also been derived. The computer result and analytic expressions for the sedimentation potential are found to satisfy an Onsager relation between sedimentation and electrophoresis. A direct proof of this relationship is given.