(320f) Measurement of the Zeta Potential and Darcy Coefficient of Porous Materials by Rotating Samples On Their Axis

A relatively new method of zeta potential measurement utilizes a planar disk sample affixed to the end of a spindle and rotated. [1] The theory underlying the method is based on the well established hydrodynamics of the rotating disk. The simplicity and convenience of the apparatus, however, invites users to affix samples of various sizes, shapes, and structures to the spindle and obtain a streaming potential; however, one must convert the measured streaming potential to zeta potential with a theory suitable for the particular geometry of the sample.  Here, porous samples having a finite thickness and open structure were placed on the spindle and rotated.  Large streaming potentials were generated and naïve application of the theory developed for planar surfaces gave proportionally large apparent zeta potentials. A treatment of the fluid flow in a rotating porous sample was then found in the fluid mechanics literature [2] and applied to this problem.  An analytical result relating the streaming potential to the zeta potential of the porous material, its Darcy law coefficient, and the thickness of the sample, was obtained.  The streaming potential depends on the square of the rotation rate at low rates and becomes independent of rotation rate at high rates.  Experiments combined with the new theory, both of which are described in this presentation, have demonstrated that one can determine the zeta potential and the permeability of porous samples by means of this approach. Plotting the reciprocal of the measured streaming potential versus the reciprocal of the square of the rotation rate gives a straight line having a slope independent of the porous structure of the sample.  A plot of the quotient of the streaming potential and the square of the rotation rate against the streaming potential gives a straight line with a slope that only depends of the Darcy coefficient of the porous sample. 

[1] 1. P. Sides, J. Newman, J. Hoggard, D. Prieve, Langmuir 22 9765-9769 (2006).

[2] D. D. Joseph, Q. J. Mech. Appl. Math. 18 325 (1965)