Intrinsic conductivity, particle shape, and the Coulter particle counting method
Edward J. Garboczi
The Coulter particle counting method has been in use for more than five decades. It records a change in resistance when a particle flows from a large reservoir through a narrow orifice to another reservoir, where the flow direction is aligned with an applied electric field and the matrix fluid is assumed to be much more conductive than the particle. The resistance goes through a pear as the particle flows through the orifice, and the height of the peak is used as a measure of particle volume. In this paper the Coulter particle counting method is shown to be directly related to the particle intrinsic conductivity, which is the parameter that controls the change in conductivity, in the dilute limit, when a particle is added to a conducting matrix. The properties of the intrinsic conductivity, when the particle is much less conductive than the matrix, are used to show hoe the Coulter particle counter can work well, within about 10% error in volume determination, for a range of equi-axed particle shapes. A simple finite element model of a Coulter counter is used to display how more unusual non-spherical shaped particles can give erroneous volumes by 20% or more, using rectangular prism-shaped particles. Using the concept of intrinsic conductivity, the Coulter particle counting process might be extended to particles that are more conductive than the fluid matrix, but with a greater sensitivity to particle shape. Finally, if the particle and fluid conductivity are close to each other, the measurement errors caused by particle shapes that are different from the calibration particle can be in principle be largely eliminated by exploiting the shape- independence of the intrinsic conductivity near this condition, which is analytically known.