The influence of particle shape on the results of the electrical sensing zone method as explained by the particle intrinsic conductivity

Abstract

The electrical sensing zone (ESZ) particle counting method has been in use for decades. It records a change in resistance when a particle flows in a conducting fluid from a large reservoir through a narrow aperture into another reservoir, where the flow direction is aligned with an applied electric field and the particle is assumed to be much less conductive than the fluid. The measured resistance of the entire system goes through a peak as the particle flows through the aperture, at the center of the aperture, and the height of the peak is assumed to be a measure of particle volume. In this paper, the sensitivity of the ESZ particle counting method is shown to be directly related to the particle intrinsic conductivity, which depends only on particle shape and conductivity relative to the matrix fluid. The intrinsic conductivity is the main parameter that influences the change in conductivity, in the dilute limit, when a particle is added to a conducting matrix. A simple finite element model of an ESZ particle counter, built from cubic voxels, along with a sphere (calibration particle), cube, and ellipsoid of equal volumes, are used to show how particle shape affects the ESZ result. Even though the specific counter geometry can affect the resistance seen, it is shown that the intrinsic conductivity still explains the main influence on the resistance results in these numerical experiments, within certain geometric bounds. 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.