Estimation of Particle Size Distributions Using Pipet-Withdrawal Centrifuges

"The mathematical treatments used in the evaluation of particle size distribution from pipet-withdrawal centrifuge data are reviewed. An error in the published procedure for multiple-sample withdrawal systems is pointed out and a corrected formulation is presented. An alternative treatment, based on a piece-wise linearization of the size distribution is described. Computer simulations of the analytical and data evaluation procedures indicate that the errors in the original formulation are not generally serious and that the corrected and alternative procedures lead to very similar estimates. Except for some cases involving very narrow size distributions, the alternative approach appears to give slightly closer estimates of the size distribution. Comparisons based on actual experimental data are also described.1 IntroductionSedimentation methods are widely used for the determination of particle size distributions. The procedures are relatively simple to use and the results are essentially absolute, requiring no external calibration. Gravity sedimentation is typically applicable to particles in the size range of about I to 50 pm and generally involves measurement of the relative concentration of particles as a function of depth and time in a dilute suspension. Particle size is calculated using Stokes, law:"