Synthesis of Grain Size Distribution Functions Determined by the Coulter Counter Method

摘要

There are many measuring methods of grain sizes. Taking into consideration the fine grained materials, one of the existing techniques is measurement of grain size by the Coulter Counter method. This method is based on the measuring the changes of electrolyte resistance during grains flow through the calibrated diaphragm. This method is relatively simple to apply, significantly precise and the results are given quickly. However, the problem is that the measurements are limited by the size of diaphragm. Because of this situation,measurement of grain sizes by this instrument is possible in range from 10% to 60% of diaphragm diameter. This limitation causes the necessity of replacing diaphragm in case when the measured grain size distribution concerns the material of large size range. In purpose of determining the total grain size distribution, the synthesis of some partial distributions, given for individual grain fractions (with different diaphragm applied), is required.This is possible to do by calculating the mixture of distribution functions, created from the partial distribution functions.Two materials were selected to research: quartzite and glass, which were comminuted in cylindrical crusher, additionally grinded, screened and then analyzed by Coulter Counter for five grain fractions: 0～125 μm, 0～80 μm, 0～56 μm, 0～40 μm and 0～25 μm. For each fraction, five different partial distributions were given (in case of glass four), which are the basis for the creating the joined grain composition. To assure the adequacy of the given distribution function, it is necessary to obtain the possibly best approximation of partial distributions. In the work, both the parametric and non-parametric methods of density approximations of investigated random variable. For each grain fraction the approximations were done by three traditional distribution functions: RRB, GSA and log-norm distribution functions and three methods of non-parametric approximation: Gauss kernel, Epanechnikov kernel and orthogonal Fourier series method. As the criterion of the certain distribution function acceptance, the value of the residual deviation was assumed, given by the formulae:where F(di) is the value of the theoretical distribution function and F0(d1) is the value of the empirical distribution, k is number of fractions.