V. G. Zhukov, V. M. Chesnokov, N. D. Lukin
All-Russian Research Institute of Starch Products – the branch of the V. M. Gorbatov Federal Science Center of Food Systems of the RAS, ul. Nekrasova, 11, pos. Kraskovo, Lyuberetskii r-n, Moskovskaya obl., 140051, Russian Federation
Abstract. The specific surface of porous media is a characteristic of the pore space for calculating numerous processes during storage and processing of various materials in food and other industries. The purpose of the study was to develop a methodology for determining the statistical cumulative functions of calculating the specific surface area in consolidated or discrete porous media depending on the selected ensembles of pore sizes from their sizes to their total in pore space. The porous medium was presented as continuous with the possibility of applying the concept of infinitesimal pore size to its analytical description. The problem of determining the cumulative function of the specific surface as a derivative from the surface of the pore space by the volume of its consolidated or discrete material was considered from these perspectives. The specific surface function was expressed in terms of pore size. In explicit form, this is a two-valued function for statistical frequency function of the histogram of pore distribution with an extremum. For the one-valuedness of the function, the pore size was presented in the form of two functions that joined at the point of the maximum value of the frequency argument. Based on them we obtained two statistical functions of the frequency distribution of the specific surface and two joined branches of its cumulative form. A dimensionless criterion was proposed for the intensity of development of the specific surface. It reflected the efficiency of the consumption of material for its development. It was the ratio of the accumulated value of the specific surface created by small pores up to the extremum of the statistical function to the specific surface of large pores beyond the extremum of the statistical function. The same criterion can be presented as a specific characteristic averaged over a unit pore of the corresponding section of the statistical function. The proposed calculation method allowed us to calculate the specific surface of a consolidated or discrete porous medium of any ensemble of sizes from a single pore to their complete set by changing the integration limits in two branches of the cumulative function of the specific surface. Its formula was convenient for embedding in the calculated dependencies of processes and equipment.
Keywords: porous medium; pores; continuity; specific surface; statistical function; lognormal distribution; cumulative specific surface function; intensity criterion.
Author Details: V. G. Zhukov, D. Sc. (Tech.), chief research fellow (e-mail: Этот адрес электронной почты защищён от спам-ботов. У вас должен быть включен JavaScript для просмотра.); V. M. Chesnokov, Cand. Sc. (Tech.), senior research fellow, (e-mail: Этот адрес электронной почты защищён от спам-ботов. У вас должен быть включен JavaScript для просмотра.); N. D. Lukin, D. Sc. (Tech.), director (e-mail: Этот адрес электронной почты защищён от спам-ботов. У вас должен быть включен JavaScript для просмотра.).
For citation: Zhukov V. G., Chesnokov V. M., Lukin N. D. Obtaining the Cumulative Function of the Specific Surface of Porous Media according to a Given Histogram of the Frequency Distribution of Pore Sizes. Dostizheniya nauki i tekhniki APK. 2019. Vol. 33. No. 11. Pp. 82–87 (in Russ.). DOI: 10.24411/0235-2451-2019-11118.