A Population Balance Model for Shear-Induced Polymer-Bridging Flocculation of Total Tailings

Shear-induced polymer-bridging flocculation is widely used in the solid–liquid separation process in cemented paste backfill, beneficial to water recycling and tailings management in metal mines. A flocculation kinetics model based on Population Balance Model (PBM) is proposed to model the polymer-bridging flocculation process of total tailings. The PBM leads to a system of ordinary differential equations describing the evolution of the size distribution, and incorporates an aggregation kernel and a breakage kernel. In the aggregation kernel, a collision frequency model describes the particle collision under the combined effects of Brownian motions, shear flow, and differential sedimentation. A semi-empirical collision efficiency model with three fitting parameters is applied. In the breakage kernel, a new breakage rate coefficient model with another three fitting parameters is introduced. Values of the six fitting parameters are determined by minimizing the difference between experimental data obtained from FBRM and modeling result through particle swarm global optimization. All of the six fitting parameters vary with flocculation conditions. The six fitting parameters are regressed with the flocculation factors with six regression models obtained. The validation modeling demonstrates that the proposed PBM quantifies well the dynamic evolution of the floc size during flocculation under the given experimental setup. The investigation will provide significant new insights into the flocculation kinetics of total tailings and lay a foundation for studying the performance of the feedwell of a gravity thickener.

Correction to: Multi-fluid modelling of bubbly channel flows with an adaptive multi-group population balance method

The article “Multi-fluid modelling of bubbly channel flows with an adaptive multi-group population balance method ” written by D. Papoulias, A. Vichansky, and M. Tandon, was originally published electronically on the publisher ’s internet portal (currently SpringerLink) on 21 October 2020 without open access. After publication in Volume 3, Issue 3, page 171–185, the author(s) decided to opt for Open Choice and to make the article an open access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2021 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, duplication, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Effect of Adding Surfactants to a Solution of Fertilizer on the Granulation Process

Granulated chelates are innovative fertilizers that are highly effective and versatile, and they ensure the best start-up effect for plants. The final properties of granules are influenced by the method of their preparation and the used substances. The diameters of the obtained granules, their size range, and the final costs of the produced fertilizer are of great importance. The paper describes granules that were produced using an agglomeration of ZnIDHA in a fluidized bed with the aid of an aqueous solution of this substance with a high dry matter content. The aim of the study was to evaluate the effect of surfactant addition to the solution on the evolution of granule size distribution during the process carried out in a batch mode and to access the possibility of describing the process dynamics using population balance approach. A sieve analysis was performed in order to determine the size of the granulate, and numerical calculations were performed to determine the value of the constant aggregation rate. Based on experimental studies, it can be seen that the increase in the diameters of granules is mainly caused by the agglomeration process, and to a lesser extent by the coating process. The addition of surfactant increased the median size of the granules in the initial granulation stage, and also lowered the surface tension. This in turn enables a lower spraying pressure to be used. A comparison of different aggregation kernels constituting an integral part of the population balance model proved that the physically motivated equipartition kinetic energy kernel performs best in this case. Moreover, the computational results show an increase in the aggregation rate when the surfactant additive is used and confirm that population balance allows the extraction of physical information about the granulation.