Collision case model for population balance equations in agglomerating heterogeneous colloidal systems: Theory and experiment

Abstract

The main goal of this work is to develop and validate a new method for characterizing the material properties of hetero-agglomerates when calculating population balances in magnetic seeded filtration processes. A new approach of computing various collision cases and probabilities and then weighting the respective agglomeration rates with them is considered to be physically justifiable. An experimental design of experiment (DOE) yielded data for the variation of multiple process parameters with a reasonable standard deviation. By measuring agglomeration kinetics, a deeper understanding of the process could be achieved and simple mathematical models were found in order to describe experimental data. The following multiple regression analysis showed good accordance with the agglomeration theory and thus the data was usable for further validation of the calculation results. By comparing calculated and experimental data and minimizing the residuals, estimates of the model parameters describing hard-to-measure material properties could be obtained. The comparison of experimental and computational regression models showed good agreement and thus validates the fundamental physical soundness of the implemented model. Furthermore, the comparison of the measured and calculated agglomeration kinetics further suggests the validity of the collision case model. Finally, this work showcases the possibilities of additional model calculations for a deeper, more thorough process understanding.

Separation of Microplastic Particles from Sewage Sludge Extracts Using Magnetic Seeded Filtration

“…Increasing the ionic strength by a factor of 100 from to did not significantly change the separation efficiency ( Fig. 2 ), which is in contrast to previous studies on MSF ( Rhein, Ruß, Nirschl, 2019 , Rhein, Scholl, Nirschl, 2019 , Rhein, Schmid, Esquivel, Nirschl, 2020 ). At all investigated particle systems are expected to be negatively charged (see Section 2.6 ), resulting in an electrostatic repulsion.…”

Opportunities and Challenges of Magnetic Seeded Filtration in Multidimensional Fractionation

“…The remaining primary collision efficiency is varied through R k according to α 1,3 = R k α 1,2 . All collision efficiencies of higher order ( α 2,1 , α 2,2 ,…) can be estimated with the collision case model described in . This model was previously validated and is only reliant on primary particle properties ( α 1,1 , α 1,2 , α 1,3 ) and agglomerate composition.…”

“…Previous work established the calculation on the basis of a validated discrete population balance equation. In this work, the model is extended to the 3D case, but also simplified, since the primary agglomeration efficiencies are predefined and held constant.…”

“…The collision efficiency vividly describes the probability that two particles agglomerate upon collision. Various models for calculating collision efficiencies exist , , which are not detailed in this work. However, the underlying main principle is the balancing of repulsive and attractive particle‐particle interactions.…”

Magnetic seeded filtration for the separation of fine polymer particles from dilute suspensions: Microplastics

“…(1) (in its full form) can be used in combination with population balances to model agglomeration processes. This was performed by many authors (also of this work) (Tsouris et al, 1995;Chin et al, 1998;Taboada Serrano et al, 2005;Rhein et al, 2019) and will not be dis cussed further here.…”