A particle scale mixing measurement method using a generalized nearest neighbor mixing index

The dependence of mixing measurement on the sampling method and scale is a major concern in the characterization of the state of homogeneity of solid particle mixtures. A novel “particle neighborhood” based mixing index, called the generalized nearest neighbor (GNN) mixing index, is developed to measure solids mixing at the particle scale. GNN is a statistically robust, grid-independent index and provides reliable particle scale mixture homogeneity values. The GNN index has a further advantage that it can be readily adapted to mixtures of unequal proportions or mixtures containing more than two species. To test the GNN index, X-ray computed tomography (CT) images are obtained to noninvasively extract detailed particle distribution of binary mixtures consisting of different-density particles in the mixing vessel. CT images are acquired at different mixing stages to accurately describe mixture homogeneity evolution during the mixing process. Mixture homogeneity values are quantified using the novel GNN mixing index, and these values are compared with measurements obtained using different mixing indices, including a standard deviation-based mixing index and a grid-independent location-based mixing index. The GNN mixing index is found to be well-suited for reliable mixture homogeneity reporting at the particle scale.This is a manuscript of an article published as Nadeem, Humair, Shankar Subramaniam, Nandkishor K. Nere, and Theodore J. Heindel. "A particle scale mixing measurement method using a generalized nearest neighbor mixing index." Advanced Powder Technology 34, no. 2 (2023): 103933. DOI: 10.1016/j.apt.2022.103933. Copyright 2022 The Society of Powder Technology Japan. Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Posted with permission

Effect of internals on the flow pattern and mixing in stirred tanks

The flow pattern, power consumption, and mixing time in a stirred vessel depend not only on the impeller design but also on the tank geometry and internals. Measurements of power consumption, mixing time, and flow pattern have been carried out in a stirred vessel of 0.5 m diameter for a standard 45° pitched-blade turbine and for a hydrofoil impeller with a variety of baffle and draft tube configurations. The comparison of the flow pattern (average velocity, turbulent kinetic energy, maximum energy dissipation rate, average shear rate, and turbulent normal stress) has been presented on the basis of equal power consumption to illustrate the extent of interaction between the rotating impeller and the internals. Comparisons of laser Doppler anemometer (LDA) measurements and computational fluid dynamics (CFD) predictions have been presented

Prediction of flow pattern in stirred tanks: new constitutive equation for eddy viscosity

The CFD simulations were carried out for the flow produced by two axial flow impellers, namely a pitched-blade downflow turbine (PBTD, Np = 2.1) and a hydrofoil impeller (Np = 0.34) by the impeller boundary condition approach. The tank was fully baffled, and the flow regime was turbulent. An attempt has been made to develop a new constitutive equation for Cμ in the description of eddy viscosity given by a standard k-ε model. The resulting predictions with the new eddy viscosity relation are compared with the experimental data. Also the comparison is sought with the predictions of impeller boundary condition approach using k-ε model with the standard and modified turbulence parameters (Ranade et al. Chem. Eng. Commun. 1989, 81, 225), zonal model of Sahu et al. (Ind. Eng. Chem. Res. 1998, 37, 2116) and the sliding mesh simulation using a standard k-ε model. For all these cases, energy balance has been established and compared with the experimental data. This paper also presents a critical review of the computational fluid dynamic (CFD) studies pertaining to the prediction of the flow produced by the axial flow impellers

Liquid-phase mixing in stirred vessels: turbulent flow regime

The published literature on the liquid-phase mixing in a turbulent flow regime has been critically reviewed and analyzed. Experimental techniques for mixing time have been described together with their relative merits. The effects of the impeller design (blade number, blade angle, blade and disk dimensions, and blade shape), the location of the impeller (off-bottom clearance, distance from the vessel center, i.e., eccentricity), and the vessel size on the liquid-phase mixing have been critically analyzed. The mixing performance dependency on the internals such as baffles (number, dimension, and position) and the draft tube has been presented in detail. Further, an extensive review on the mathematical models proposed for the liquid-phase mixing has been presented, and the utility of the computational fluid dynamics modeling for the mixing optimization has been illustrated. Finally, suggestions have been made for the selection of an energy-efficient impeller-vessel configuration, and directions have been given for future studies

Assessing solid particle mixing using X-ray radiographic particle tracking

Mixture homogeneity values are obtained from a binary mixture in a vertically bladed mixer utilizing data extracted from a single tagged particle. X-ray radiography was performed to image the mixer vessel during the mixing process, and the location of the tagged particle was tracked throughout. Mixture homogeneity is quantified using a standard deviation-based Location Distribution Mixing Index (LDMI), the Modified Generalized Mixing Mean Mixing Index (MGMMI), and the Gini Index, all adapted to single-particle data. Mixture homogeneity values obtained using these indices were compared to data extracted using X-ray Computed Tomography (CT), which was quantified using a particle scale mixing index. It was observed that the LDMI was superior in determining the magnitude of mixing, whereas the Gini index was more suited to predicting mixing endpoints. Methods presented in this study pave the way for new process analytical technologies that extract in-line mixture homogeneity values using velocimetric methods while removing the necessity of uniquely identifying and discriminating between tagged particles.This is a manuscript of an article published as Nadeem, Humair, Prajjwal Jamdagni, Shankar Subramaniam, Nandkishor K. Nere, and Theodore J. Heindel. "Assessing solid particle mixing using X-ray radiographic particle tracking." Chemical Engineering Research and Design (2023). DOI: 10.1016/j.cherd.2023.05.003. Copyright 2023 Institution of Chemical Engineers. Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0). Posted with permission

Cu-Catalyzed Couplings of Aryl Iodonium Salts with Sodium Trifluoromethanesulfinate

A convenient method for the preparation of aryl trifluoromethylsulfones from the reactions of diaryliodonium salts with sodium trifluoromethanesulfinate in the presence of copper catalysts is described. Cuprous oxide in DMF was found to be the optimal catalyst for the reaction. The reaction conditions are tolerant of various functional groups as well as of various counteranions of the iodonium salt. The synthetic utility of the process is demonstrated by performing the reaction on a preparative scale (88 g)