Dispersed Phase Systems Research Articles

A deep learning-powered intelligent microdroplet analysis workflow for in-situ monitoring and evaluation of a dynamic emulsion

Accurately determining microdroplet size and uniformity in dispersed phase systems is key for assessing emulsion stability, and essential for quality monitoring and control of emulsion products. Microscopic imaging probes have provided intuitive and advanced insights for characterizing particle microscopic morphology and dispersion in multiphase flows. However, wide size distributions, edge-cutting, overlapping, and high-density target droplets can compromise the image processing accuracy, thereby affecting the precise assessment of emulsion status. In this study, we present a deep learning-based intelligent workflow for microdroplet characterization using an in-situ high-speed particle imaging probe combined with advanced image processing techniques. With the assistance of progressive automatic annotation, a droplet image database was constructed for training the Mask R-CNN model. By incorporating image patching and supervised data augmentation strategies, our well-trained model with accuracy of 95.5% can precisely detect, localize, and segment microscale droplets with various patterns. Additionally, the shape reconstruction module visualizes true shapes of overlapping and edge-cutting droplets, facilitating precise quantification of droplet size information. To validate the feasibility and generalizability of the proposed workflow, we obtained sufficient droplet images through offline sampling during emulsion processes while employing back and front illumination for in-situ monitoring. The automated method achieves precise droplet detection and size measurement, demonstrating its immense potential in online monitoring, evaluation, and control of emulsion quality.

Particle sizing in non-dilute dispersions using diffusing wave spectroscopy with multiple optical path lengths

Non-dilute dispersed phase systems, such as foams, emulsions, and suspensions, are an important class of final formulations and chemical process intermediates in a variety of industries. The utility of these systems hinges on their stability over the lifetime of use, and therefore an accurate assessment of chemical and physical dynamics, asformulated, is required. We describe a unified treatment of diffusing wave spectroscopy (DWS) data using a range of optical path length with a goniometric instrument. DWS correlation data from multiple angles and robust Monte Carlo simulations are used to determine accurate values of the photon transport mean free path length. The variance on each correlation function is used to determine the physical time range that the mean squared displacement can be analyzed. Using standard solid particle suspensions of polystyrene and SiO2, we determine the average particle size with accuracy comparable to dynamic light scattering.

Monte Carlo Simulations in Aviation Contrail Study: A Review

This article provides a review of the role of stochastic approaches, in particular Monte Carlo calculations, in the study of aviation-induced contrails at different characteristic lengths, ranging from micrometers to the planetary scale. Pioneered in the 1960s by Bird, Direct Simulation Monte Carlo has for long time been considered unfeasible in extended dispersed-phase systems as clouds. Due to the impressive increase in computational power, Lagrangian Monte Carlo approaches are currently available, even for studying cloud formation and evolution. Some aspects of these new approaches are reviewed after a detailed introduction to the topic of aircraft-induced cloudiness. The role of Monte Carlo approaches in reducing the different source of uncertainty about the contribution of aviation contrails to climate change is introduced. Perspectives on their role in future experimental and theoretical studies are discussed throughout the paper.

Statistical optimization of extraction column parameters for the zinc (ll) solvent extraction by D2EHPA in a continuous mode

The efficiency of zinc(II) extraction with di(2-ethylhexyl) phosphoric acid (D2EHPA) diluted in kerosene has been investigated in batch and continuous extraction columns, enabling a comparison between the performance of spray and packed column. The effect of pH of the aqueous phase, reaction time, and extractant volume ratio were considered as the operational variables in a lab-scale mixer-settler in batch mode. The optimum values for each variable were determined and used as the constant values in the pilot-scale continuous setup for optimization of the extraction process in the columns. A pilot-scale setup can provide more relatable results to industrial-scale production. The effect of dispersed phase flow rate, system temperature, nozzle diameter, and height of packing were investigated in continuous mode in spray and packed pilot-scale columns. To minimize the number of experiments, the response surface methodology (RSM) design of experiments (DOE) was adopted using five levels for each parameter. The effect of each variable and their binary and ternary interactions were analyzed by analysis of variance (ANOVA) with a confidence level of 95%. Maximum zinc extraction efficiency in the batch mode was 93.63%, which occurred at the pH of 2, a reaction time of 25 min, and an extractant volume ratio of 15% (V/V D2EHPA to kerosene). Maximum zinc extraction in the spray and packed columns were 76.13% and 84.06%, respectively. Despite the lower extraction efficiency in the continuous mode, a considerably lower required organic to aqueous ratio make these setups more favorable over traditional mixers.

Theoretical and experimental analyses of thermal properties of porous polycrystalline mullite

Abstract This paper examined experimentally and theoretically the thermal diffusibility (α), heat capacity (C P1 ) at a constant pressure (1 atm, 101.33 kPa) and thermal conductivity (κ=C P1 α) for the porous mullite ceramics with 0–55% porosity in a wide temperature range from 298 to 1073 K. The change in the κ values with temperature or porosity for the porous mullite was similar to the temperature dependence or porosity dependence of the α values, which were greatly reduced by the air included in the pores. The κ values for the porous mullite were theoretically analyzed with two model structures of pore–dispersed mullite continuous phase system (A model) and mullite–dispersed pore continuous phase system (B model). The measured κ values at 0–23% porosity agreed well with the κ values calculated for model A structure. In the high porosity range from 33% to 55%, the measured κ values deviated from the κ curve calculated for model A structure and approached the κ value curve for model B structure with increasing porosity. The real microstructure of 30–60% porosity is equivalent to the mixed microstructure of model A and model B for the thermal conductivity measurement.

Achieving Target Emulsion Drop Size Distributions Using Population Balance Equation Models of High-Pressure Homogenization

Population balance equation (PBE) models have been used extensively to predict drop size distributions (DSDs) of dispersed phase systems. In our previous publications, we have used the PBE framework to develop increasingly sophisticated process models for oil-in-water emulsification in high-pressure homogenizers. The goal of this study was to utilize these PBE models for integrated emulsion product and process design through the formulation and solution of homogenizer optimization problems. For a specified number of homogenization passes, the initial amount of surfactant and the pressure of each pass were determined by solving a nonlinear least-squares optimization problem such that the target DSD were achieved. Three alternative objective functions that differed with respect to the distribution specification and the penalty on surfactant usage were formulated and solved for different target DSDs. The model predictions were successfully validated by performing homogenization experiments using the optimized formulation and homogenization variables.

Predicting the combined effects of oil and surfactant concentrations on the drop size distributions of homogenized emulsions

Population balance equation (PBE) models have been used extensively to predict drop size distributions (DSDs) of dispersed phase systems. Over the past decade, we have used the PBE framework to develop increasingly sophisticated process models for oil-in-water emulsions prepared with high pressure homogenizers. While these models can qualitatively predict the effects of formulation variables on the DSD, quantitatively accurate predictions over wide ranges of oil and surfactant concentrations remain elusive. The goal of this study was to develop a new PBE model that produced accurate DSD predictions in both the “surfactant limited regime” and the “surfactant rich regime” with a single set of adjustable model parameters. We found that the key modifications of our previous models required to generate a predictive model were: (1) reformulation of the two breakage frequency functions to behave properly with respect to drop size; (2) replacement of the constant continuous phase viscosity with a calculated emulsion viscosity that increased strongly with oil content; (3) reformulation of the drop breakage and coalescence functions to behave properly with respect to oil content; and (4) replacement of the equilibrium model of surfactant adsorption with a size independent dynamic model. Adjustable model parameters were estimated by nonlinear optimization using measured DSDs collected at 30 wt% oil and 2 wt% surfactant and at 30 wt% oil and 0.1 wt% surfactant. The parameterized PBE model generated satisfactory DSD predictions for 10–50 wt% oil and 0.1–2 wt% surfactant.

The Foundation of the Population Balance Equation: A Review

In dispersed multi-phase flow modeling using population balances (PBs), the dispersed phase system is considered as a population of entities of the dispersed phase distributed not only in physical space but also in an abstract property space. Different frameworks exist for the formulation of the population balance equation (PBE): (i) continuum mechanical principles, (ii) statistical Boltzmann-like equation, or (iii) probability principles. The source terms, that is, birth and death of the entities in the population, are defined from mechanistic principles. This article presents a review of the foundation of the PBE.

Numerical Solutions of Population Balance Equations within Liquid/Gas‐Liquid Flow Simulations

AbstractNumerical solvers based on population balance equations (PBE) coupled with flow equations are a promising approach to simulate liquid/gas‐liquid dispersed flows, which are very commonly observed in nature and in industrial processes. The challenges for the numerical solution of the coupled equation systems are discussed and detailed numerical recipes are presented whose main ingredients are the method of classes, positivity‐preserving linearization and the high‐order FEM‐AFC schemes, additional to the FeatFlow in‐house flow solver package. Liquid‐liquid flows through static mixers and dispersed phase systems in a flat bubble column are studied with the accordingly developed computational tool. The suggested recipes were validated by comparing the numerical results against experimental data.

Compartmentalization Effects on the Rate of Polymerization and the Degree of Control in ATRP Aqueous Dispersed Phase Polymerization

Compartmentalization in atom transfer radical polymerization (ATRP) in an aqueous dispersed phase system has been investigated theoretically to understand the effects of particle size on the rate of polymerization and the degree of control on the livingness and polydispersity index (PDI) for the system n-butyl methacrylate/CuBr/EHA6TREN. The simulations indicate that there exists a defined range of particle sizes where the rate of polymerization is higher than that of a bulk system and where PDI and frequency of termination remain below that of bulk polymerization. For this highly active catalyst system, the livingness of the chains is a function only of the particle size and is independent of the rate of reaction. Furthermore, simulations conducted with very low catalyst concentrations suggest that the rate of polymerization is dependent on the absolute amount of catalyst in the system rather than the steady-state Cu(I)/Cu(II) ratio that applies for bulk polymerization. At low catalyst concentrations, th...

Control of Particle Morphology in Ab Initio RAFT Mediated Emulsion Polymerization

Recent advances in the use of reversible addition–fragmentation chain transfer (RAFT) polymerization in dispersed phase systems have paved the way for the fine control of the morphology of latex particles that was not possible by conventional free radical polymerization techniques. With this approach, living amphiphilic block copolymers are synthesized that self-assemble to form micelles. The hydrophilic segment is formed from a water-soluble monomer which stabilizes the latex particles as polymerization proceeds and the latex particles grow. The hydrophobic ends of the RAFT diblocks ultimately grow into the polymer that forms the body of the particles. This paper presents examples of ways in which these advances can be used to engineer latex particles with unique morphologies that exhibit specific application properties.

ポリマー粒子の最前線 ポリマー粒子合成の基礎―核生成と粒子成長の動力学

Polymeric microspheres are mostly produced by heterogeneous free radical polymerizations such as micro-emulsion, emulsion, mini-emulsion and dispersion polymerizations. Based on historically important kinetic and mechanistic studies of emulsion polymerization, the current fundamental understanding of particle nucleation and growth in these heterogeneous free radical polymerizations is briefly but systematically summarized from the viewpoint of free radical polymerizations in microscopic dispersed phase systems.

Application of population balances in the chemical industry — current status and future needs

This contribution deals with the application of population balances in the chemical industry for the modelling of dispersed phase systems. Two examples involving industrial production processes are presented. The first example concerns the investigation of sustained oscillations occurring in a production scale crystallizer equipped with an external fines dissolution loop. For this example it will be shown, that population balance-based models can be used to analyse and overcome such oscillations. The second example describes questions occurring in the design and the operation of a solids production process. To investigate these questions, population balance-based models in connection with flow sheet simulation techniques can be used.In the second part of this contribution future needs for a more routine application of population balances are identified from an industrial point of view.

Direct simulation Monte Carlo for simultaneous nucleation, coagulation, and surface growth in dispersed systems

A Monte Carlo simulation technique is developed to describe dispersed phase systems. The method is formulated for simultaneous coagulation, nucleation and surface growth, but can be extended to include other processes. These processes are considered in an initially constant simulation volume. The changes in the particle ensemble are determined by a random choice procedure, while the particle number in the simulation volume changes according to the chosen events. Every time, when the particle number in the simulation volume increases or decreases by a factor of two of its initial value, the simulation volume is halved or doubled, respectively. Therefore, this method is called a stepwise constant-volume Monte Carlo simulation. It allows to use only several thousands simulation particles, even if the particle number concentration experiences changes of several orders of magnitude. The simulations are validated through a comparison with the exact mathematical solutions for several simple cases. An example of simultaneous nucleation and coagulation in the free-molecular region demonstrates, that the stepwise constant-volume Monte Carlo simulations lead to more accurate results than the constant-number Monte Carlo simulations.

Direct simulation Monte Carlo for simultaneous nucleation, coagulation, and surface growth in dispersed systems

A Monte Carlo simulation technique is developed to describe dispersed phase systems. The method is formulated for simultaneous coagulation, nucleation and surface growth, but can be extended to include other processes. These processes are considered in an initially constant simulation volume. The changes in the particle ensemble are determined by a random choice procedure, while the particle number in the simulation volume changes according to the chosen events. Every time, when the particle number in the simulation volume increases or decreases by a factor of two of its initial value, the simulation volume is halved or doubled, respectively. Therefore, this method is called a stepwise constant-volume Monte Carlo simulation. It allows to use only several thousands simulation particles, even if the particle number concentration experiences changes of several orders of magnitude. The simulations are validated through a comparison with the exact mathematical solutions for several simple cases. An example of simultaneous nucleation and coagulation in the free-molecular region demonstrates, that the stepwise constant-volume Monte Carlo simulations lead to more accurate results than the constant-number Monte Carlo simulations.

Performance of a perforated rotating disc contactor in the continuous extraction of a protein using the PEG–cashew-nut tree gum aqueous two-phase system

The characterisation of bovine serum albumin (BSA) mass transfer mechanisms in a perforated rotating disc contactor (PRDC) using an aqueous two-phase system (ATPS) composed of poly(ethylene glycol) (PEG) and a polysaccharide, the cashew-nut tree gum, was described. The PEG-rich phase was used as the dispersed phase and protein transfer took place from the dispersed to the continuous phase. Studies of the effect of dispersed phase velocity, system composition and disc rotation speed on either protein mass transfer coefficients or column hold-up showed that the dispersed phase hold-up and the volumetric mass transfer coefficient increased with increasing the dispersed phase velocity and disc rotation speed.

Comparison of numerical methods for the simulation of dispersed phase systems

This contribution deals with a new numerical method for an accurate and efficient simulation of particulate processes. As an example for dispersed phase systems a detailed model for crystallization processes is considered. After the model derivation, which is based solely on physical principles, different techniques for the numerical simulation of the mathematical model are discussed. State-of-the-art finite volume schemes based on the ‘method of lines’ approach are compared to the recently published ‘Space–time conservation element and solution element method’. The presented simulation results show a strong dependence on the chosen numerical method. Guidelines for a proper selection of numerical methods for the treatment of population balance based models are given.

Studies of virtually insoluble systems with large interfacial area: CdTe–ZnO

Abstract Exchange of matter at CdTe/ZnO heterojunctions was studied in (a) polycrystalline CdTe with dispersed ZnO and (b) single crystals of CdTe in contact with compressed ZnO powders. Scanning electron microscopy with electron microprobe analysis, differential thermal analysis and X-ray diffraction were the experimental techniques utilized to investigate CdTe–ZnO. Samples (a) were heated to 950°C or 1110°C and (b) to 950°C, for 60 min. Zn x Cd (1− x ) Te formed at CdTe/ZnO interfaces by thermal treatment. The magnitude of the diffusion of Zn in CdTe was estimated and found in agreement with earlier studies. A superlattice, attributable to ordering of zinc in CdTe, was suggested by preliminary single crystal XRD data from Zn x Cd (1− x ) Te microcrystals. Diffusion of zinc was faster in single crystals than in polycrystals. The study of CdTe with dispersed ZnO complements a series of studies on dispersed second phase materials. The work was carried out over the last 30 years at Professor J.B. Wagner's research laboratories, with the following outcome: Transport depended on surface area of the dispersed phase and of the matrix. Changes in electrical and mass transport, and in phase transformation temperatures, due to the presence of dispersoids, were consistent with an interpretation by the space charge model. The present results on the chemistry and microstructure CdTe with dispersed ZnO, in conjunction with the knowledge accrued on transport in dispersed second phase systems, indicate a potential application of this material in photovoltaic devices.

Proton conducting composites of heteropolyacid hydrates dispersed with salt hydrates

Proton conduction in the composites of heteropolyacid hydrates (Phosphotungstic acid : PTA·nH2O and Phosphomolybdic acid : PMA·nH2O) with salt hydrates like Aluminium sulphate and Ammonium paratungstate (APT) as dispersoids has been studied and compared with the composites PTA : Al2O3 and PMA : Al2O3. Thermal analysis, XRD and IR studies on acid and salt hydrates dispersed phase systems reveal the formation of composites. A significant increase in the ionic conductivity has been observed in the composites. It has been found that the conductivity of 0.5PTA + 0.5Al2(SO4)3·16H2O is ∼1.1 × 10−2 S·cm−1 and that of 0.55PMA + 0.45APT is ∼1.3 × 10−3 S·cm−1 at 65% R.H. The temperature and humidity dependence of bulk electrical conductivity of the composites is also reported.

Modeling Ice Crystal Coarsening in Concentrated Disperse Food Systems

ABSTRACTRecrystallization of ice in frozen concentrated aqueous sugar solutions was treated as a diffusion controlled process and has been modeled using a combination of a modified Lifshitz, Slyozov and Wagner theory for coarsening in dispersed phase systems and a mean field theory. The model has been tested using aqueous fructose solutions, water ices and ice creams under a range of time and temperature histories. The model provides data which are in accord with experiments and also suggests that recrystallization cannot be modeled using only diffusion. In certain circumstances other processes must also be considered.