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Scale-up of the liquid-liquid extraction columns like asymmetric rotating impeller column (ARIC) from laboratory to industry is an expensive procedure in terms of resources, inventory, human resources, and time. Local hydrodynamics of the column governs the breakage and coalescence of the drop and thus the mass transfer performance of the column. The correlations developed for scale-up procedures by experimentation at laboratory scale cannot ensure the local properties like velocities, turbulence, and dispersed phase holdup to be the same in the large scale columns. In the present work, the CFD methodology has been proposed for the scale-up of ARICs. CFD simulations have been carried out in three geometrically similar ARICs, to check for the kinematic similarity. The predicted dispersed phase holdup is found to agree with the experimental results with an average absolute value of the relative error within 20%. The local velocities and turbulence properties are compared for three scales. The local velocities and turbulence are observed to scale with the tip speed. CFD simulations show that the flow patterns and turbulence scale with increased column diameter and scale-up can be made based on geometric similarity at equal specific power and tip speed.

Breakage occurs in several particulate systems that are simulated using the discrete element method (DEM), namely crushing and grinding as well as inadvertently in several others that include transportation, handling, mixing, separation and geotechnical applications. Different approaches may be used to describe particle breakage using DEM, but in cases in which particle breakage influences significantly the flow behaviour of the material, imbedding the breakage description in DEM provides the only valid alternative. This study describes the implementation of a detailed breakage model based on particle replacement with spheres in the commercial software EDEM. It accounts for variability and size-dependency in particle fracture energies, weakening of particles by unsuccessful stressing events, as well as addressing several reported shortcomings in sphere replacement schemes. The model is verified in great detail on the basis of single-particle breakage information and validated using measurements in unconfined particle beds of mineral ores.

The Archimedes Tube Crystallizer (ATC) is a small-scale coiled tubular crystallizer operated with air-segmented flow. As individual liquid segments are moved through the apparatus by rotation, the ATC operates as a pump. Thus, the ATC overcomes pressure drop limitations of other continuous crystallizers, allowing for longer residence times and crystal growth phases. Understanding continuous crystallizer phenomena is the basis for a well-designed crystallization process, especially for small-scale applications in the pharmaceutical and fine chemical industry. Hydrodynamics and suspension behavior, for example, affect agglomeration, breakage, attrition, and ultimately crystallizer blockage. In practice, however, it is time-consuming to investigate these phenomena experimentally for each new material system. In this contribution, a flow map is developed in five steps through a combination of experiments, CFD simulations, and dimensionless numbers. Accordingly, operating parameters can be specified depending on ATC design and material system used, where suspension behavior is suitable for high-quality crystalline products.

The breakage of agglomerates due to wall impact within a turbulent two-phase flow is studied based on a recently developed model which relies on two artificial neural networks (ANNs). The breakup model is intended for the application within an Euler-Lagrange approach using the point-particle assumption. The ANNs were trained based on comprehensive DEM simulations. In the present study the entire simulation methodology is applied to the flow through two sharp pipe bends considering two different Reynolds numbers. In a first step, the flow structures of the continuous flow arising in both bend configurations are analyzed in detail. In a second step, the breakage behavior of agglomerates consisting of spherical, dry and cohesive silica particles is predicted based on the newly established simulation methodology taking agglomeration, fluid-induced breakage and breakage due to wall impact into account. The latter is found to be the dominant mechanism determining the resulting size distribution at the bend outlet. Since the setups are generic geometries found in dry powder inhalers, important knowledge concerning the effect of the Reynolds number as well as the design type (one-step vs. two-step deflection) can be gained.

Single octanol droplet fragmentations in channel flow have been investigated by use of high speed imaging. The resulting raw data have been analyzed, interpreted and used to elucidate the fluid particle breakage phenomena, enabling improved understanding and motivating development of more universal population balance equation closures. The breakage kernel functions considered are the breakage time, the breakage probability, the average number of daughters and the daughter size distribution. These functions have been determined from the same set of data ensure consistency. The impact of the drop size and the turbulent energy dissipation rate on the different kernel functions were investigated. The breakage probability and average number of daughters functions correlate reasonably with the Weber number. Similarly, the breakage time correlates adequately with known model concepts. However, the correlations may not be considered universal as the parameter values obtained are not in agreement with values reported in the literature.

Droplet dynamics at double T-junction microdisperser are usually occurred in multiphase flow and complex fluids within microfluidics and microreactors. However, the mechanism of droplet dynamics in double T-junction microdisperser with the double input of the continuous phase remains unclear. In this article, the deformation and breakup of droplets in double T-junction microdisperser is experimentally studied with the double input of the continuous phase. Various flow patterns are observed for the dynamics of droplets. The droplet deformation is analyzed and discussed, and a prediction formula for the maximum droplet deformation is proposed. In addition, the breakup dynamics of droplets are studied systematically. The breakup of the droplet can be divided into squeezing stage, transition stage and pinch-off stage. The influence of the capillary number and the viscosity ratio of both phases on each stage of the droplet breakup are discussed. Finally, it is found that in the transition zone between the deformation and breakup of droplets, the tail of a droplet is often accompanied by corrugated filaments, and the filament breakage presents either tip streaming or self-similar fractures.

Funding Information: The authors are grateful for the financial support from the Academy of Finland through the project ( 309830 ) Ice Block Breakage: Experiments and Simulations (ICEBES) . AP worked on the article while visiting Thayer School of Engineering at Dartmouth College (Hanover, NH, USA) during spring 2020. Thanks are extended to Prof. Erland Schulson for hosting and for valuable discussions on the topic of this paper. Finnish Maritime Foundation is acknowledged for partial funding of the visit. Funding Information: The authors are grateful for the financial support from the Academy of Finland through the project (309830) Ice Block Breakage: Experiments and Simulations (ICEBES). AP worked on the article while visiting Thayer School of Engineering at Dartmouth College (Hanover, NH, USA) during spring 2020. Thanks are extended to Prof. Erland Schulson for hosting and for valuable discussions on the topic of this paper. Finnish Maritime Foundation is acknowledged for partial funding of the visit. Publisher Copyright: © 2021 The Author(s) This study uses a unique experimental system to explore the breakage of laboratory-grown, floating saline ice blocks under ice-to-ice contacts. This topic is important to the understanding and modeling of force transmission through ice rubble fields. In a collection of ice blocks subjected to compressive loading, force is transmitted via force chains, and their stability plays a crucial role in ice-structure interaction processes. Peak loads are limited by the buckling of these force chains or breakage at the ice block contacts. Lack of information on the breakage mechanism motivates the present effort. In the experiments, three ice blocks were set up to form two ice-to-ice contacts, after which the three-block system was compressed to failure. The force transmitted through each contact and the failure process of the blocks were recorded. In total 32 tests with varying contact areas were performed. In about 75% of the cases, the load transmitted by an ice-to-ice contact was limited by shear failure. The key property limiting the magnitude of the force transmitted by an ice-to-ice contact was found to be shear strength; blocks typically failed in shear on planes having the characteristics of ‘Coulombic shear faults’. Quasi-static force equilibrium analysis of these shear failures showed that the floating ice blocks with a naturally occurring temperature gradient used in this study had a shear strength of 279 kPa. Other failure modes, including crushing, splitting and ‘Y-shaped’ conjugate failure, were occasionally observed.

A three-dimensional CFD model coupled with a mesoscale mass transfer model was developed to simulate the absorption of CO2 in the microporous tube-in-tube microchannel reactor (MTMCR). The simulation results were validated by experimental data and empirical correlations, with the discrepancies within ±20%. The local breakage and coalescence of the gas-liquid interfaces enhanced mass transfer in the annular microchannel. The higher ReG and ReL means lower ratio between energy for mass transfer and surface, and also, larger contribution of interfacial area to the mass transfer. Additionally, an entrance-effect zone was revealed, and the entrance-effect zone enlarged with the increase in ReG and ReL. The overall mass transfer coefficient and entrance-effect zone enlarged significantly with appropriate decrease in the length of the gas-liquid collision zone. Results of this work could provide a theoretical basis for the further optimization of MTMCR.

The present study develops comprehensive drop size distribution by coupling numerical modeling with experimental data to optimize the heavy metal extraction in a modified rotating disc contactor column. Droplet behavior was illustrated based on the maximum entropy principle, population balance model, normal and log-normal functions. For case studies, the vanadium extraction from sulfate solution by mixtures of D2EHPA and TBP extractants and metal stripping from the loaded organic phase by ammonium solution was employed as the reactive agents to generate chemical reactions. The modeling results indicated that the agitation speed and mass transfer direction have more profound influences on the drop size distribution, whereas only partially associated with the phase flow rates. Mathematical optimizations based on the Lagrange multipliers method are conducted to formulate the new correlations in terms of the maximum entropy principle (MEP). The population balance model (PBM) was utilized to characterize the distribution internal coordinate with main parameters in the breakage and coalescence of drops. From output results for drop size distribution, the population balance approach validated significantly with the experimental data for reactive systems in an MRDC column.

Fracture initiation and propagation in fluid-saturated rocks are controlled by interaction between fluid flow and rock deformation . The description of hydromechanical coupling is essential for modeling the fracture process. In this paper, an improved hydromechanical model is proposed in the framework of the particle flow simulation method. This model provides a better description of hydraulic properties before and after breakage of bonds and can efficiently describe fluid flow through porous rock matrix and along fractures. The efficiency of the proposed model is first assessed by comparisons with analytical solutions and typical experimental evidences. A series of numerical simulations are then realized to investigate effects of some key parameters such as confining stress, fluid injection rate and viscosity on the initiation and propagation of fractures.

Stainless-steel bend pipe is used to transport the media that contains H2S and NH3 in sewage stripping unit. An obvious leakage occurs at the lateral wall and inner ridge of the elbow during service. Failure analysis is carried out by using traditional characterization techniques and computational fluid dynamics (CFD) simulation. Meanwhile, the effects of thermocouple length and elbow curvature radius on the failure behavior are also studied using numerical simulation methods. Results demonstrate that the high risk area obtained from CFD simulation coincides with the practical breakage area. Not only the corrosive medium dissolving in sewage contributes to the failure of the elbow, but also the inserted thermocouple leads to the uneven distribution of flow velocity inside the pipe which aggravates the local erosion-corrosion of the elbow. On the basis, a series of protective recommendations are put forward.

In this paper, the dynamic evolution of nanoparticles in a turbulent Taylor–Couette flow was studied by means of a numerical simulation. The initial particle size was 200 nm, and the volume concentration was 1 × 10−5. The Reynolds-averaged N–S equation for Taylor–Couette flow was solved numerically using the realizable k-ε model combined with the standard wall function. The numerical result of the velocity distribution is in good agreement with the experimental results. Additionally, the dynamic equation for the particle number distribution function was solved numerically using the Taylor series expansion moment method (TEMOM). The variation characteristics of particle number density, diameter and polydispersity in the flow were analyzed. The results show that particle breakage is obvious in the region with strong vorticity due to the large shear strength, which leads to a significant change in the particle number density, diameter and polydispersity. Furthermore, the effects of the gap width between two cylinders and the Reynolds number on the distribution of the particle number density, size and polydispersity are discussed.

An anisotropic drop breakage model is applied to CFD–PBM simulations of turbulent emulsification in a high–pressure homogeniser. We compare the exponent of Sauter mean diameter – pressure drop correlations with published experimental results and with exponents obtained using existing drop breakage models. Its theoretical value assuming homogeneous isotropic turbulence is - 0.6 , while experiments have shown exponents of smaller magnitude. A breakage frequency model using the full spectrum of isotropic turbulence is found to produce a value of the exponent near - 0.6 . Our newly developed anisotropic breakage model predicts an exponent of smaller magnitude, closer to experiments. Breakage frequency based on isotropic turbulence exhibits non–monotonic behaviour (by predicting a maximum value for a certain drop size); the effect of turbulence anisotropy is to reduce non–monotonicity. It is shown that this reduction in non–monotonicity drives the decrease in the magnitude of the exponent.

The discrete element method (DEM) has been extensively used to study the micro-mechanical behavior of sand subjected to quasi-static strain rates. In most of these studies, the sand specimens were prepared with an upscaled particle size distribution (PSD) to reduce the computational cost. However, the effectiveness of this upscaling approach in replicating the dynamic sand response is not well understood, especially at high stresses where significant particle breakage occurs. In this paper, several split Hopkinson pressure bar (SHPB) tests reported in literature are modeled in DEM using two methodologies: 1) applying the reported strain rates directly to the DEM specimen without accounting for wave propagation in the incident and transmission bars; and 2) modeling the complete SHPB test setup including the incident and transmission bars. The results show that with well-calibrated parameters for contact behavior and particle crushing, specimens with upscaled PSD provide similar dynamic stress-strain response and PSD evolution as those reported in literature. This study shows the importance of particle breakage in the stress-strain response under high stresses as the specimens without particle breakage provide a much stiffer response compared to the specimens with particle breakage. The developed DEM model may be a useful tool to model the complete SHPB test setup as the incident, reflected and transmitted stress waves can be accurately replicated.

Particle breakage is an important factor affecting the strength and deformation of coarse-grained soil. In order to study the compaction characteristics and particle breakage effect of coarse-grained soil, the compaction tests of coarse-grained soil with different stone content and water content were designed. The results show that the dry density of coarse-grained soil first increases and then decreases with the increase of water content. With the increase of stone content, the maximum dry density and optimal moisture content of coarse-grained soil increase. After compaction test, the coarse-grained soil has obvious particle breakage phenomenon, and the particle breakage index increases with the increase of stone content and water content. The fractal dimension D can characterize the coarse-grained content of coarse-grained soil. With the increase of coarse-grained content, the fractal dimension D decreases gradually.

Existing DEM researches related to particle breakage usually assume that particles are regular shapes and debris is spherical. In this paper, a method combining relatively realistic particle shape and realistic breakage is proposed to study particle breakage in the DEM. The particle morphology was derived from the scanned real particles and was convex treated. The breakable particle was modelled as an aggregate composed with coplanar and glued Voronoi polyhedra. Then, a series of drained triaxial tests under different confining pressures were conducted. The macroscopic characteristics, including the shear strength, dilatancy and particle breakage, are qualitatively in agreement with previous literatures, which show the rationality of the proposed method. Further, the microscopic characteristics, including the coordination number and sliding contact, were investigated to explore the effect of particle breakage on the macroscopic shear behaviour. Finally, the analysis-related anisotropy coefficients were evaluated to probe the microscopic origins of the peak and critical shear strengths.

Upon employing the theoretical frame of breakage mechanics for geological materials and homogenization, a new elasto-plastic constitutive model is proposed to investigate the dynamic mechanical behaviors and volumetric strain of frozen soil under cyclic loading. In this model, using a mesoscopic method to formulate the breakage of frozen soil by idealizing it as a binary medium, assuming respectively the unbroken state as bonded element and the damage state as frictional element. During the loading process, the evolution of the nonuniform deformation and ice cementation breakage is described by the local strain concentration coefficient and breakage ratio, respectively. The dynamic triaxial compression test data for different confining pressures, coarse particle contents, and dynamic deviatoric stress amplitudes are utilized to confirm the suitability of the new elasto-plastic constitutive model. In the results, the model presented the stress-strain curves and volumetric strain curves of frozen soil under cyclic loading which captured the basic dynamic characteristics, such as nonlinear variation, hysteresis behaviors, and plastic strain accumulation behaviors. Herein, the extensive experimental validation shows the applicability of the proposed model.

The present study completes the development of a model for predicting the effect of wall impacts on agglomerates in turbulent flows. Relying on an Euler-Lagrange hard-sphere approach this physical phenomenon is described in an efficient manner allowing practically relevant multiphase flow simulations at high mass loadings. In a recent study (Khalifa and Breuer, 2020) conditions for the onset of breakage and the resulting fragment size distribution were derived. In the present investigation a data-driven description of the post-breakage kinetics of the fragments is developed based on extensive DEM simulations taking a variety of impact conditions (impact velocity, impact angle, agglomerate size) into account. The description relates the velocity vectors of the fragments after breakage to three parameters: The reflection angle, the spreading angle and a velocity ratio of the magnitude of the fragment velocity to the impact velocity of the agglomerate. Relying on the DEM results Weibull distribution functions are used to describe the parameters of the wall-impact model. The shape and scale parameters of the Weibull distributions are found to mainly depend on the impact angle of the agglomerate. Consequently, relationships between the shape and the scale parameters and the impact angle are established for each of the three parameters based on a fourth-order regression. This allows to determine the velocity vectors of the fragments randomly based on the corresponding Weibull distributions of the reflection angle, the spreading angle and the fragment velocity ratio. The devised model is evaluated in a turbulent duct flow at five Reynolds numbers and three agglomerate strengths given by powders consisting of primary particles of different size. The analysis first concentrates on the pure wall-impact breakage but then also includes agglomerate breakup due to turbulence, drag forces and rotation allowing to determine the shares of the different physical phenomena. It is found that with increasing Stokes number the wall-impact breakage occurs less effectively due to the reduced responsiveness of the agglomerates to the secondary flow motions in the duct. However, in the very high range of St + other mechanisms such as the turbophoresis and the lift force augment the breakage at walls. Comparing the contributions of the different breakage mechanism reveals that the wall impact is dominant at the lowest Reynolds numbers, whereas the drag stress prevails at high Re.