Drop Breakage Research Articles

Spherical agglomeration kinetics: A mechanistic approach

Spherical agglomeration, a process of in-suspension particle size enlargement, can substantially improve critical quality attributes of powders. In this work, a paracetamol-heptane-water system is used to investigate the kinetics of spherical agglomeration, demonstrating for the first time the influence of true bridging liquid to solid ratio (TBSR) and suspension loading on the evolving size, shape and density of agglomerates. A critical range of TBSR is identified where robust agglomerates are formed that are round, moderately dense, and have a controlled size distribution. Immersion nucleation, drop breakage, and agglomerate densification by impact are the controlling rate processes. Increasing mixing intensity reduces agglomerate size, porosity and agglomeration time. Increasing solids loading increases agglomeration time while yielding smaller agglomerates with lower porosity. A first order consolidation model quantitatively predicts the agglomeration kinetics as well as agglomerate properties with increasing TBSR, and is a powerful tool for design and scale up.

Drop Size Distribution in Agitated Contactor: A Review

The breakage rate of liquid drops in the dispersed phase is a key way to improve the heat and mass transfer between the continuous/dispersed phases. This work includes a review of experimental results of liquid drop breakage in an agitated tank. The study highlighted the experimental conditions that were investigated as well as the important findings about the impact of operating conditions on some breakup parameters. The conflicts and discrepancies in the findings of those studies were identified and analyzed. The review found that many experimental parameters affect the drop breakage rate. The breakage probability (BP), number of fragments, and breakage time (BT) are direct functions of power input.

A simplified drop breakage model for emulsion-producing fluidic devices: Application to fluidic oscillator, helical coil and vortex-based cavitation device

Droplet size distribution (DSD) is one of the key quality attributes of liquid–liquid emulsions. Various fluidic devices are used to generate emulsions. Most of the currently available models for estimating DSD are complicated to implement and computationally expensive. In this work, we have developed a simplified drop breakage model that is easy to implement and computationally inexpensive. This model approximates DSDs in three droplet populations, each characterised by a mean diameter. The developed drop breakage model was applied to simulate Sauter mean diameters of oil-in-water emulsions generated using three fluidic devices covering a broad range of shear rates and droplet sizes namely: vortex-based cavitation device (VD), helical coil (HC), and fluidic oscillator (FO). The variation of DSD with the number of passes (np) through the emulsion-producing fluidic devices was measured experimentally. The Sauter mean diameter (d32) and number of droplets (n) in each population were estimated from the measured DSD data. The procedure to estimate model parameters is presented. The simplified breakage model presented here was able to simulate the influence of the number of passes and operating conditions on Sauter mean diameter as well as breakage efficiency. VD was found to exhibit the highest drop breakage efficiency. FO was found to be a preferred choice for low (< 20 J/kg) energy consumption, HC for the middle range (20 – 100 J/kg) and VD for the higher (> 100 J/kg) range of energy consumption. The developed approach and model provide a simplified way of simulating the Sauter mean diameters of emulsions for a variety of emulsion-generating devices.

Heat transfer in drop-laden turbulence

Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: $Pr=1$ , $Pr=2$ , $Pr=4$ and $Pr=8$ . The drop volume fraction is $\varPhi \simeq 5.4\,\%$ for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of $Pr$ , but also on their size and on their own dynamics (topology, breakage, drop–drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of $Pr$ slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by $t/Pr^{2/3}$ . Accordingly, the heat transfer coefficient $\mathcal {H}$ (respectively its dimensionless counterpart, the Nusselt number $Nu$ ) scales as $\mathcal {H}\sim Pr^{-2/3}$ (respectively $Nu\sim Pr^{1/3}$ ) at the beginning of the simulation, and tends to $\mathcal {H}\sim Pr^{-1/2}$ (respectively $Nu\sim Pr^{1/2}$ ) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions.

Hybrid modeling of drop breakage in pulsed sieve tray extraction columns

Accurate models for pulsed sieve tray extraction columns (PSEs) depend on the correct prediction of the drop diameter to estimate extractive mass transfer across the phase boundary. Phenomenologically, the drop diameter is determined by a balance of drop breakage and coalescence. While for most industrial solvent systems, coalescence plays a minor role; breakage is mostly the dominant phenomenon determining the drop diameter. However, most modeling approaches for drop breakage in PSEs are characterized by a trade-off between a broad validity range and good prediction accuracy. To overcome this limitation, we developed a hybrid breakage model for drop breakage in PSEs in which a physical-empirical model basis is enhanced by data-driven parameter estimator models (PEMs). The hybrid model is based on a revised form of Garthe’s breakage model, for which we developed a linear PEM for the model parameters and two data-driven PEMs for dstab and d100, respectively. The hybrid breakage model was validated on 743 experimental data sets and evaluated based on the pull metric. In a sensitivity analysis, the model correctly predicted the breakage probability over a wide range of solvent properties, operating conditions, and sieve tray geometries. In future studies, the hybrid breakage model can be incorporated into extraction column models without an initial parametrization.

CFD analysis of drop generation in cross-junction microchannel

The development of microfluidic devices, which handle small volumes of fluids for mechanical, chemical and medical purposes, is accelerating. Drop microfluidics is a booming field. This study aimed to attain a better understanding of drop generation in a cross-junction device. Hence, the generation of drops in the cross-junction microchannel was numerically and two-dimensionally simulated. For this purpose, the open-source code of Gerris was implemented. Also, the effect of Ca and We number on the drop generation process was evaluated. The AMR technique is utilized to simulate drop motion. Six distinct regimes are identified, namely, long alternating (LA), short alternating (SA), alternating with different sizes (ADS), small drops (SD), jetting (J) and parallel (P). In combination with (LA and SA) regimes, the size of one drop is larger than the hydraulic diameter and the other is smaller. In the large alternating regime, the length of the drops decreases when Weber numbers increase and the drop generation frequency increases as the We number increases. In each transition from one regime to another, the pinch-off location suddenly increases, and then in each regime, with the increment of the We number, the location of drop breakage decreases.

Synthesis of gold nanoparticles in emulsion–emulsion precipitation route: Experiment, mechanism and simulation

Soft templates like water-in-oil emulsion drops (of 1-100μm diameter), have been used for synthesis of nanoparticles; with specific mean particle diameter and narrow particle size distribution. In this context, two separate emulsions have been reacted by an emulsion–emulsion precipitation route. Consequently, two different kinds of interacting populations coexist — emulsion drops evolving through drop coalescence and breakage, with multiple nanoparticle populations growing inside each emulsion drop. However, no model framework currently exists to simulate these two highly interacting populations, for predicting evolution of nanoparticle size. To this end, presently gold nanoparticles (GNPs) have been used as a model system, to explore the nanoparticle formation mechanism. The metal salt precursor and reducing agent (NaBH4 or N2H4) are prepared in two separate water-in-oil emulsions and are reacted upon mixing to form GNPs. A kinetic Monte Carlo (kMC) scheme accounting for drop coalescence, drop breakage, nucleation, particle growth and particle–particle coagulation was developed to handle simultaneous size and number evolution of aqueous emulsion drops and GNP populations. We find that, the mean GNP diameter decreases (from 6.9 to 3.5 nm) with increasing molar ratio (M) of reducing agent to precursor concentration. Further, increasing the precursor concentration at a fixed M, does not affect the final particle size. Our kMC simulation results not only agree well with experimental mean particle diameter and coefficient of variation (COV) of particle diameter, but was also validated with full particle size distribution of GNPs. So, M can be used as a tunable parameter for controlling GNP diameter experimentally.

14‐3: Drop Resistance Optimization Through Post‐Hoc Analysis of Chemically Strengthened Glass

In the market of the mobile cover glass, the development of chemically strengthened glass is focused on the drop resistance improvement. The cover glass which protects the display panel is a typical brittle material that the micro cracks tends to be occurred underneath a glass surface by physical impacts. The micro cracks tends to be propagated by tensile stress and it is known as a general procedures on glass breakage. In purpose of the cover glass strength improvement, compressive stress is applied to the glass surface using chemical strengthening method by ion exchange. However, since the central area of the glass is relatively subjected to tensile stress, the glass is instantly broken when the propagated cracks are reached on the tensile stress exerted area. The glass specifications have been managed for maintaining the strength using parameters of compressive stress (CS), depth of compression (DOC), and central tension (CT). However, there was no method to judge the most effective factor for impact drop resistance. In order to solve this problem, we developed a machine learning program for cover glass that can predict the breakage height based on stress and mapped evaluation data based on the measured stress profile data and the actual drop breakage simulated evaluation. Especially, eXplainable AI (XAI) method is used to identify the effective factors on drop breakage height. And the test and measurement data were applied to various chemically strengthened glass for analysis.In this study, it was possible to predict the drop breakage height only by measuring the stress profile of chemically strengthened glass. The feature value of chemically strengthened that has the most effect on the drop breakage resistance on rough surfaces was identified to be stress value at 30um in the case of alkali aluminosilicate glass. And it was proved that the drop breakage height was improved by 25% only by increasing the compressive stress at 30um depth.

Experimental study of single bubble breakage in turbulent flow field: Evaluation of breakage models

The breakage of bubbles in a turbulent fluid flow is studied to gain more insight into the gas bubbles breakage mechanisms and assist evaluating the breakage models used in Population Balance Modelling (PBM) for more accurate predictions. Experimental tests were performed for air bubbles in flows with different levels of turbulence intensity. A few of the existing models were evaluated against the experimental results and the measurements were used for determination of constant parameters of breakage functions. Moreover, new modifications to existing models were proposed to improve the prediction of breakage functions for the case of cascade breakage. The new functions proposed for the case of cascade breakage of bubble were also tested for liquid drop breakage. A discussion regarding the practicality of the conventional breakage models is presented.

Towards harnessing hydrodynamic cavitation for producing emulsions: Breakage of an oil drop in a vortex based cavitation device

Emulsions are used as delivery vehicles for many active and functional chemical ingredients. There is an increasing need for developing new ways of producing emulsions on demand having desired critical quality attributes. Hydrodynamic cavitation (HC), which is a process of generation, growth and collapse of vapour cavities leading to intense localised shear and energy dissipation, offers an attractive platform for producing emulsions. In this work, we present experimental and computational results of a breakage of a single oil drop injected in a HC device. A single drop of oil was injected in a continuous stream of demineralised water flowing through a vortex based HC device. Tween 20 surfactant (2%) was used to prevent coalescence. The droplet size distribution (DSD) at the outlet of HC device was characterised using the imaging method. A detailed 3D computational model was developed to simulate turbulent cavitating flow through the considered HC device and resulting drop breakage and droplet size distribution. The developed model was used to quantitatively relate Sauter mean diameter (d32) and droplet size distribution (DSD) at the outlet with the operating parameters of the HC device. A single-pass through the vortex based HC device was able to bring down droplet size from ∼103 µm to ∼101 µm. The data and the model discussed in this work will provide a systematic basis for developing models, cavitation devices and operating protocols to produce emulsions with desired DSD.

Modeling surfactant and drop size dynamics in polydisperse liquid-liquid systems with population balances

A population balance framework based on high order moment conserving method of classes is extended to capture surfactant dynamics and its effect on drop size distributions. The proposed method is flexible for incorporating various closure models for drop breakage and coalescence, mass transfer, and physical equilibria between dispersed and continuous phase as well as for adsorption to the interface. The method is first schematically explained and derived in a generic form, and then appropriate closure models are discussed. The model is accurate and fast and can be implemented in process models, parameter optimization algorithms, and computational fluid dynamics software due to its high accuracy with limited number of additional variables.

Numerical study of microfluidic emulsion dynamics under the influence of heterogeneous surface wettability

Surface wettability plays a vital role in various natural phenomena and technical applications, such as coating, printing, membrane technology, microfluidic devices, and porous media flow. We numerically investigate the dynamics and stability of liquid–liquid dispersion flowing in a microfluidic channel with heterogeneous surface wettability, using a conservative phase-field lattice Boltzmann method. First, we validate the implementation of the wetting boundary conditions. We then perform three-dimensional simulations of a single drop motion immersed in another immiscible liquid in a square microchannel with alternating surface wettability: hydrophilic, hydrophobic, and again hydrophilic sections. The viscosity of the dispersed liquid (oil) is ten times higher than that of the continuous one (water), while the two liquids have equal densities. Depending on the drop length and Capillary number, calculated based on the drop velocity and the dynamic viscosity of the continuous phase, four different flow patterns are observed when the drop passes through the hydrophobic section. The distinct flow patterns include passing without any changes in drop shape or dynamics, adhesion of the dispersed liquid to the walls, phase inversion (i.e., water becomes the dispersed phase), and drop breakage. These outcomes are in close agreement with the experimental data. A detailed explanation of the choice of the numerical parameters is presented. The critical aspect of capturing the observed drop behavior is introducing an intervening thin-film of the continuous phase of at least three diffuse interface thicknesses (between the drop and channel walls).

Drop breakage in a single‐pass through vortex‐based cavitation device: Experiments and modeling

AbstractLiquid–liquid emulsions are used in many sectors such as personal care, home care, and food products. There is an increasing need for developing compact and modular devices for producing emulsions with desired droplet size distribution (DSD). In this work, we have experimentally and computationally investigated an application of vortex‐based hydrodynamic cavitation (HC) device for producing emulsions. The focus is on understanding drop breakage occurring in a single‐pass through the considered HC device. The experiments were performed for generating oil‐in‐water emulsion containing 1%–20% rapeseed oil. The effect of pressure drop across the HC device in the range of 50–250 kPa on drop breakage was examined. DSD of emulsions produced through a single pass was measured using the focussed beam reflectance measurements. Comprehensive computational fluid dynamics (CFD) model based on the Eulerian approach was developed to simulate multiphase cavitating flow. Using the simulated flow, population balance model (PBM) with appropriate breakage kernels was solved to simulate droplet breakage in a vortex‐based HC device. The device showed an excellent drop breakage efficiency (nearly 1% which is much higher than other commercial devices such as rotor–stators or sonolators) and was able to reduce mean drop size from 66 to ~15 μm in a single pass. The CFD and PBM models were able to simulate DSD. The presented models and results will be useful for researchers and engineers interested in developing compact devices for producing emulsions of desired DSD.

Drop sizes and population balance model for a Karr column

AbstractDrop sizes were investigated and measured in a Karr column. A stagewise population balance model was presented considering drop breakage and coalescence. The same breakage mechanisms observed in the single drop study were also found in column. The breakage probability model was selected by comparing the model from single drop study and the widely used models. Model parameters were calculated based on a two‐step optimization method. The results showed that the drop sizes decreased with an increase in reciprocating intensity, but changed slightly with phase velocities. The predicted drop sizes were compared to the experimental data in previous studies and good agreement was achieved. Finally, the population balance model along with some existing correlations were compared with the experimental data. It was found that the population balance model and correlations with the low agitation term provided better predictions of drop sizes in the Karr column. Transport Phenomena and Fluid Mechanics: Karr column, drop size distribution, population balance model, parameter optimization.

Assessment of population balance approach and maximum entropy on drop size behavior of vanadium extraction from sulfate solution in continuous pilot plant column

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.

Single oil drop breakage in water: Impact of turbulence level in channel flow

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.

Application of a drop breakage model using the full energy spectrum and a specific realisation of turbulence anisotropy

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.

Single drop breakage in a reciprocating plate column

Single drop breakage was investigated in a lab-scale reciprocating plate column. A high-speed camera was used to capture the drop breakage process and drop interactions with the plate. Image processing was completed to collect information on breakage location, breakage probability, breakage time and number of daughter drops under different operating conditions. The flow structure near the reciprocating plate was calculated using a computational fluid dynamics simulation with a moving reference frame. Two breakage mechanisms were observed experimentally, those mainly due to shear stress and those due to plate wettability. Spatial and temporal analysis was completed for the numerical shear stress distribution, and were compared to the breakage locations observed in the experiments. Breakage probability results showed that drops were more likely to breakup at higher reciprocating intensities, for lower interfacial tension systems and for a plate with fewer holes. Initial breakage time was measured but consistent values were not obtained. The number of daughter drops was influenced by the operating conditions and higher energies added to the system, resulting in the formation of more fragments. Finally, a correlation for breakage probability and an estimate of the critical Weber number were proposed.

Modeling drop breakage using the full energy spectrum and a specific realization of turbulence anisotropy

AbstractThe assumption of homogeneous isotropic turbulence when modeling drop breakage in industrially relevant geometries is questionable. We describe the development of an anisotropic breakage model, where the anisotropy is introduced via the inclusion of a perturbed turbulence spectrum. The selection of the perturbed spectrum is itself motivated by our previous large‐eddy simulations of high‐pressure homogenizers. The model redistributes energy from small to large scales, and assumes that the anisotropic part of the Reynolds stresses is confined to the energy‐containing range. The second‐order structure function arising from the perturbed spectrum is used in the standard framework of Coulaloglou and Tavlarides to calculate breakage frequency. While the base model exhibits non‐monotonic behavior (by predicting a maximum value for a certain drop size), the effect of anisotropy is shown to increase breakage frequency in length scales larger than this peak, thereby reducing non‐monotonicity. This effect is more pronounced for small turbulence Reynolds numbers.

Experimental investigation on single drop breakage in two-stream impinging microchannels

Experimental study on drop breakage is carried out in the microchannels utilizing head-on impingement configuration by observing a single drop breakup process. In this study, the breakage of oil drops with a diameter ranging from 30 to 200 μm is investigated in the vicinity of flows impingement region by using high-speed photography at varied flow rate conditions. The most prominent phenomenon of the single drop breakup in the two streams impinging flow field is that the drop tends to break into multiple fragments. The breakage time and the number of daughter drops in the resulting population are statistically analysed and found to be highly dependent on the mother drop size and energy dissipation rate. Two different micro-system geometries, the 600–600 system and the 600–300 system, are compared to evaluate the advantages and disadvantages of swirl flow developed due to the off-axis layout of inlet channels in the 600–300 system. The results show that swirl flow establishes a low-pressure area acting as the dead zone, where a drop can be trapped and then drastically stretched to breakup. Compared with the 600–600 system, the detrimental effect of swirl flow inside the 600–300 system on increasing the breakage time can be offset by a much greater amount of daughter drops generated. In general, the 600–300 system performs more effectively than the 600–600 system because of the less isotropic flow feature. And this superiority is more distinct when the energy dissipation rate is higher.