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The initial coalescence of a pendant drop at bulk liquid was jointly investigated by an ultrahigh-speed DC electrical device, a high-speed camera, and a fast micro-Particle Image Velocimetry (micro-PIV). Extended to highly viscous...
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The initial coalescence of a pendant drop at bulk liquid was jointly investigated by an ultrahigh-speed DC electrical device, a high-speed camera, and a fast micro-Particle Image Velocimetry (micro-PIV). Extended to highly viscous non-Newtonian liquids, the variation of the coalescing width vs time confirms the distinct regimes reported for drop-drop configuration: linear in the inertially limited viscous regime; square root in the inertial regime; possibly a transient viscous regime in between with a logarithmic correction. The measured flow fields during coalescence reveal the transformation of surface energy to kinetic energy, so that the highly located inertia could play a dominant role in relation to the viscous force.
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We construct an extension of the A-coalescent to a spatial continuum and analyse its behaviour. Like the A-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced indi...
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We construct an extension of the A-coalescent to a spatial continuum and analyse its behaviour. Like the A-coalescent, the individuals in our model can be separated into (i) a dust component and (ii) large blocks of coalesced individuals. We identify a five phase system, where our phases are defined according to changes in the qualitative behaviour of the dust and large blocks. We completely classify the phase behaviour, including necessary and sufficient conditions for the model to come down from infinity.
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In this paper, we consider coalescing random walks on a general connected graph G = (V ,E).We set up a unified framework to study the leading order of the decay rate of P_t , the expectation of the fraction of occupied sites at ti...
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In this paper, we consider coalescing random walks on a general connected graph G = (V ,E).We set up a unified framework to study the leading order of the decay rate of P_t , the expectation of the fraction of occupied sites at time t , particularly for the 'Big Bang' regime where t ?t_(coal):= E(inf{s : There is only one particle at time s}). Our results show that P_t satisfies certain 'mean-field behaviors' if the graphs satisfy certain 'transience-like' conditions. We apply this framework to two families of graphs: (1) graphs given by the configuration model whose degree distribution is supported in the interval [3, d] for some d ≥ 3, and (2) finite and infinite transitive graphs. In the first case, we show that for 1?t ? |V |, Pt decays in the order of t~(-1), and (tP_t)~(-1) is approximately the probability that two particles starting from the root of the corresponding unimodular Galton-Watson tree never collide after one of them leaves the root. The number (tP_t)~(-1) is also roughly |V |/(2tmeet), where tmeet is the mean meeting time of two independent walkers. By taking the local weak limit, we prove convergence of tP_t as t →∞for the corresponding unimodular Galton-Watson tree. For the second family of graphs, we consider a growing sequence of finite transitive graphs G_n = (V_n,E_n), satisfying that tmeet = O(|V_n|) and the inverse of the spectral gap t_(rel) is o(|V_n|). We show that trel ? t ? t_(coal), (tP_t)~(-1) is approximately the probability that two random walks never meet before time t , and it is also roughly |V |/(2t_(meet)). In addition, we define a natural 'uniform transience' condition, and show that in the transitive setup it implies the above estimates of tP_t for all 1?t ?t_(coal). Estimates of tP_t are also obtained for all infinite transient transitive unimodular graphs, in particular, all transient transitive amenable graphs.
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A model is developed for the coalescence of unequal-sized amorphous primary particles commonly found in aerosol aggregates.Computational efficiency is achieved by deriving an analytical expression for the surface geometry of the c...
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A model is developed for the coalescence of unequal-sized amorphous primary particles commonly found in aerosol aggregates.Computational efficiency is achieved by deriving an analytical expression for the surface geometry of the coalescing particles and subsequently decoupling surface evolution from the fluid dynamic equations.Calculated shrinkage lengths and surface areas are in good agreement with results reported from finite element calculations for all particle size ratios considered.Results indicate that above a size ratio of 4,the normalized coalescence rate is independent of size ratio.Applying these results to the coalescence of SiO_2 particles indicates that rates are primarily dependent on the diameter of the smaller particle,although coalescence times do not scale linearly with either particle size ratio or total particle mass.Comparison with the widely used exponential model of Koch and Friedlander suggests that rates of surface area decrease are under-predicted by the Koch and Friedlander model.Modified values of the decay constant for both equal sized and heterogeneously sized particles are therefore proposed,with the value decreasing with increasing size ratio of the coalescing pair.
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For two approaching oil droplets, a region of arrested coalescence lies between full coalescence and total stability. Here the fusion of two droplets begins, but they are stopped from fully relaxing into one spherical droplet. The...
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For two approaching oil droplets, a region of arrested coalescence lies between full coalescence and total stability. Here the fusion of two droplets begins, but they are stopped from fully relaxing into one spherical droplet. The internal rigidity of the solid fat network within each droplet can provide the resistance necessary to arrest the shape change driven by Laplace pressure. These intermediate doublet structures lead to the partially-coalesced fat networks important for the desired physical properties of ice cream and whipped topping. The use of micromanipulation techniques allows coalescence events between two oil droplets to be microscopically observed. In this study, oil droplets composed of different fats were manipulated at varying elastic moduli, interfacial tension, and radii. It was seen that increasing the elastic moduli of the droplets or increasing droplet radii resulted in coalescence being arrested earlier. Under these experimental conditions, different interfacial tensions did not change the coalescence behavior between two oil droplets.
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Coalescent simulations are a widely used approach for simulating sample genealogies, but can become computationally burdensome in large samples. Methods exist to analytically calculate a sample's expected frequency spectrum withou...
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Coalescent simulations are a widely used approach for simulating sample genealogies, but can become computationally burdensome in large samples. Methods exist to analytically calculate a sample's expected frequency spectrum without simulating full genealogies. However, statistics that rely on the distribution of the length of internal coalescent branches, such as the probability that two mutations of equal size arose on the same genealogical branch, have previously required full coalescent simulations to estimate. Here, we present a sampling method capable of efficiently generating limited portions of sample genealogies using a series of analytic equations that give probabilities for the number, start, and end of internal branches conditional on the number of final samples they subtend. These equations are independent of the coalescent waiting times and need only be calculated a single time, lending themselves to efficient computation. We compare our method with full coalescent simulations to show the resulting distribution of branch lengths and summary statistics are equivalent, but that for many conditions our method is at least 10 times faster. (C) 2017 Elsevier Inc. All rights reserved.
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Oil-in-water emulsions stabilized with methylcellulose (MC) varied in stability depending on the composition of the fat phase. When droplets were composed entirely of liquid oil, MC was able to form a continuous, protective film a...
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Oil-in-water emulsions stabilized with methylcellulose (MC) varied in stability depending on the composition of the fat phase. When droplets were composed entirely of liquid oil, MC was able to form a continuous, protective film around the droplets. Therefore, when two liquid oil droplets were brought into contact, they underwent extreme shape deformation but did not coalesce, even when excess force was used. Subsequently, interfacial crystals extending into the aqueous phase from palm kernel oil droplets were aimed into an entirely liquid oil droplet. The MC-coated droplet would deform wherever the crystal contacted; however, the protruding crystals could not penetrate into the liquid oil droplet. Conversely, when the target droplet was composed of a small amount of solid fat that resulted in localized crystalline regions and the interfacial crystals of the second droplet were aimed at this region, they then easily pierced the droplet. This demonstrates that MC is an excellent stabilizer for liquid oil droplets but internal lipid crystals within fat globules can alter MC surface conformation to allow for crystal penetration and arrested coalescence.
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? 2023 The Author(s)A novel coalescence kernel with high predictive properties is constructed to be used within the population balance framework. The kernel includes the product of a collision frequency term and a novel binary coa...
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? 2023 The Author(s)A novel coalescence kernel with high predictive properties is constructed to be used within the population balance framework. The kernel includes the product of a collision frequency term and a novel binary coalescence probability expression. The probability expression employs critical velocity estimations from film drainage simulations that also considers particle surface and kinetic energies. Thus, the proposed expression possesses characteristics of all three commonly used approaches: film drainage, energy, and critical velocity models. The probability of a collision having a certain velocity and angle is considered through probability density functions while adapting to the Eulerian frame. A maximum collision angle that allows coalescence is defined. The kernel is free of artificially introduced tuning parameters and predicts the size distributions in bubbly pipe flow experiments exceptionally well, including complex behaviors such as emergence of secondary peaks in the distribution. The theory presented is equally valid for bubbles and droplets.
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In water-in-oil-in-water (W1/O/W2) double emulsions several irreversible instability phenomena lead to changes. Besides diffusive processes, coalescence of droplets is the main cause of structural changes. In double emulsions, inn...
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In water-in-oil-in-water (W1/O/W2) double emulsions several irreversible instability phenomena lead to changes. Besides diffusive processes, coalescence of droplets is the main cause of structural changes. In double emulsions, inner droplets can coalesce with each other (W1-W1 coalescence), inner droplets can be released via coalescence (W1-W2 coalescence) and oil droplets can coalesce with each other (O-O coalescence). Which of the coalescence pathways contributes most to the failure of the double emulsion structure cannot be determined by common measurement techniques. With monodisperse double emulsions produced with microfluidic techniques, each coalescence path can be observed and quantified simultaneously. By comparing the occurrence of all possible coalescence events, different hydrophilic surfactants in combination with PGPR are evaluated and discussed with regard to their applicability in double emulsion formulations. When variating the hydrophilic surfactant, the stability against all three coalescence mechanisms changes. This shows that measuring only one of the coalescence mechanisms is not sufficient to describe the stability of a double emulsion. While some surfactants are able to stabilize against all three possible coalescence mechanisms, some display mainly one of the coalescence mechanisms or in some cases all three mechanisms are observed simultaneously.
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Emulsification is a common process in the production in many non-solid foods. These food-emulsions often have high disperse phase volume fractions and slow emulsifier dynamics, giving rise to substantial coalescence during emulsif...
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Emulsification is a common process in the production in many non-solid foods. These food-emulsions often have high disperse phase volume fractions and slow emulsifier dynamics, giving rise to substantial coalescence during emulsification. Optimal design and operation of food-emulsification requires experimental methods to study how emulsification in general and coalescence in particular progresses under different conditions. Methods for coalescence quantification during emulsification has been suggested in literature but they are rarely used in food-emulsification research. This contribution offers a critical review of the different methods that have been suggested with special emphasis on their applicability to technical food-emulsification. The methods are critically compared in terms of design limitations, degree of quantification and applicability. A state-of-the-art in the form of two methods is identified and guidelines for their application are suggested. (C) 2016 Elsevier Ltd. All rights reserved.
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