Multiple Coalescence Research Articles

Droplet dynamic behaviors on gas diffusion layer surface of various wettabilities in a PEMFC gas flow channel

ABSTRACT Droplet dynamic behaviors in a gas flow channel (GFC) of proton exchange membrane fuel cell (PEMFC) with gas diffusion layer (GDL) of various wettabilities are observed by using the volume of fluid (VOF) method in this work. Droplet deformation, detachment, breakup, and multiple droplets coalescence are investigated via an analysis of forces over the droplet. Results show that droplets tend to detach from a hydrophobic GDL surface at a high airflow velocity; while exhibiting significant deformation even breakup on a hydrophilic GDL surface. Besides, the interaction among the pressure force, shear force, wall adhesion force (arising from surface tension), and lift force over the droplet is examined to qualitatively elucidate the droplet dynamic behaviors. It is found that a hydrophobic GDL with a moderate airflow velocity can facilitate water removal from the GFC and maintain a relatively small spreading area; however, too high or too low an airflow velocity can cause a breakup or a slow drainage of the droplet, especially on a hydrophilic GDL surface. Thus, the design and operation of the PEMFC should consider both the wettability of GDL surface and the airflow velocity to achieve effective water management.

A large‐deviations principle for all the cluster sizes of a sparse Erdős–Rényi graph

AbstractLet be the Erdős–Rényi graph with connection probability as N → ∞ for a fixed t ∈ (0, ∞). We derive a large‐deviations principle for the empirical measure of the sizes of all the connected components of , registered according to microscopic sizes (i.e., of finite order), macroscopic ones (i.e., of order N), and mesoscopic ones (everything in between). The rate function explicitly describes the microscopic and macroscopic components and the fraction of vertices in components of mesoscopic sizes. Moreover, it clearly captures the well known phase transition at t = 1 as part of a comprehensive picture. The proofs rely on elementary combinatorics and on known estimates and asymptotics for the probability that subgraphs are connected. We also draw conclusions for the strongly related model of the multiplicative coalescent, the Marcus–Lushnikov coagulation model with monodisperse initial condition, and its gelation phase transition.

Water Distribution in Fuel Cell Gas Channels Using a Mechanistic Discrete Particle Model

Water removal and accumulation in fuel cell gas channels is a complex phenomenon which is a consequence of the strength of the capillary forces and inertial forces (1 < Re < 1000). The presence of water in the channel restricts the access of oxygen to diffuse through the gas diffusion layers to the catalyst layer. The air supplied exchanges momentum to the droplets and water clusters, causing detachment when the adhesion force is overcome.Water emerging from discrete locations as droplets interact with both the channel walls and each discrete water cluster, depending on the configuration and operating conditions. Complexity increases as multiple detachment and coalescence events occur over large channel lengths and time scales. Modelling these systems with traditional method computational fluid dynamic (CFD) methods is computationally expensive so we have developed a new mechanistic discrete particle model to handle the liquid water two-phase flow.Taking inspiration from interface resolving volume of fluid (VoF) simulations of water flow in gas channels, we use analytically equations determined by the equilibrium contact angle in different configurations on the channel wall to predict detachment times and coalescence events. We compare the prediction of water area coverage ratio and channel saturation to the VoF simulations and can also estimate dynamic pressure drop.Using this model, we are able to investigate the dynamic effects of liquid water accumulation and distribution in the channel, with often periodic detachment events arising from the formation of liquid plugs. Consequently, the model is able to investigate the effect of the channel wall wettability, from hydrophilic to hydrophobic and the impact that has on the distribution and accumulation of water in the system.We compare the speed of this model against the VoF simulations to show that this type of modelling of two-phase flow in the channel can enable higher resolution accuracy when coupled with continuum scale approaches. Furthermore, with this approach it is possible to investigate the effect of: channel dimensions, liquid water flow rate and spatial location of liquid water emergence. This should allow for designed fuel cell structures to be evaluated. Figure 1

A probabilistic approach to the leader problem in random graphs

We study the fixation time of the identity of the leader, that is, the most massive component, in the general setting of Aldous's multiplicative coalescent, which in an asymptotic sense describes the evolution of the component sizes of a wide array of near‐critical coalescent processes, including the classical Erdős‐Rényi process. We show tightness of the fixation time in the “Brownian” regime, explicitly determining the median value of the fixation time to within an optimal O(1) window. This generalizes Łuczak's result for the Erdős‐Rényi random graph using completely different techniques. In the heavy‐tailed case, in which the limit of the component sizes can be encoded using a thinned pure‐jump Lévy process, we prove that only one‐sided tightness holds. This shows a genuine difference in the possible behavior in the two regimes.

Discrete softening-damage model for fracture process representation with embedded strong discontinuities

A damage softening model is implemented into a discrete lattice framework with embedded strong discontinuities for the discontinuous representation of fracture. Such a model fits heterogeneous framework and allows capturing the complex fracture mechanisms in quasi-brittle materials under various quasi-static and dynamic loading conditions. Finite element implementation of damage softening constitutive model provides a very powerful computational tool for a description of material degradation processes which happen during monotonic loading, as well as unloading and reloading on the damaged material. In particular, the proposed model can capture the processes such as reduction of material stiffness, crack opening-closing mechanisms and reloading that follows the inverse of compliance modulus. Numerical examples are performed to demonstrate the effectiveness and robustness of the model fracture capabilities. The two examples deal with quasi-static fracture mechanisms of a heterogeneous material. The fragmentation of a cylinder in dynamics framework subjected to internal pressure and inertial forces is given as well. The plots of all components of internal energy (the dissipated fracture energy, elastic strain and kinetic energy) in dynamic fracture process are provided. The model of this kind can simulate multiple cracks formation, coalescence, propagation and mesh independent results.

Multiple Crack Propagation and Coalescence in Finite Elements with Minimal Local Remeshing Using the Subregion Generalized Variational Principle

Multiple crack propagation and coalescence in two-dimensional linear elastic media were modeled using the finite-element method (FEM) in conjunction with the subregion generalized variational principle. The proposed approach computes the stress intensity factor (SIF) accurately, as proved in a previous work. The approach results in regular geometric meshes. A multiple crack propagation scheme was developed in this study. The scheme follows the crack propagation by moving just the complementary energy subregion on the basis of the regular mesh. Consequently, it requires only minimal local remeshing without affecting most of the existing mesh. The scheme can handle crack coalescence easily. These advantages simplify the modeling and thus improve the efficiency. Four numerical examples, including a structure containing 10 cracks, were investigated to demonstrate the accuracy and efficiency of the proposed approach.

Experimental and Numerical Investigation on Shear Failure Behavior of Rock-like Samples Containing Multiple Non-Persistent Joints

The instability of rock slopes and underground engineering structures is usually caused by shear sliding along discontinuities, such as joints or faults, which are usually non-persistent. It is important to study the shear failure behavior of non-persistent joints to better understand the instability mechanism of jointed rock masses. In this research, rock-like samples containing multiple non-persistent joints were prepared and used for direct shear tests under constant normal load. The test results showed that the shear failure of multiple non-persistent joints usually involves multiple coalescence modes of rock bridges, which are affected by joint configurations and normal stress. Under the same normal stress, the shear strength, and dilation behavior are mostly dominated by joint persistency, which essentially determines the roughness of the macroshear fracture surface. Furthermore, the acoustic emission characteristics of non-persistent joints were evaluated by the hit rate, energy rate, and b value. A lower b value, indicating a more intense shear failure, is usually related to a smaller joint persistency and medium joint spacing. Finally, the cracking process, force evolution, and micro-cracking mechanism of multiple non-persistent joints were revealed using particle flow code.

Efficient coalescence of microdroplet in the cross-focused microchannel with symmetrical chamber

A cross-focused microchannel with symmetrical chamber is constructed to improve coalescence efficiency of droplets. The flow behavior of droplets and time scale are investigated experimentally. Results show that the flow patterns could be divided into four regimes: long droplet, multiple coalescence, double coalescence and non-coalescence. Moreover, the evolutions of deformation value and rotation angle of droplets are studied to understand the mechanism of droplets coalescence. Asynchronous coalescence could appear in this configuration on account of the existence of stagnancy time. The dimensionless liquid drainage time declines exponentially with the dimensionless velocity of continuous phase. The present configuration allows droplets to coalesce asynchronously, which greatly expands applicable operation region and accordingly facilitates the controllability of droplets coalescence.

Microfluidic Chamber Design for Controlled Droplet Expansion and Coalescence.

The defined formation and expansion of droplets are essential operations for droplet-based screening assays. The volumetric expansion of droplets causes a dilution of the ingredients. Dilution is required for the generation of concentration graduation which is mandatory for many different assay protocols. Here, we describe the design of a microfluidic operation unit based on a bypassed chamber and its operation modes. The different operation modes enable the defined formation of sub-µL droplets on the one hand and the expansion of low nL to sub-µL droplets by controlled coalescence on the other. In this way the chamber acts as fluidic interface between two fluidic network parts dimensioned for different droplet volumes. Hence, channel confined droplets of about 30–40 nL from the first network part were expanded to cannel confined droplets of about 500 to about 2500 nL in the second network part. Four different operation modes were realized: (a) flow rate independent droplet formation in a self-controlled way caused by the bypassed chamber design, (b) single droplet expansion mode, (c) multiple droplet expansion mode, and (d) multiple droplet coalescence mode. The last mode was used for the automated coalescence of 12 droplets of about 40 nL volume to produce a highly ordered output sequence with individual droplet volumes of about 500 nL volume. The experimental investigation confirmed a high tolerance of the developed chamber against the variation of key parameters of the dispersed-phase like salt content, pH value and fluid viscosity. The presented fluidic chamber provides a solution for the problem of bridging different droplet volumes in a fluidic network.

Stochastic block model in a new critical regime and the interacting multiplicative coalescent

This work exhibits a novel phase transition for the classical stochastic block model (SBM). In addition we study the SBM in the corresponding near-critical regime, and find the scaling limit for the component sizes. The two-parameter stochastic process arising in the scaling limit, an analogue of the standard Aldous’ multiplicative coalescent, is interesting in its own right. We name it the (standard) Interacting Multiplicative Coalescent. To the best of our knowledge, this object has not yet appeared in the literature.

Dynamics of phase separation of sheared inertialess binary mixtures

When a viscous binary mixture subject to an applied shear flow is rapidly quenched into the unstable region of its phase diagram, the resulting phase separation is influenced by two competing effects. On one hand, nuclei of the minority phase tend to grow with a constant growth rate, while, on the other hand, they are stretched along the flow direction, forming thinner and thinner layered domains that eventually break. We simulate the dynamics of this system with a thermodynamics-based diffuse interface model, accounting for the full interplay between hydrodynamics (i.e., the Navier–Stokes equations) and species conservation (i.e., the Cahn–Hilliard equation) coupled via the Korteweg body-force. We show that periodic steady-state configurations with stable droplets are obtained for low capillary numbers while phase separation takes place along bands oriented in the direction of the flow in the case of strong shear because, in the long term, diffusion in the cross-flow direction prevails on the convective flow field. The dynamics of phase separation is highly non-linear and diverse even for inertialess flow, featuring multiple coalescence and breakups: although some typical time scaling for the characteristic droplet size in the flow and cross-flow directions can be obtained, the full evolution cannot be characterized only by the capillary number. The wide range of droplet morphologies predicted by the model, from round and elongated shapes to bands and hollow droplets, suggests interesting applications for manufacturing of polymers and soft materials.

Numerical study on electrohydrodynamic multiple droplet interactions.

We present a numerical study of inviscid multiple droplet coalescence and break-up under the action of electric forces. Using an embedded potential flow model for the droplet hydrodynamics, coupled with an unbounded exterior electrostatic problem, we are able to perform computations through various singular events and analyze the effects of the electrical field intensity on droplet interactions. Laboratory experiments on the electrodynamics of droplet pairs show a much richer, and sometimes unexpected, behavior than that of isolated droplets. For example, it has been found that opposite charged droplets tend to repel each other when the electric field intensity is above a certain critical value. Although the mathematical model employed in this work incorporates very simple flow and electric assumptions, many of the droplet coalescence patterns seen in laboratory experiments can be reproduced. In this model, the interaction pattern of two droplets of radii R_{0} separated a distance D_{0}, depends on the ratio X_{0}=D_{0}/R_{0} and the applied uniform electric field intensity, E_{∞}. By performing a vast number of numerical simulations we are able to characterize the coalescence modes before and after drop merging as a function of these two parameters. The simulations predict that droplet repulsion occurs within a narrow interval of E_{∞} values, different for each X_{0}. Surprisingly, in this E_{∞} interval, a sharp transition between two power-law precoalescence flow regimes is seen. The evolution of several flow characteristics before and after coalescence, and the shape of the deformed droplets at coalescing time and the double cone angle, are also addressed and analyzed in detail. Cone angles below 35^{∘} lead to droplet coalescence for any X_{0} value, which is in accordance with previously reported studies. Finally, it is shown that the model and algorithm can handle multiple droplet interactions. The simulations qualitatively match results from water in oil experiments in microchannels, despite the fact that the exterior fluid is not considered in the mathematical model.

The eternal multiplicative coalescent encoding via excursions of Lévy-type processes

The multiplicative coalescent is a mean-field Markov process in which any pair of blocks coalesces at rate proportional to the product of their masses. In Aldous and Limic (Electron. J. Probab. 3 (1998) Paper no. 3) each extreme eternal version of the multiplicative coalescent was described in three different ways, one of which matched its (marginal) law to that of the ordered excursion lengths above past minima of a certain Lévy-type process. Using a modification of the breadth-first-walk construction from Aldous (Ann. Probab. 25 (1997) 812–854) and Aldous and Limic (Electron. J. Probab. 3 (1998) Paper no. 3), and some new insight from the thesis by Uribe Bravo (Markovian bridges, Brownian excursions, and stochastic fragmentation and coalescence (2007) UNAM), this work settles an open problem (3) from Aldous (Ann. Probab. 25 (1997) 812–854) in the more general context of Aldous and Limic (Electron. J. Probab. 3 (1998) Paper no. 3). Informally speaking, each eternal version is entirely encoded by its Lévy-type process, and contrary to Aldous’ original intuition, the time for the multiplicative coalescent does correspond to the linear increase in the constant part of the drift of the Lévy-type process. In the “standard multiplicative coalescent” context of Aldous (Ann. Probab. 25 (1997) 812–854), this result was first announced by Armendáriz in 2001, while its first published proof is due to Broutin and Marckert (Probab. Theory Related Fields 166 (2016) 515–552), who simultaneously account for the process of excess (or surplus) edge counts.

Probabilistic modeling and simulation of multiple surface crack propagation and coalescence

In the low cycle fatigue (LCF) regime, fatigue failure of metallic materials with high strength and less impurities generally dominates by multiple surface crack propagation and coalescence, in which its final failure shows a stochastic nature on crack initiation, propagation and coalescence under cyclic loadings. According to this, the competing failure modes of multiple surface cracks and interior cracks are studied through coupling numerical simulations with fracture mechanics methods. In particular, a probabilistic procedure for modeling multiple surface crack propagation and coalescence is established by incorporating Monte Carlo simulation with experimental evidences, including surface crack density and crack length distributions measured from LCF replica tests of 30NiCrMoV12 steel. In addition, it calculates the probability of coalescence of neighboring cracks with allowance for their interactions and local plastic deformation at the crack tips. Finally, it estimates the remaining usage lives of specimens from initial state to critical cracks by propagation and coalescence of dispersed cracks.

Statistics of the front of state switching propagation in a 1D nanosystem with the multiple nucleation of new phase domains on randomly distributed active centers formed by local defects

State switching processes play an important role in the control of nanodevices and properties of many quasi-1D objects in physics, chemistry and biology. The switching a metastable state into an energetically preferable state in extended systems often occurs through the nucleation and extension of domain of the new phase. In real systems new domains arise as a rule on defects or sample edges. Usually considered limit cases are the propagation of the edge domain wall over the whole system or multiple nucleation and coalescence of domains in the volume of the material. This paper deals with the more general situation of front propagation of the switching state from the sample edge simultaneously with the multiple nucleation of the new phase domains on randomly located defects in the volume. The distinction of the considered model from a large number of close ones is the account of the combination of two factors: (1) the study of the propagation of the state switching front from the sample boundary in a semi-infinite system, and (2) a detailed statistical description of the front runs in the fluctuating medium in terms of distribution functions, that is, beyond the framework of the mean-field approach. The corresponding statistically-kinetic problem of ‘the relay’ run lengths of the state switching front is exactly solved with the calculation of the distributions of the lengths of run and times of state switching in an ensemble of 1D systems. Also the full generating function for finding the average magnitude and dispersion of run lengths as well as higher moments of the distribution of run lengths of the state switching front is calculated.

Multilocus nuclear markers provide new insights into the origin and evolution of the blackbuck (Antilope cervicapra, Bovidae)

Evolutionary relationships between members of the Antilopina taxon have been much debated in recent years. The ‘true antelope’ clade is currently comprised of 4 genera viz., Gazella, Nanger, Eudorcas and the monotypic genus Antilope, that includes A. cervicapra. Most studies have focused on the mitochondrial genome or morphological data to study their relationships. However, signals from mitochondrial data can often be misleading when compared with nuclear markers, as has been shown in multiple taxonomic groups. In this study, we revisit the phylogenetic relationships among members of Antilopina, particularly the phylogenetic position of A. cervicapra, using 12 nuclear markers and compare it with the mitochondrial tree. Furthermore, we explore the implications of the results of this study on the taxonomy and biogeography of Indian antelopes. The nuclear phylogenetic trees built using multiple coalescent and concatenated methods all supported a paraphyletic genus Gazella. Antilope was nested within Gazella as opposed to being sister to it, which was suggested by previous studies and our results based on mitochondrial markers. Our fossil-calibrated larger bovid phylogeny, based on nuclear markers, suggested that the Antilope lineage diverged from its sister species more recently in the Pleistocene, rather than in late Miocene as per previous studies. Our biogeographic analyses suggest that the lineage leading to genus Antilope dispersed into India from the Saharo-Arabian realm around 2 mya, post the expansion of grasslands. We speculate that the adaptations of this savanna-grassland specialist did not allow them to extend their range beyond the Indian subcontinent. Whereas, the only other true antelope in India, G. bennetti, extended its range into India more recently, probably after the establishment of the Thar desert in northwest India.

Hydraulic fracture simulation based on hydro-mechanical coupled element partition method

Element partition method (EPM) is a fracture simulation method. It takes advantage of geometry feature of triangular element to derive the stiffness matrix of a cracked element. Once a fracture runs across a triangular element, this element will be transformed into a cracked element. The contact and friction between crack faces are automatically incorporated into the numerical model. By this means, any number of fractures can be embedded into a prescribed background mesh without introduction of any extra degree of freedom. It avoids the setup of joint element and remeshing issues in fracture simulation. Hence, the EPM presents great advantage in dealing with the massive fractures. To simulate the hydraulic fracture more effectively, a fully hydro-mechanical coupled equation is established for the cracked element. It can account for the interactions between the mechanical field and the hydraulic field in a cracked element. The KGD verification suggests that this method is validated in hydraulic fracture simulation. It can effectively simulate the multiple hydraulic fracture propagation and coalescence. It provides a simple and efficient simulation method for hydraulic fracturing in the complex reservoir.

Feller property of the multiplicative coalescent with linear deletion

We modify the definition of Aldous’ multiplicative coalescent process (Ann. Probab. 25 (1997) 812–854) and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model (J. Stat. Phys. 137 (2009) 459–499) and the so-called rigid representation of such scaling limits (Electron. J. Probab. To appear).

Defects as a root cause of fatigue failure of metallic components. I: Basic aspects

Abstract According to the definition of the ASM handbook [ [1] , [3] ], a defect is “an imperfection … that can be shown to cause failure by a quantitative analysis and that would not have occurred in the absence of the imperfection”. The topic of the present three-part review is a discussion of defects which can cause failure in cyclically loaded structures. The features discussed comprise material defects such as non-metallic inclusions, pores or micro-shrinkages, etc. and geometric defects such as surface roughness and secondary notches which have their origin in manufacturing, and defects such as surface damage due to scratches, impact events or contact fatigue as well as corrosion pits which arise in service. In this first part, the discussion is prefaced by an introduction to basic aspects which are essential for a deeper understanding of the characteristics and mechanisms how the defects influence fatigue crack initiation and propagation. These include the life cycle of a fatigue crack from initiation up to fracture, crack arrest, multiple crack initiation and coalescence, and the material and geometrical properties affecting these.

A study of concrete cover separation failure in FRP-plated RC beams via an inter-element fracture approach

The phenomenon of concrete cover separation failure in FRP strengthened RC elements, unlike plate-end and mid-span debonding failure modes, has been not analyzed in depth in the literature and simplified strength models are mainly available, which possess a limited predictive capability. To this end in the present work, a novel numerical approach to investigate cover separation in FRP-plated RC beams is proposed, based on an inter-element cohesive fracture approach able to simulate multiple crack onset, propagation and coalescence in concrete structures, used in combination with an embedded truss model for taking into account the interaction between concrete cracks and tensile steel rebars. This approach has been validated by performing complete failure simulations for benchmark crack propagation examples, and subsequently has been exploited for predicting the load-carrying capacity and the related failure mode of real-scale retrofitted RC elements. Suitable comparisons with available experimental results have clearly shown the reliability and the effectiveness (in terms of numerical accuracy) of the proposed fracture approach.