Onset Of Coalescence Research Articles

High-speed tracking of coalescence and mixing of optically controlled droplets

We are presenting an all-optical platform for on-demand and nonintrusive studies of coalescence of micron-sized liquid droplets in air. The platform has the purpose to mimic the airborne conditions occurring in typical environments where droplet interactions are involved. By means of the Förster resonance energy transfer mechanism, we have been able to track the dynamics of two coalescing glycerol droplets, with a radius of ∼10µm and a temporal resolution of 86µs. At the onset of coalescence, a fast mixing is observed. Such an effect depletes the fluorescence of the donor fluorophore to half its initial intensity on a timescale below the temporal resolution of our platform, whereas a complete mixing is observed to occur on a timescale of seconds. The experimental platform design and findings facilitate an increased understanding of the microphysics of collisions, coalescence, and the subsequent mixing/diffusion of droplets on the micrometer lengthscale and the microsecond timescale. Published by the American Physical Society 2024

Numerical Investigation of Gas Bubble Interaction in a Circular Cross-Section Channel in Shear Flow

This work’s goal is to numerically investigate the interactions between two gas bubbles in a fluid flow in a circular cross-section channel, both in the presence and in the absence of gravitational forces, with several Reynolds and Weber numbers. The first bubble is placed at the center of the channel, while the second is near the wall. Their positions are set in such a way that a dynamic interaction is expected to occur due to their velocity differences. A finite element numerical tool is utilized to solve the incompressible Navier–Stokes equations and simulate two-phase flow using an unfitted mesh to represent the fluid interface, akin to the front-tracking method. The results show that the velocity gradient influences bubble shapes near the wall. Moreover, lower viscosity and surface tension force account for more significant interactions, both in the bubble shape and in the trajectory. In this scenario, it can be observed that one bubble is trapped in the other’s wake, with the proximity possibly allowing the onset of coalescence. The results obtained contribute to a deeper understanding of two-phase inner flows.

Characterization and modeling of the damage mechanisms in ductile steel metal-matrix composites: Application to virtual forming

The aim of this work is to investigate the damage mechanisms and stiffness loss in Fe-TiB2 metal-matrix composites during plastic deformation. First, experimental results of interrupted tensile tests are performed to quantify the evolution of damage, using SEM observations, as well as the decrease of Young’s modulus as a function of the tensile strain. The experimental results are then used to calibrate a two-step homogenization model for metal-matrix composites in which the nucleation and growth of voids modify incrementally the overall elastic properties. The model is finally applied to the numerical prediction of stiffness loss in a problem of metal forming based on Nakazima tests. Overall, the stiffness loss predicted before the onset of coalescence is moderate and its distribution is homogeneous, emphasizing that Fe-TiB2 metal-matrix composites could be used in applications requiring metal forming.

Damage characterization in a ferritic steel sheet: Experimental tests, parameter identification and numerical modeling

The Gurson–Tvergaard–Needleman (GTN) model includes several parameters of different nature. Some of them have micromechanical roots while others are strictly phenomenological. Hence, a methodology should be developed in order to obtain a robust set of parameters with both numerical and physical meaning. The material parameters of the GTN model are found using an identification methodology based on experimental-numerical results. The method is applied on a DC01 ferritic steel sheet. An extended version of the Gurson model, incorporating plastic anisotropy, mixed isotropic-kinematic hardening, void nucleation, growth, coalescence and shear is used. Material parameters are obtained based on an inverse optimization and a sensitivity analysis on specimens with different geometries. The onset of coalescence, reflected as the loss of load carrying capacity in the force-displacement curve, is correctly predicted by the extended GTN model. The strain distribution, obtained by digital image correlation, is also correctly simulated. Nevertheless, the model does not to predict the increase of strain observed experimentally, because of the decoupling between hardening and the damage variable. In this respect, the article provides experimental evidence of the limitations of a GTN model based on a strain-controlled nucleation law with heuristic extensions of hardening.

Damage evolution and void coalescence in finite-element modelling of DP600 using a modified Rousselier model

Numerical simulations of uniaxial tensile deformation of DP600 steel were carried out using a modified Rousselier ductile damage model at different strain rates ranging from 0.1 to 100 s−1. Since the original Rousselier model does not consider any secondary void nucleation or coalescence criteria, it was modified by including a strain-controlled void nucleation function, a coalescence criterion and a void growth acceleration function as the post-coalescence regime identifier. The predicted flow behaviour, the evolution of damage and critical strain and void volume fraction at the onset of coalescence were assessed to evaluate the performance of the proposed model at each strain rate. In addition, X-ray tomography analysis was employed to evaluate the void volume fraction predicted by each void coalescence criterion. The modified Rousselier model showed good agreement with the experimentally determined strain and void volume fraction at the onset of coalescence. Also, it could successfully predict the damage distribution and the final damage geometry of DP600 tensile specimens.

Fluid mechanics calculations in physics of droplets II: A study of head-on collisions for the system water–heptane

In this study, the finite volume method is employed to simulate the coalescence collision between water drops immersed in a continuous phase (n-heptane). It chooses a range of values for the velocity of collisions for the finite volume calculations yielding different possible outcomes of the collision process (permanent coalescence, formation of satellite drops, etc.). The streamlines are calculated for the process of coalescence and fragmentation of drops. These streamlines allow the understanding of the dynamics of the droplets immersed in the n-heptane phase. The effect of the interfacial tension is shown in the oscillations that the droplets exhibit, which after some time tends to the spherical form. It can be seen that when the velocity of collision is 0.2 m/s the droplets do not form an interfacial film just before the onset of coalescence. On the other hand, when the inertial forces are more important with a velocity of collision of 3.5 m/s the system shows an interfacial film of circular section, and when the velocity of collision is increased to a value of 16.0 m/s the system of drops forms a multiple satellite droplets but at the beginning of the dynamics where the circular interfacial film appears.

Magnetism and morphology of Co nanocluster superlattices onGdAu2/Au(111)–(13×13)

We present a comprehensive study of the magnetism and morphology of an ultrahigh density array of Co nanoclusters self-assembled on the single atomic layer GdAu2 on Au(111) template surface. Combining scanning tunneling microscopy, x-ray magnetic circular dichroism, and magneto-optical Kerr effect measurements, we reveal a significant enhancement of the perpendicular magnetic anisotropy energy for noncoalesced single atomic layer nanoclusters compared to Co/Au(111). For coverages well beyond the onset of coalescence, we observe room-temperature in-plane magnetic remanence.

The coalescence of liquid drops in a viscous fluid: interface formation model

AbstractThe interface formation model is applied to describe the initial stages of the coalescence of two liquid drops in the presence of a viscous ambient fluid whose dynamics is fully accounted for. Our focus is on understanding (a) how this model’s predictions differ from those of the conventionally used one, (b) what influence the ambient fluid has on the evolution of the shape of the coalescing drops and (c) the coupling of the intrinsic dynamics of coalescence and that of the ambient fluid. The key feature of the interface formation model in its application to the coalescence phenomenon is that it removes the singularity inherent in the conventional model at the onset of coalescence and describes the part of the free surface ‘trapped’ between the coalescing volumes as they are pressed against each other as a rapidly disappearing ‘internal interface’. Considering the simplest possible formulation of this model, we find experimentally verifiable differences with the predictions of the conventional model showing, in particular, the effect of drop size on the coalescence process. According to the new model, for small drops a non-monotonic time dependence of the bridge expansion speed is a feature that could be looked for in further experimental studies. Finally, the results of both models are compared to recently available experimental data on the evolution of the liquid bridge connecting coalescing drops, and the interface formation model is seen to give a better agreement with the data.

A NUMERICAL AND EXPERIMENTAL INVESTIGATION OF COALESCENCE BETWEEN CYLINDRICAL HOLES

A sequential digital image technique was employed to detect the onset of coalescence between pairs of holes in tensile specimens. The coalescence event was induced between cylindrical holes that were positioned with various spacing and ligament orientations. Using finite-element analysis as a framework, the coalescence predictions of a classic micromechanical model were compared with the experimental coalescence results. It was found that the predicted strains at coalescence could be significantly improved by accounting for local work-hardening in the ligament region between the two holes. Digital image correlation was used to extract strain values from the digital image record, for both the far-field and the intervoid ligament.

Size effects in ductile failure of porous materials containing two populations of voids

Abstract The ductile failure behavior of porous materials containing two populations of voids of different size is investigated numerically by means of 3D cell model calculations. In contrast to previous studies a non-local Gurson model is used to describe the secondary void population in the matrix material. Due to the internal length scale incorporated in the non-local model, it is possible to describe the size of the secondary voids in the matrix material. The results are obtained for loading states with different stress triaxialities and Lode parameters. The influence of the size of the secondary voids is analyzed and it is shown that larger secondary voids lead to a higher stress carrying capacity. This size effect is studied for different primary void arrangements. Furthermore, the strain and primary void volume fraction at the onset of coalescence are presented and cross references to experimental findings are drawn.

Molecular-dynamics study of the viscous to inertial crossover in nanodroplet coalescence

We have studied the coalescence of three-dimensional (3D), quasi-two-dimensional (quasi-2D), and 2D liquid, equal-size Cu and Si nanodroplets in the viscous and inertial regimes using classical molecular-dynamics simulations. At the onset of coalescence, a bridge (of radius $r$) between the droplets forms and develops until the merge is complete. For the 3D and quasi-2D systems, our results show a transition from a viscous-dominated regime at very short time, where $r\ensuremath{\propto}{\ensuremath{\tau}}^{1}$, to a regime dominated by inertial forces at longer time, with $r\ensuremath{\propto}{\ensuremath{\tau}}^{0.5}$, in agreement with theoretical models; the viscous regime is not observed in two dimensions, where only inertial forces seem to be operating. A detailed analysis of the 3D data suggests that the viscous-to-inertial crossover length ${l}_{c}({R}_{0},T)$ (with ${R}_{0}$ being the initial radius of the droplets and $T$ being the temperature) behaves differently in the two systems. While ${l}_{c}\ensuremath{\propto}{R}_{0}^{1/2}$ and depends only weakly on temperature in l-Cu, as theory predicts, ${l}_{c}\ensuremath{\propto}{R}_{0}^{0.96}{T}^{0.41}$ in l-Si. We conclude from these observations and corresponding experimental data that the prefactor for the dependence of $r$ on time in the inertial regime is not ``universal'' and actually depends on system properties, including initial radius, viscosity, and surface tension.

A criterion for the onset of void coalescence under combined tension and shear

Depending on the relative positions of voids and on the loading conditions, shear loading components can play an important role in the void coalescence process leading to ductile fracture. Yet, most void coalescence criteria including the original criterion of Thomason, and its various extensions/improvements, take only normal loads into account and neglect the contribution from shear loads to coalescence. Shear can affect both the stress/strain at the onset of coalescence and the direction of deformation localization. In this paper, first, the predictive capabilities of different coalescence criteria without shear effect are critically assessed and the expressions involved in the original Thomason criterion are fine-tuned by comparing with 3D finite element calculations performed on a unit cell containing a spheroidal void. Then, the improved Thomason criterion is theoretically extended—by using limit load analysis—to incorporate the effect of shear. The predictions of this new coalescence criterion are in good agreement with the results produced by 3D finite element calculations, for both loadings involving or not a shear component.

Void growth and coalescence in single crystals

Void growth and coalescence in single crystals are investigated using crystal plasticity based 3D finite element calculations. A unit cell involving a single spherical void and fully periodic boundary conditions is deformed under constant macroscopic stress triaxiality. Simulations are performed for different values of the stress triaxiality, for different crystal orientations, and for low and high work-hardening capacity. Under low stress triaxiality, the void shape evolution, void growth, and strain at the onset of coalescence are strongly dependent on the crystal orientation, while under high stress triaxiality, only the void growth rate is affected by the crystal orientation. These effects lead to significant variations in the ductility defined as the strain at the onset of coalescence. An attempt is made to predict the onset of coalescence using two different versions of the Thomason void coalescence criterion, initially developed in the framework of isotropic perfect plasticity. The first version is based on a mean effective yield stress of the matrix and involves a fitting parameter to properly take into account material strain hardening. The second version of the Thomason criterion is based on a local value of the effective yield stress in the ligament between the voids, with no fitting parameter. The first version is accurate to within 20% relative error for most cases, and often more accurate. The second version provides the same level of accuracy except for one crystal orientation. Such a predictive coalescence criterion constitutes an important ingredient towards the development of a full constitutive model for porous single crystals.

Void growth to coalescence in a non-local material

The size-effect in metals containing distributed spherical voids is analyzed numerically using a finite strain generalization of a length scale dependent plasticity theory. Results are obtained for stress-triaxialities relevant in front of a crack tip in an elastic-plastic metal. The influence of different material length parameters in a multi-parameter theory is studied, and it is shown that the important length parameter is the same as under purely hydrostatic loading. It is quantified how micron scale voids grow less rapidly than larger voids, and the implications of this in the overall strength of the material is emphasized. The size effect on the onset of coalescence is studied, and results for the void volume fraction and the strain at the onset of coalescence are presented. It is concluded that for cracked specimens not only the void volume fraction, but also the typical void size is of importance to the fracture strength of ductile materials.

Coalescence of viscous liquid drops

We report on studies of the early stage of coalescence of two liquid drops. The drops were high viscosity silicon oil immersed in a water-alcohol mixture of the same density in order to eliminate the effects of gravity. The viscosity was sufficiently large that measurements could be made under the conditions of Stokes flow. Measurements were made of the radius of the neck between the drops as a function of the time from the onset of coalescence, and the results compared with theoretical predictions.

Antiphase boundary network: A route to extract the island nucleation density

Epitaxial growth of Si or Ge on Si(001) and Ge(001) surfaces leads to the formation of an antiphase boundary network because adjacent (2×1) reconstructed islands can either be in-phase or out-of-phase with each other. We show that this antiphase boundary network can be used to extract the saturation island nucleation density well after the onset of coalescence. This method is more accurate than the commonly used method of counting the islands in the low coverage regime.

Coalescence and capillary breakup of liquid volumes

The problem of the mathematical modeling of coalescence and breakup of liquid volumes surrounded by an inviscid gas is considered. As is shown, an unphysical singularity in the known self-similar solutions of the Navier–Stokes equations intended to describe the topological transition of the flow domain arises as a consequence of the assumption that the free surface becomes smooth immediately after the onset of coalescence or remains so up to the very moment of breakup. Then the standard kinematic boundary condition prescribes that fluid particles belonging to the free surface remain there at all times and thus couples the scales for lengths and velocities in a self-similar solution leading to the singularity. An alternative approach allowing one to remove the singularity at a macroscopic level is formulated. Its key idea is that the topological transition, being a particular case of an interface formation/disappearance process, is associated with a free-surface cusp either propagating away from the point of initial contact of two volumes leading to their coalescence or “severing” a liquid thread connecting them in the case of breakup. The interface becomes (or, in a reverse flow, ceases to be) smooth at a finite distance from the point where, in the standard approach, a singularity would have taken place. An earlier developed macroscopic theory of interface formation/disappearance is applied without any ad hoc changes.

Evolution of morphology in compatibilized vs uncompatibilized polyamide blends

The development of phase morphology in non-reactive vs reactive polyamide blends with a styrene acrylonitrile (SAN) copolymer and SEBS (a styrenic triblock copolymer with ethylene-butylene midblocks) in a co-rotating twin screw extruder was investigated using electron microscopy techniques. For the polyamide/SAN systems, significant differences were observed between the evolution of morphology in non-reactive binary blends vs blends compatibilized with a reactive imidized acrylic (IA) polymer which is miscible in the SAN phase and has functional groups which are capable of reacting with the amine end groups in the polyamide phase. While a steady decrease in the dispersed phase particle size was observed in general for the non-reactive nylon 6/SAN blends with both increasing screw length and speed, for the ternary nylon 6/SAN/IA blends a dramatic drop in the dispersed phase particle size was observed in the initial region of the screw almost immediately after melting of the pellets followed by some coalescence of dispersed phase in the latter stages leading to a dual population of particle at the exit of the extruder. The extent and onset of coalescence after attainment of minimum particle size in the initial region of the screw in reactive nylon 6/SAN blends was found to be strongly dependent on the screw speed and configuration. The extent of chemical reaction along the extruder screw for reactive nylon 6/SAN blends was dependent on the screw speed, extruder configuration and flow rate. While similar differences in the evolution of morphology were observed between non-reactive and reactive polyamide/SEBS systems, changing the polyamide type from monofunctional (nylon x, e.g. nylon 6) to difunctional (nylon x, y, e.g. nylon 6,6) revealed interesting differences even within these reactive blends. Significant differences in both the development of morphology and reaction profile along the screw were also observed between binary and ternary nylon 6/rubber blends containing similar concentrations of reactive maleic anhydride functionality in the rubber phase using a fixed screw speed and configuration.

Misfit-related effects in the epitaxial growth of iron on W(110)

Time-resolved in situ STM has been used to investigate the growth of iron on W(110). In the submonolayer range, a strong inhibition of island coalescence is present up to 0.6 ML due to the misfit of 9.4%. The onset of coalescence can be correlated with the magnetic percolation in these thin layers. Growth at higher temperature leads to the development of a sequence of dislocation networks which start from the second iron layer on with a wider spaced one-dimensional array. With the third layer a second one-dimensional network in [001]-direction appears, showing relaxation to the bulk Fe lattice constant in only one direction. A further layer is necessary to introduce a two-dimensional network, leading to a fully relaxed Fe-layer. The growth of wedge-shaped 3D-islands on a misoriented W(110)-sample in the Stranski-Krastanov growth regime enables us to study different local layer thicknesses simultaneously. It is thus possible to examine the decrease in influence of the dislocation network on the surface topography.

Homoepitaxial growth on Pd(100)

We have studied the temperature- and coverage-dependent variation of diffraction-spot profiles during growth of Pd on Pd(100), using conventional low-energy electron diffraction (LEED). The crystal temperature is varied from 100 to 500 K during deposition, and the coverage is varied from 0 to 5 monolayers. The diffraction spot profiles are separable into two components: the Bragg peak, reflecting layer occupations; and a broad “foot”, reflecting the distribution of particles within layers. Between 200 and 400 K, the broad component adopts a ring-like appearance, with intensity maxima bracketing the Bragg peak. Development of the ring structure is associated with the onset of diffusion at 170–200 K (activation barrier of 12–14 kcal/mol). The diameter of the ring indicates an average separation between island centers of 28 ± 5 Å, at 300 K and at coverages below the onset of coalescence. Oscillations in the ring intensity as a function of coverage occur out-of-phase with oscillations in the Bragg intensity, and are associated with the successive filling of individual layers. By 500 K, both oscillations disappear, apparently due to the advent of step propagation as a major mechanism for film growth when diffusional processes accelerate.