Bubble interaction in low-viscosity liquids

An experimental study investigated how freely rising ellipsoidal bubbles approach each other, make contact and coalesce or breakup. Pulsed planar swarms of 10–20 bubbles with Eötvös numbers from 6.0 to 27.5 were released simultaneously in aqueous solutions of 0–48 wt% sugar with Morton numbers from 3.2 × 10⁻¹¹ to 3.7 × 10⁻⁶. Bubble interaction was recorded by a video camera following the rising bubbles. Essentially, all coalescence and breakup events occurred after, not during, wake-induced collisions by a complex process related to the bubble vortex shedding cycle. This same process was also found in multi-bubble clusters and may account for excess turbulent kinetic energy generation in bubbly flow.     

Investigation of binary drop rebound and coalescence in liquids using dual-field PIV technique

Experiments on binary drop collisions within an index-matched liquid were conducted for Weber numbers (We) in the range of 1–50. Drop pairs of water/glycerin mixture were injected horizontally into silicone oil and, due to gravitational effects, travelled on downward trajectories before colliding. A dual-field high-speed PIV measurement system was employed to quantify drop trajectories and overall collision conditions while simultaneously examining detailed velocity fields at the collision interface. Sequences of velocity and vorticity fields were computed for both larger and smaller fields of view. In the We range examined, both rebounding and coalescing behavior occurred. Coalescence was found to result from a combination of vortical flow within drops and strong drop deformation characteristic of higher We. Flow through the centers of opposing ring vortices, strengthened by drop deformation, enhanced drainage of the thin film in the impact region, leading to film rupture and coalescence. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Evaporation of pure liquids with increased viscosity in a falling film evaporator

The present study investigated fluid dynamics and heat transfer of viscous pure liquids in a falling film evaporator. This is of special benefit as it avoids mass transfer effects on the evaporation behaviour. Experiments at a single-tube glass falling film evaporator were conducted. It allowed a full-length optical film observation with a high-speed camera. Additionally the evaporator was equipped with a slotted weir distribution device. Test fluids provided viscosities ranging from μ = 0.3 to 41 mPa s. The Reynolds number was between 0.7 and 1,930. Surface evaporation and the transition to nucleate boiling were studied to gain information about the film stability at maximum wall superheat. A reliable database for laminar and laminar-wavy viscous single component films was created. The experimental results show a significant enhancement in the wave development due to the film distribution. A wavy flow with different wave velocities was superposed to the film in each liquid load configuration without causing a film breakdown or dry spots on the evaporator tube. It was found that nucleate boiling can be allowed without causing film instabilities over a significant range of wall superheat.     

Hydrodynamics of thin liquid films. Rate of thinning of emulsion films from pure liquids

A hydrodynamic theory of the process of thinning of one-sided and symmetrical emulsion films is presented. The theory is essentially based on three assumptions: 1. the film is considered as being thin in the hydrodynamic sense; 2. the film surfaces are assumed to be plane-parallel, and 3. the dissipation of energy outside the film and the adjacent regions of the dispersion phase is neglected. The complete set of Navier-Stokes equations for the dispersion phase are solved. The case of non-steady flow is also considered. Some approximated equations valid for systems of practical importance are obtained.     

Micromechanics of coalescence in ductile fracture

Significant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for finite-element implementation. The model is defined by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantified for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate δ in the Tvergaard-Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape effects is used. Results are presented and discussed in the limiting case of a non-hardening material for different initial microstructures and various stress states. Predicted values of δ are extremely sensitive to stress triaxiality and initial spacing ratio. The effect of initial porosity is significant at low triaxiality whereas the effect of initial void shape is emphasized at high triaxiality.     

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.     

Experimental study of turbulence-induced coalescence in aerosols

In this paper, measurements of the rate of aerosol coalescence in a well characterized turbulent flow are presented. The time dependence of the aerosol droplets’ mean radius upon initiation of flow in an oscillating grid generated turbulence chamber is determined using a phase-Doppler method. Together with a measurement of the aerosol number density from a light attenuation probe, the observed rate of change of the aerosol droplets’ mean radius can be related to the rate constant for the coalescence of two droplets. The Kolmogorov shear rate, which is the primary parameter in theories predicting coalescence rate, is determined from measurements of the root-mean-square fluctuating velocity and the integral length scale. Our experimental results are compared with theoretical predictions, obtained by solving of the population balance equation. Various expressions are considered for the coalescence rate constant to be used in the population balance equation. First, we considered various combinations of ideal coalescence rate constants, i.e. obtained theoretically neglecting particle interactions. Our data are then found to be in good agreement with theoretical predictions that take into account the simultaneous effects of turbulent shear induced and Brownian motion induced coalescence. Second, our results are compared with a theory that considers the effects of turbulent shear and Brownian motion as well as the non-continuum hydrodynamic and van der Waals interparticle interactions. The measured experimental values are generally 50–100% higher than those predicted by this theory. This discrepancy could be explained by the small polydispersity of the aerosol which may result in coalescence induced by differential sedimentation and turbulent acceleration.     

Void interaction and coalescence in polymeric materials

Beyond pressure-sensitivity, plastic deformation of glassy polymers exhibits intrinsic softening followed by progressive rehardening at large strains. This highly nonlinear stress–strain behavior is captured by a constitutive model introduced in this work. In the first part of the paper, we focus on void growth and coalescence in an axisymmetric representative material volume consisting of a single large void and a population of discrete microvoids. Our study shows that microvoid cavitation, enhanced by strain softening, accelerates the process of void coalescence resulting in brittle-like failure at lowered stresses and strains. Pressure-sensitivity also reduces stress-carrying capacity as well as influences the strain for void coalescence; plastic dilatancy effects are relatively milder. In the second part of the paper, we introduce a population of discrete spherical voids within a three-dimensional computational model to study void growth and damage ahead of a crack front. Our studies reveal a distinctive change in the deformed void shape from oblate to prolate when strain softening is followed by high rehardening at large plastic strains. By contrast, an extended strain softening regime promotes oblacity and facilitates multiple void interaction and their cooperative growth over large distances ahead of the crack front. This multi-void failure mechanism is exacerbated by pressure-sensitivity.     

DROPLET COLLISION AND COALESCENCE MODEL

A new droplet collision and coalescence model was presented,a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results,further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence,numerical simulations were carried out for model validation.Results show that the model presented is mesh-independent and less time consuming,it can not only maintains the system momentum conservation perfectly,but not susceptible to initial droplet size distribution as well.     

Void growth and coalescence in anisotropic plastic solids

Large strain finite element calculations of unit cells subjected to triaxial axisymmetric loadings are presented for plastically orthotropic materials containing a periodic distribution of aligned spheroidal voids. The spatial distribution of voids and the plastic flow properties of the matrix are assumed to respect transverse isotropy about the axis of symmetry of the imposed loading so that a two-dimensional axisymmetric analysis is adequate. The parameters varied pertain to load triaxiality, matrix anisotropy, initial porosity and initial void shape so as to include the limiting case of penny-shaped cracks. Attention is focussed on comparing the individual and coupled effects of void shape and material anisotropy on the effective stress–strain response and on the evolution of microstructural variables. In addition, the effect of matrix anisotropy on the mode of plastic flow localization is discussed. From the results, two distinct regimes of behavior are identified: (i) at high triaxialities, the effect of material anisotropy is found to be persistent, unlike that of initial void shape and (ii) at moderate triaxialities the influence of void shape is found to depend strongly on matrix anisotropy. The findings are interpreted in light of recent, microscopically informed models of porous metal plasticity. Conversely, observations are made in relation to the relevance of these results in the development and calibration of a broader set of continuum damage mechanics models.     

Size-dependent coalescence kernel in fertilizer granulation-A comparative study

Granulation is a key process in several industries like pharmaceutical, food, fertilizer, agrochemicals, etc. Population balance modeling has been used extensively for modeling agglomeration in many systems such as crystallization, aerosols, pelletisation, etc. The key parameter is the coalescence kernel, β（ij） which dictates the overall rate of coalescence as well as the effect of granule size on coalescence rate. Adetayo, Litster, Pratsinis, and Ennis （1995） studied fertilizer granulation with a broad size distribution and modeled it with a two-stage kernel. A constant kernel can be applied to those granules which coalesce successfully. The coalescence model gives conditions for two types of coalescence, Type I and II. A twostage kernel, which is necessary to model granule size distribution over a wide size distribution, is applied in the present fluidized bed spray granulation process. The first stage is size-independent and non-inertial regime, and is followed by a size-dependent stage in which collisions between particles are non-random, i.e. inertial regime. The present work is focused on the second stage kernel where the feed particles of volume i and j collide and form final granule ij instead of i ＋j （Adetayo et al., 1995） which gives a wider particle size distribution of granules than proposed earlier.     

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.     

Experimental study on the influence of SO2 gas injection to pure liquids on pool boiling heat transfer coefficients

SO₂ gas is injected into the different pure liquids using new innovative method via meshed tubes. Many experiments have been performed to investigate the influence of gas injection process on the pool boiling heat transfer coefficient of pure liquids around the horizontal cylinder at different heat fluxes up to 114 kW m^?2. Results demonstrate that presence of SO₂ gas into the vapor inside the bubbles creates a mass transfer driving force between the vapor phase inside the formed bubbles and liquid phase and also between the gas/liquid interfaces. Local turbulences and agitations due to the gas injection process around the nucleation sites leads the pool boiling heat transfer coefficient to be dramatically enhanced. Besides, some of earlier well-known correlations were unable to obtain the reasonable values for the pool boiling heat transfer coefficients in this particular case. Therefore, the most accurate correlation among the examined correlations was modified to estimate the pool boiling heat transfer coefficient of pure liquids. Experimental data were in a good agreement with those of obtained by the new modified correlation with absolute average deviation of 10 %.     

Bubble collapse in solid-liquid two-phase fluid

Equations of motion for bubble collapse in solid-liquid two-phase fluid have been derived, in which the resistance coupling effects between the liquid and solid particles have been considered. The motion of particles during the bubble collapse and the effects of particles on bubble collapse have been calculated and discussed. Qualitative relations between the concentration and the size of the particles and the rate of bubble collapse have been obtained. Institute of Water Conservancy and Hydroelectric Power Research     

Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Bubble growth in a Hele-Shaw cell

The general form of the solution is obtained for the problem of the development of a bubble in a Hele-Shaw channel. This solution belongs to the class of parameterized solutions characterized by the property that the partial derivatives of the mapping function are rational in the auxiliary plane. A generalized problem of the system dynamics is written for the free parameters and its complete integrability is proved. An example of the development of an asymmetric bubble with the formation of a single fiord is given.