Simulating the early stage of high-shear granulation using a two-dimensional Monte-Carlo approach

A two-dimensional (2-D) model of a granulation process is presented in this paper. It aims to simulate an entire granulation batch without the use of an initial experimental or fictitious 2-D density function, by taking the experimental operating conditions into account. The mass of liquid and solid in the granules are the two predicted internal variables. The 2-D population balance equation is solved by a Constant Number Monte-Carlo method. This is a stochastic technique tracking the evolution of a population, whilst performing the calculations with a fixed number of particles. This is achieved by reducing or increasing the sample volume when an event results in a net production or a net decrease in the number of particles, respectively. An original multi-population approach is developed to describe the early stage of the process, where small numbers of granules are formed amongst a large number of primary particles. It consists of separating the primary particles from the granule population. A specific intensive variable is introduced to keep track of the repartition of masses. The overall density function is reconstructed a posteriori from the combination of the two populations. This approach allows the simulation to commence from the initial addition of liquid at the start of the process, rather than to start from an early granule size distribution. The early stage of the granulation process, frequently referred as nucleation, can therefore be studied numerically. Four different mechanisms are implemented. Nucleation and re-wetting describe the addition of liquid to the system. The interactions between liquid and solid phases are modelled by a layering process. An aggregation model is also included to simulate the growth of particles undergoing frequent collisions. Finally, the relevance of this new model is demonstrated by confronting the simulations to real experimental data.     

Measurement of Relative Electrostatic Potential Difference for Coalescence Modeling

Coalescence is strongly affected by trace components. Studies suggest the usage of the Derjaguin-Landau-Verwey-Overbeek force in coalescence modeling. Thus, data regarding the electrostatic potential are needed. Determination of the partition coefficient of a charged dye dissolved in salt-containing two-phase systems allows to evaluate the electrostatic potential difference relative to a reference system by evaluation with the extended Albertsson model. The corresponding first settling tests show the strong effect of the relative electrostatic potential difference on the dispersion behavior.     

Estimation of Coalescence Parameters in an Agitated Extraction Column Using a Hybrid Algorithm

A method based on a genetic algorithm (GA) combined with Levenberg‐Marquardt (LM) method applicable to the population balance model for coalescence parameter estimation in a liquid‐liquid biphasic system is presented. The toluene/water system in a rotating disk contactor was taken as an example. Estimation methods for such a problem are often based on deterministic optimization models that are rather instable and divergent around a local minimum. To overcome these limitations, the present study involves the introduction of a semi‐stochastic method that is able to provide at first the estimation of coalescence parameters from the GA based on an inverse approach, exploiting the principle of GA. The LM algorithm was applied to ensure that the results are not restricted to a local minimum.     

Dispersion and Phase Separation of Water‐Oil‐Amphiphile Systems in Stirred Tanks

Drop size distributions and phase separation behavior of water‐oil‐nonionic amphiphile systems are investigated using an in situ endoscope measurement technique and an external camera in stirred tanks in batch mode. The fitting procedure and the simulation results of a phase separation model are analyzed under the condition that either the swarm sedimentation speed or the mean drop size during sedimentation is known. The steady‐state drop size distributions are self‐similar over the whole range of process parameters, but not in the decaying turbulence field after agitation stop. The coalescence rate in the first seconds after agitation stop clearly affects the separation behavior, so that a prediction of the separation time based on the initial conditions in steady state is not trivial.     

Coalescence Modeling for Design of Technical Equipment

A coalescence model in the context of the ReDrop concept (Representative Drops) is proposed to design technical equipment for separating liquid‐liquid dispersions in settlers or extraction columns. A fundamental study of drop interactions has been performed to obtain the complete picture of coalescence. The model proposed accounts for collision frequency of the drops, bouncing probability, and coalescence probability, for which the film‐drainage approach is applied. The model proposed allows considering the appropriate formulation for different types of equipment. Especially noteworthy is that the coalescence probability fundamentally differs from the expression of Coulaloglou and Tavlarides, which is frequently used, but which shows inconsistencies at fundamental level.     

SINTERING KINETICS AND TRANSPORT PROPERTY EVOLUTION OF LARGE MULTI-PARTICLE AGGREGATES

Ultrafine (“nano”-) particles produced from highly supersaturated vapors or liquids are usually aggregated, often containing thousands of small 'primary' particles bound together in tenuous structures characterized by mass fractal dimensions less than 3. Such aggregates have large initial surface area but are metastable with respect to more compact configurations. Available restructuring mechanisms include surface energy driven coalescence, which, in the case of viscous flow at high gas temperatures, is ultimately able to obliterate all evidence of the original (“primary”) particles. We here exploit the notion that, provided an aggregate is sufficiently large, it can be treated like a spatially non-uniform porous medium, undergoing finite-rate surface energy driven viscous flow sintering leading to final collapse to a single dense sphere. For this purpose, after a D_ƒ ≌s const stage of sintering [associated with a corresponding increase in mean apparent primary particle ('grain') size], we use an extension of the sintering rate models of Mackenzie and Shuttleworth (1949) and Scherer (1977), treating the material of the restructuring aggregate to be a Newtonian viscous fluid. We predict and report here the time-dependent increase in fractal dimension, D_ƒ, and associated decreases in: aggregate outer (maximum) radius, mobility radius, and changes in accessible surface area with dimension-less time [real time in multiples of the characteristic sintering time, μ (R₁)_t=0/σ cr, where u is the material's viscosity (R_l)_t=0 is the effective initial grain radius and a the material surface tension]. In these units, we find that the total required coalescence time does not increase with N as sensitively as N^1/3 an important observation for processes involving very large aggregates. With validation and the indicated extensions, our pseudo-continuum methods are efficient enough to be used for estimating the morphological- and transport property-evolution of entire populations of restructuring aggregates, perhaps characterized by some non-separable probability density function pdf(N, D_ƒ,R₁,) locally, in non-isothermal combustion-synthesis reactors.     

Coalescence Characteristics of Side-by-Side Growing Bubbles in Carboxymethyl Cellulose Solutions

New experimental data are presented on the coalescence dynamics of twin bubbles at two adjacent nozzles in carboxymethyl cellulose (CMC) solutions. The coalescence process was recorded by using a fast video technique and the images were then analyzed to evaluate the regime, efficiency, and patterns of bubble coalescence. The results reveal that the coalescence process contains the four periods of spherical expansion, rapid mergence, overall growth, and instant departure. The coalescence efficiency always passes through five stages with the gas flow rate; it grows with the CMC solution concentration, but decreases with the surfactant concentration, except at very low gas flow rates. The bubble coalescence pattern strongly depends on the nozzle spacing, but conditionally on the gas flow rate and the solution properties.     

Drop breakage and coalescence in the toluene/water dispersions with dissolved surface active polymers PVA 88% and 98%

The influence of two PVAs of the same molecular weight (13,000–23,000) and different degree of hydrolysis equal to 88% and 98% on breakage and coalescence of toluene droplets in the liquid/liquid dispersion were considered for PVA concentration range 0.001–0.01%. Analysis of experimental results shows that drop coalescence is significant only in the system containing 0.001% PVA. Drop coalescence for polymer concentration range 0.002–0.01% is strongly limited. Therefore, population balance was solved using breakage and coalescence expressions with assumed partially mobile drop interfaces for the lowest PVA concentration. For c ≥ 0.002% drop size distributions were properly predicted using only breakage model. Multifractal formalism was used to take into account intermittent character of turbulence and explain drop behavior. Larger drop size reduction by PVA of lower degree of hydrolysis observed experimentally was confirmed by the model.     

Splitting failure in brittle rocks containing pre-existing flaws under uniaxial compression

Splitting failure of rock specimen containing pre-existing crack-like flaws under compression is numerically investigated using Rock Failure Process Analysis (RFPA^2D). Crack growth from single, triple and multi-crack-like flaws contained in numerical specimens are studied. The analysis of parameters, such as angle and length of the flaws, specimen width and the arrangement of flaw locations, is conducted to examine its influence on the growth and coalescence behaviour. Flaw length, flaw location and stress interaction between the nearby flaws are found to be important factors affecting the behaviour of crack initiation, propagation and coalescence.     

Phase Diagram for Predicting In Situ Fibrillation of LCP During Molding

The present work represents an important attempt at constructing a phase diagram for predicting the type and extent of fibrillation of the liquid crystalline polymer (LCP) phase in LCP-based polymer blends. A polycarbonate (PC)/LCP polymer blend was utilized in the current study. The combined effects of three factors, namely, the shear rate, the LCP content in the blend, and interfacial adhesion between the LCP phase and the matrix polymer (PC) were considered. In contrast, work in reported literature has usually considered the individual effect of only one or at most two of these three factors. A thermotropic liquid crystalline polymer, LC5000, consisting of 80/20 of hydroxybenzoic acid and poly(terephthalate) was employed. The effect of interfacial adhesion between the LCP and the PC matrix on fibrillation was considered by using a compatibilizer for the PC/LCP blend. It was demonstrated that the constructed phase diagram could successfully be used to predict and illustrate the conditions under which in situ fibrillation of the LCP phase would occur in the LCP-based blend.