Effect of compatibilization on the deformation and breakup of drops in step-wise increasing shear flow

Drop deformation and breakup were investigated in the presence of a block copolymer in step-wise simple shear flow using a home-made Couette cell connected to an Anton Paar MCR500 rheometer. Polyisobutylene (PIB) was used as the matrix, while five different molecular weights of polydimethylsiloxane (PDMS) were selected to provide drops with a relatively wide range of viscosity ratio. A block copolymer made of PDMS-PIB was used for interfacial modification of the drop-matrix system. The copolymer concentration was 2 wt% based on the drop phase. The experiments consisted in analyzing the drop shape and measuring the variation of the length to diameter ratio, L/D, both in steady state and in transient regimes till breakup. This allowed revising of the classical Grace curve that reports the variation of the critical capillary number for breakup as a function of viscosity ratio and providing also a new one for blends compatibilized with an interfacial active agent with a given molecular weight.     

Identical Feed Drops in a Flow Vessel May not Always Be Desirable

In this paper, the effect of feed size and daughter drop size distributions on the steady‐state drop size distribution in a continuous flow vessel is discussed. For identical sizes of feed drops, a new criterion has been proposed to ensure the complete breakage of the feed drops giving rise to smooth continuous drop size distributions. This has been predicted on the basis of two competing time scales, namely, breakage and residence times.     

The effect of coalescence on drop size distribution in an agitated liquid-liquid dispersion

A procedure involving high speed cine photography and novel optical probes has been used to study droplet interaction phenomena in liquid-liquid dispersions. Coalescence and breakup events were observed and the rate of coalescence was measured at various positions in a stirred tank for dispersions of methylisobutylketone in water. For the conditions studied, drop breakup occurred near the impeller and droplet coalescence predominated at other locations, as expected. However, the extent of this behavior was unexpected. Beyond distances from the impeller region of order of only $\text{1}\text{6}$ the impeller diameter, breakup was virtually nonexistent. Outside the impeller region, extensive coalescence measurements showed (1) collisions between droplets are extremely inefficient for this chemically equilibrated system—at most 10% of collisions result in a coalescence, (2) only binary coalescence occurs even at the highest dispersed phase concentration investigated, (3) coalescence rate shows little preference on drop size, and (4) the coalescence rate is directly proportional to turbulence level; that is, the highest coalescence rates occur closest to the impeller. On the basis of these measurements, drop balance methods and a circulation path model were used to relate the drop size distribution at various locations in the region where coalescence predominates. In this case good agreement was obtained between measured and predicted drop size distributions.     

DROP PRODUCTION IN COUETTE AND MEDIA MILL DEVICES

The media mill is a device used in the paint and pigment industry for mixing and dispersing solid/liquid mixtures. The media consists of spheres which are agitated in a vessel and the hydrodynamic interactions between these media spheres cause the fine-scale dispersion. The details of the flow are very complex. A technique to characterize the dispersion efficiency of a media mill is presented which involves monitoring the maximum drop diameters of a dispersed organic phase in an aqueous continuous phase. The largest surviving drops reflect the maximum shear and elongation fields that exist in the flow. The maximum drop size scales as impeller speed to the -0·82 power. This dependence is much lower than the dependence for a Rushton turbine in a tank, which would be -1·38. The mechanism of breakup is clarified by experiments in a Couette geometry for large drop size to gap ratios, where the dependence of drop size on shear rate also scales to the -0·82 power. An analysis of the hydrodynamics involved in two approaching spheres explains the similarity between drop formation in a media mill and the narrow gap Couette cell; drop-solid surface interactions strongly influence breakup in both geometries.     

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.     

Effect of Impeller Vertical Position on Drop Sizes in Agitated Dispersions

The effect of impeller height relative to the vessel bottom was studied by measuring the drop size distributions of kerosene dispersions in water at two positions inside a stirred tank. Measurements were taken at 1/3, 1/ 2, and 2/3 of total vessel height for rotational speeds 250, 300, 350 and 400 RPM and for hold‐up fractions 0.02 and 0.04. Results show an influence of impeller height on drop sizes ranging from a Sauter mean diameter decrease of 7.8 % to an increase of 35 % relative to the ones obtained with the impeller at the center of the vessel     

Sheet formation during drop deformation and breakup in polyethylene/polycarbonate systems sheared between parallel plates

A polycarbonate drop was sheared inside a polyethylene matrix in a transparent rotating parallel plate device at 220 °C and low shear rates. A flat sheet was formed during the initial shearing of the drop. The drop then developed into either a thin thread or a sheet with a thin cylindrical tip. Sheet formation was found to occur at a critical strain or time. A stress ratio (S_r) between the matrix breakup stress, made up of the matrix normal stress and viscous stress, and the drop restoring stress, made up of the drop normal stress and the interfacial stress, is used to characterize the sheet formation during the drop deformation and breakup process. It was found that the viscosity ratio (η_r), stress ratio (S_r) and Deborah number (De) of the system could be used to predict the drop deformation and breakup.     

Evaluation of a New High‐Pressure Dispersion Unit (HPN) for Emulsification

Emulsification plays an important role in the formulation of lipophilic pharmaceutical agents. These substances are often included in the disperse phase of an oil‐in‐water emulsion. To reach a high bioavailability and a good long‐term stability, drop sizes much less than 1 micron are required. For the generation of such emulsions, energy densities of a quality which can only be reached in high‐pressure systems, are necessary. Actually available apparatus, such as high‐pressure homogenizers fitted with valves, microfluidizer or jet disperser, reach particle sizes of about 0.2 micron in continuous processes. It is indispensable to produce emulsions with smaller globules in order to receive a maximum of diversity in application. Therefore, dispersion units with a higher efficiency in drop breakup are needed. Especially in the case of parenterally administered medicament formulations an average particle size between 0.04 and 0.1 microns is requested which is up to now not reachable by continuous emulsification. In this study the drop breakup behavior of a new high‐pressure nozzle is investigated with the example of oil‐in‐water emulsions and compared to the breakup behavior of a state‐of‐the‐art nozzle and to available data published.     

Influence of Different Silica Nanoparticles on Drop Size Distributions in Agitated Liquid‐Liquid Systems

The impact of different silica nanoparticles on rheology, interfacial tension and drop size distributions in liquid‐liquid systems is determined experimentally. The particles vary in wettability and specific surface area. In contrast to commonly used high‐energy devices for Pickering emulsion preparation, low energy input by stirring allows to quantify drop breakage and coalescence in steady state and dynamic conditions. The experiments can provide essential information for drop size model development in nanoparticle‐stabilized emulsions.     

Drop formation in a co-flowing ambient fluid

Drop formation at a capillary tip in laminar flow is investigated experimentally. The disperse phase is injected via a needle into another co-flowing immiscible fluid. Two different drop formation mechanisms are distinguished: Either the drops are formed close to the capillary tip—dripping—or they break up from an extended liquid jet—jetting. The effect of the process and material parameters on the drop formation depends on the breakup mechanism and has to be investigated for each flow domain separately. In this study, we focus on dripping. The drop breakup is affected by the flow dynamics of both the disperse and the continuous phase. Consequently, we investigate the effect of flow rates, fluid viscosities and interfacial tension on the droplet size and observe the dynamics of satellite drop generation. Whereas the fundamentals of disperse fluid injection via a capillary into an ambient fluid have been investigated extensively, the focus of this article is on providing a comprehensive experimental data set for proving the applicability of this technique as a dispersing tool. It is shown that drop formation at a capillary tip into a co-flowing ambient liquid represents a promising technique for the production of monodisperse droplets where the droplet size is controlled externally by the flow strength of the continuous phase. The breakup dynamics changes significantly at the transition point from dripping to jetting. Consequently, the transition point between the flow domains represents an important operating point. In this article, dripping is demarcated from jetting by studying the influence of the various material and process parameters on the transition point.     

Reynolds number scaling of flow in a Rushton turbine stirred tank. Part I—Mean flow, circular jet and tip vortex scaling

We consider scaling of flow within a stirred tank with increasing Reynolds number. Experimental results obtained from two different tanks of diameter 152.5 and 292.1 mm, with a Rushton turbine operating at a wide range of rotational speeds stirring the fluid, are considered. The Reynolds number ranges from 4000 to about 78,000. Phase-locked stereoscopic PIV measurements on three different vertical planes close to the impeller give phase-averaged mean flow on a cylindrical surface around the impeller. The scaling of θ- and plane-averaged radial, circumferential and axial mean velocity components is first explored. A theoretical model for the impeller-induced flow is used to extract the strength and size of the three dominant elements of the mean flow, namely the circumferential flow, the jet flow and the pairs of tip vortices. The scaling of these parameters with Reynolds number for the two different tanks is then obtained. The plane-averaged mean velocity scales with the blade tip velocity above a Reynolds number of about 15,000. However, parameters associated with the jet and tip vortices do not become Reynolds number independence until Re exceeds about 10⁵. The results for the two tanks exhibit similar Reynolds number dependence, however, a perfect collapse is not observed, suggesting a sensitive dependence of the mean flow to the finer details of the impeller.     

Prediction of phase inversion in agitated vessels using a two-region model

Phase inversion in agitated vessels was studied using a two-region model. In this model, breakup and coalescence were assumed to take place in the vicinity of the impeller and away from that region, respectively. The mechanism of phase inversion was regarded as the result of an imbalance between the breakup and coalescence processes. Hence phase inversion was assumed to occur when the coalescence frequency exceeded that of breakup. In addition, the concept of a radial distribution function was adopted in the model in order to account for droplet coalescence in concentrated dispersions. Using the two-region model, the effect of interfacial tension, viscosity, density and impeller size on the width of the ambivalent range was investigated. The predictions agree well with experimental data particularly for the upper curve of the ambivalent range; however, the organic phase fraction of the lower curve is in some cases underestimated by the model.     

Experimental study on drop formation in liquid-liquid fluidized bed

Drop formation in liquid-liquid fluidized bed was investigated experimentally. The normal water was injected via a fine-capillary spray nozzle into the co-flowing No. 25 transformer oil with jet directed upwards in a vertical fluidized bed. Experiments under a wide variety of conditions were conducted to investigate the instability dynamics of the jet, the size and size distribution of the drops. Details of drop formation, drop flow patterns and jet evolution were monitored in real-time by an ultra-high-speed digital CCD (charge couple device) camera. The Rosin-Rammler model was applied to characterize experimental drop size distributions. Final results demonstrate that drop formation in liquid-liquid system takes place on three absolutely different developing regimes: bubbling, laminar jetting and turbulent jetting, depending on the relative Reynolds number between the two phases. For different flow domains, dynamics of drop formation change significantly, involving mechanism of jet breakup, jet length pulsation, mean size and uniformity of the drops. The jet length fluctuates with time in variable and random amplitudes for a specified set of operated parameters. Good agreement is shown between the drop size and the Rosin-Rammler distribution function with the minimum correlation coefficient 0.9199. The mean drop diameter decreases all along with increasing jet flow rate. Especially after the relative Reynolds number exceeds a certain value about 3.5×10⁴, the jet disrupts intensely into multiple small drops with a diameter mainly ranging from 1.0 to and a more and more uniform size distribution. The turbulent jetting regime of drop formation is the most preferable to the dynamic ice slurry making system.     

Numerical investigation of upstream pressure fluctuation during growth and breakup of pendant drops

Growth and breakup of pendant drops from the tip of a capillary is of great importance due to its wide applications and the richness of the underlying physics. During the growth and breakup of a pendant drop, the size variation will produce pressure fluctuation in the upstream, which is studied numerically with the level set method to predict the interface. The numerical results are validated against experimental images showing the growth and breakup of pendant drops obtained from a high speed camera. The effects of the surface tension and the outer diameter of the capillary on the amplitude and the period of the pressure fluctuation are examined. Compared to other methods of surface tension measurement, this method shows potential advantages of its good accuracy, simplicity, and low cost.     

Experimental study of drop size distributions at high phase ratio in liquid-liquid dispersions

An experimental investigation has been carried out in order to analyse the drop size distributions of a liquid-liquid dispersion in a stirred vessel at high phase ratio. Two liquid-liquid systems have been investigated: one at low and one at high coalescence rate. A sampling technique has been developed in order to measure the drop size distributions in the mixer with the help of a laser granulometer. A statistical approach has been attempted to derive the most probable drop size distribution in the mixer and the results have been compared with the experimental primary distributions. The comparison suggests that the energy dissipation cannot be considered as uniformly distributed in the mixer. The mean diameter of the distribution has been correlated to the global mechanical input power and to the volume phase fraction (phase ratio) for both systems in the frame of the classical Hinze-Kolmogorov theory. The results show that for each volume fraction studied, the mean diameter of the dispersion is a decreasing power law of the Weber number with an exponent equal to −0.6 at low phase ratio. However, it appears that for both systems studied this exponent is a decreasing function of the phase ratio. This result reveals the existence of a more complex breakup mechanism with high phase ratio than that assumed in the theory which has to be discriminated from dampening effect of the dispersed phase upon the turbulent energy of the bulk phase. The study of the secondary distributions mean diameter seems to be in good agreement with the numerical predictions of Stone (Annu. Rev. Fluid Mech. 26 (1994) 65). The ratio between the mean diameter of the primary distribution to the satellite drop mean diameter is a growing function of the viscosity ratio.     

About bubble breakup models to predict bubble size distributions in homogeneous flows

We present results of a study of the equilibrium between coalescence and breakup of bubbles in homogeneous media with isotropic turbulence. The Boltzmann equation for the particle distribution function (pdf) was evaluated in steady state, using a multigroup approach. Binary bubble breakup was assumed. We used uniform function, delta function, and the model proposed by Luo and Svendsen (1996) for the bubble size distributions resulting from a breakup. The bubble breakup rate was calculated with Luo and Svendsen (1996) and Prince and Blanch (1990) models. Significant differences in bubble breakup rate, and therefore in bubble size distribution, are predicted by both models. The models were compared to the bubble size distributions measured by Boyd and Varley (1998) in air-water flow. The transient response of the bubble size distribution and interfacial area density was also analyzed. This work is of significance in the prediction of reaction rates when they are dependent on bubble size distribution.     

In situ visualization of drop deformation,erosion, and breakup in high viscosity ratio polymeric systems under high shearing stress conditions

In this paper, deformation and breakup under simple shear of single molten polymer drops in a polymer matrix were investigated. Flow visualization was carried out in a Couette‐Flow apparatus under relatively high shear rates and temperatures up to 230°C. Drop/Matrix combinations were composed of polystyrene drops of 0.5–0.6 mm in diameter in polyethylene matrix, and ethylene–propylene copolymer drops of approximately the same size in polypropylene matrix. The deformation and breakup processes were studied under steady state and time‐dependent shearing conditions. Either for steady state or time‐dependant shearing conditions, drop elasticity generated at relatively high shear rates helped the drops to align perpendicular to the flow direction, i.e., parallel to vorticity axis. Also, the most striking non‐Newtonian effects for the high viscosity ratio systems were the surface erosion and the drop splitting mechanisms. The particles eroded off the main droplet surface were very fine, in the range of 10–50 μm, and led to a significant reduction in main drop size before its final breakup. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2582–2591, 2006     

TURBULENT FLOW IN STIRRED TANKS: SCALE-UP COMPUTATIONS FOR VESSEL HYDRODYNAMICS

A numeric model for turbulent flow was used to compute the flow patterns in Rushton turbine agitated vessels. The cases considered cover two orders of magnitude for the three different scaling criteria of constant impeller Reynolds number, power input per unit mass, and impeller tip speed. The constant power input scale-up criteria maintains the turbulence levels throughout the vessel during scale-up. The circulation times, however, increase with vessel size for this scaling criteria. The other scaling criteria of constant impeller tip speed and impeller Reyonds number lead to decreasing turbulence levels in the tank along with further increases in circulation times.     

Unsteady mass transfer around spheroidal drops in potential flow

Unsteady mass transfer in the continuous phase around spheroidal drops in potential flow and at high Peclet numbers has been theoretically studied. Analytical solutions for the concentration profile, the molar flux, the concentration boundary layer thickness, and the time to reach steady state are presented. The solution to the problem was obtained by the useful equations derived by Favelukis and Mudunuri for axisymmetric drops of revolution, with the only requirements being the shape of the drop and the tangential velocity at the surface of the drop. The solution suggests that, as the eccentricity increases, the total quantity of material transferred to or from the drop decreases (for prolate spheroids) and increases (for oblate spheroids). It was also determined that when the dimensionless time is greater than 2, then steady state is in practice obtained, with prolate drops attain steady-state conditions faster than oblate drops.     

Size Distribution of Drops Formed from Nozzles in Air at Velocities below Jetting

The drop size distribution of drops formed from four nozzles (d = 0.5, 1.8, 2.7 and 3.6 mm) were measured for the flow rate range Q = 0.1–1.17 cm³/s and Reynolds number 56–448. Distilled water was used as the dispersed phase and air as the continuous one. The experimental drop size distributions were described satisfactorily by the theoretical upper limit number and volume distributions. The experimental data of minimum and maximum diameters versus the respective Sauter mean diameters gave straight lines with slopes of 0.81 and 1.18, respectively.