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.     

Visualization of block copolymer distribution on a sheared drop

We have visualized a fluorescently-labeled poly(styrene-b-methylmethacrylate) (NBD-PS-b-PMMA) block copolymer on the surface of a polymethylmethacrylate (PMMA) drop in a polystyrene (PS) matrix. Confocal microscopy revealed that the block copolymer distributed uniformly on the drop surface before deformation. However, in shear flow the copolymer concentration was higher at the tips and edges of the drop. Visualization of drop deformation using a counter-rotating apparatus showed enhanced drop deformation for a drop with block copolymer resulting in larger area generation. Drops with block copolymer showed widening even for shear strains exceeding 10, in contrast to bare drops, which first widened and then shrank. These results agree qualitatively with the observed distribution of fluorescent block copolymer. Copolymer concentration is highest in the regions of high curvature, where lowering interfacial tension should be most effective in retarding drop retraction. Block copolymer on these highly curved surfaces is found to be very effective since the exact theory for zero interfacial tension by Cristini fits our drop widening results well.     

Dispersion of water into oil in a rotor–stator mixer. Part 1: Drop breakup in dilute systems

Most previous studies of liquid–liquid dispersion in complex geometry are limited to turbulent flow at low continuous phase viscosity. In this study, a viscous continuous phase was employed over a range of flow conditions including both the laminar and turbulent regimes. Equilibrium drop size was measured for water dispersed into viscous food grade mineral oils in a batch Silverson L4R rotor–stator mixer. The influence of fluid viscosities and interfacial tension (by adding an oil-soluble surfactant) were examined. In order to isolate the effect of drop breakage from coalescence, Part 1 is limited to dilute conditions (water phase fraction, ? = 0.001). In the laminar regime, drop breakup was more likely due to a simple shear breakage mechanism than one for extension. Following Grace (1982), a semi-empirical drop size correlation was developed. For turbulent flow, the validity of the sub-Kolmogorov inertial stress model for correlating equilibrium mean drop size was verified. Surfactants were found to mostly decrease drop size by lowering interfacial tension. Except for laminar systems near the critical micelle concentration, where Marangoni stresses appear to play some role, the effect of surfactants on the drop size could be correlated using the equilibrium or static interfacial tension. The influence of water phase fraction and coalescence is considered in Part 2 ( Rueger and Calabrese, 2013) of this paper.     

Drop break-up in turbulent pipe flow downstream of a restriction

This work addresses the drop fragmentation process induced by a cross-sectional restriction in a pipe. An experimental device of an upward co-current oil-in-water dispersed flow (viscosity ratio λ≈0.5) in a vertical column equipped with a concentric orifice has been designed. Drop break-up downstream of the restriction has been studied using a high-speed trajectography. The first objective of this work deals with a global analysis of the fragmentation process for a dilute dispersion. In this context, the operating parameters of the study are the orifice restriction ratio β, the flow Reynolds number, Re and the interfacial tension, σ. The break-up domain has been first mapped on a β(Re) graph and drop size distributions have been measured for different flow Reynolds numbers. It was observed that the mean drop diameter downstream of the restriction linearly increases as a function of the inverse of the square root of the pressure drop. This behaviour is in agreement with the observations previously made by Percy and Sleicher [A.I.Ch.E. Journal, 1983, 29(1), 161-164]. In addition, experiments based on the observation of single drop break-up downstream of the orifice have allowed the identification of different break-up mechanisms, and the determination of statistical quantities such as the break-up probability, the mean number of fragments and the daughter drop distribution. The drop break-up probability was found to be a monotonous increasing function of the Weber number based on the maximal pressure drop through the orifice. The mean number of fragments is also an increasing function of the Weber number and the reduced mean daughter drop diameter decreases as the Weber number increases. The daughter drop distributions are multimodal at low and moderate Weber numbers as a result of asymmetrical fragmentation processes. The statistical analysis of single drop break-up experiments was implemented in a simple global population balance model in order to predict the evolution of the size distribution across the restriction at different Reynolds numbers, in the limit of dilute dispersions.     

An experimental investigation on the breakup of surfactant-laden non-Newtonian jets

The combined effect of polymers and soluble surfactants on the dynamics of jet breakup, and especially on satellite drop formation, was experimentally investigated. Xanthan gum and Carbopol^® 934 NF were dissolved in water with Sodium Dodecyl Sulfate as the surfactant. Controlled disturbances were imposed at the laminar jet interface using a piezoelectric vibrating nozzle with breakup dynamics recorded using a high-speed camera. Drop and ligament diameters were measured from the digital images. The focus of the work was investigating how bulk and interfacial properties of the prepared fluids influenced ligament and drop evolution. It was found that if the proper concentration of surfactant (close to the critical micelle concentration, CMC) was selected, and if the flow time scales were large enough, Marangoni interfacial stresses may lead to an increase in satellite drop size as previously reported for breakup simulations of shear-thinning jets covered with insoluble surfactant. It was also experimentally confirmed that the introduction of surfactant contributes to a delay in jet breakup.     

Determination of the interfacial tension of low density difference liquid-liquid systems containing surfactants by droplet deformation methods

The interfacial tension, σ, between two low density difference liquids containing a surfactant was determined using drop deformation method with a computer-controlled parallel bands apparatus. This device applies a linear homogeneous shear flow field to a fluid matrix in which a droplet of another immiscible and buoyancy-free fluid is immersed. The flow induces topological changes on the initially spherical drop, which deforms into an ellipsoid and orients respect to the flow direction. The time evolution of the sheared droplets was recorded with two CCD cameras (placed along the x and z directions) for extended times, allowing the steady state of the drops to be achieved accurately, and further digitally analyzed. Appropriate theories corresponding to each flow-induced mechanism of the droplet under shear (steady-state deformation and orientation) were employed for determining the interfacial tension, under the basis of reaching equilibrium states of deformation of the sheared drop. The calculated σ values via the drop deformation theories were checked for a wide range of viscosity ratios of binary systems conformed by silicon oils as droplets and a water solution of polyvinylpyrrolidone as continuous phase (both Newtonian), being found that σ is independent on λ. These values were compared with measurements carried out in a conventional tensiometer, using the drop volume method. The comparison showed a very good agreement between both techniques.     

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

The direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high-speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219-234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/d_max can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.     

Erosion and breakup of polymer drops under simple shear in high viscosity ratio systems

The deformation and breakup of a single polycarbonate (PC) drop in a polyethylene (PE) matrix were studied at high temperatures under simple shear flow using a specially designed transparent Couette device. Two main breakup modes were observed: (a) erosion from the surface of the drop in the form of thin ribbons and streams of droplets and (b) drop elogation and drop breakup along the axis perpendicular to the velocity direction. This is the first time drop breakup mechanism (a), “erosion,” has been visualized in polymer systems. The breakup occurs even when the viscosity ratio (η_r) is greater than 3.5. although it has been reported that breakup is impossible at these high viscosity ratios in Newtonian systems. The breakup of a polymer drop in a polymer matrix cannot be described by Capillary number and viscosity ratio only; it is also controlled by shear rate, temperature, elasticity and other polymer blending parameters. A pseudo first order decay model was used to describe the erosion phenomenon and it fits the experimental data well.     

Characterization of liquid‐liquid dispersions with variable viscosity by coupled computational fluid dynamics and population balances

Sustaining stable liquid‐liquid dispersion with the desired drop size still relies on experimental correlations, which do not reflect our understanding of the underlying physics and have a limited prediction capability. The complex behavior of liquid‐liquid dispersions inside a stirred tank, which is equipped with a Rushton turbine, was characterized by a combination of computational fluid dynamics and population balance equations (PBE). PBE took into account both the drop coalescence and breakup. With the increasing drop viscosity, the resistance to drop breakage also increases, which was introduced by the local criteria for drop breakup in the form of the local critical Webber number (We_c). The dependency of We_c on the drop viscosity was derived from the experimental data available in the literature. Predictions of Sauter mean diameter agree well with the experimentally measured values allowing prediction of mean drop size as a function of variable viscosity, interfacial tension, and stirring speed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2403–2414, 2015     

Temperature-composition phase diagrams of binary blends of block copolymer and homopolymer

The temperature-composition phase diagrams for six pairs of diblock copolymer and homopolymer are presented, putting emphasis on the effects of block copolymer composition and the molecular weight of added homopolymers. For the study, two polystyrene-block-polyisoprene (SI diblock) copolymers having lamellar or spherical microdomains, a polystyrene-block-polybutadiene (SB diblock) copolymer having lamellar microdomains, and a series of polystyrene (PS), polyisoprene (PI), and polybutadiene (PB) were used to prepare SI/PS, SI/PI, SB/PS, and SB/PB binary blends, via solvent casting, over a wide range of compositions. The shape of temperature-composition phase diagram of block copolymer/homopolymer blend is greatly affected by a small change in the ratio of the molecular weight of added homopolymer to the molecular weight of corresponding block (M_H,A/M_C,A or M_H,B/M_C,B) when the block copolymer is highly asymmetric in composition but only moderately even for a large change in M_H,A/M_C,A ratio when the block copolymer is symmetric or nearly symmetric in composition. The boundary between the mesophase (M₁) of block copolymer and the homogeneous phase (H) of block copolymer/homopolymer blend was determined using oscillatory shear rheometry, and the boundary between the homogeneous phase (H) and two-phase liquid mixture (L₁+L₂) with L₁ being disordered block copolymer and L₂ being macrophase-separated homopolymer was determined using cloud point measurement. It is found that the addition of PI to a lamella-forming SI diblock copolymer or the addition of PB to a lamella-forming SB diblock copolymer gives rise to disordered micelles (DM) having no long-range order, while the addition of PS to a lamella-forming SB diblock copolymer retains lamellar microdomain structure until microdomains disappear completely. Thus, the phase diagram of SI/PI or SB/PB blends looks more complicated than that of SI/PS or SB/PS blends.     

Temperature and Time Dependence of Copolymer Mixtures on Interfacial Adhesion at PS/PMMA Interfaces

The effect of copolymer mixtures on the interfacial adhesion between slabs of PS and PMMA was investigated as a function of composition, time and temperature using the asymmetric double cantilever beam (ADCB) method. The nature of the interface was further probed using atomic force microscopy (AFM) and dynamic secondary ion mass spectroscopy (D-SIMS). The results show that mixtures of graft and block copolymers are much more effective than pure block copolymers in enhancing the interfacial adhesion. The most effective mixture consisted of a block copolymer of molecular weight 70K and a copolymer with two PS grafts of molecular weight 30K. This mixture yielded an interfacial fracture toughness of G_c = 127.5 J/m² as compared with G_c = 38.2 J/m² and G_c = 3.5 J/m² for the pure block and graft copolymer, respectively.

G_c at the PS/PMMA interface reinforced only with block copolymer was maximal after an annealing temperature of 150°C for 1 hr. It decreased by an order of magnitude when the temperature was increased to 180°C or the joining time was increased from 1 to 10 hours. G_c at the interface reinforced with a graft/diblock copolymer mixture was also maximum at an annealing temperature of 150°C but it decreased only by a factor of 2 with increasing joining time or temperature. Dynamic Secondary Ion Mass Spectroscopy (DSIMS) data show that this effect may be due to decrease in the diffusion of the copolymer from the interface when the mixture is present, i.e, the diblock copolymer is trapped within the graft copolymer.     

Drop size distribution and mean drop size in a pulsed packed extraction column

Drop size distribution and mean drop size are used for calculation of interfacial area available for mass transfer. In this study, the drop size distribution and Sauter mean drop diameter (d₃₂) have been investigated using three different liquid systems in the absence of mass transfer in a pilot plant pulsed packed column. The drop size was measured at four different points along the active column height. Three operating variables have been studied including the pulse intensity (af) and flow rates of both liquid phases. The effect of liquid properties and height of the active column were also investigated. A combination of the pulse intensity and interfacial tension had the largest effect on the drop size distribution while none of the flow rates were of significance. The height of the column played an important role at the bottom of the active column, but the associated effect was reduced with increase of the height. Finally, a normal probability function of number density was proposed for prediction of the drop size distribution with an Average Absolute Relative Error (AARE) of 8.8% for their optimized constant. Furthermore, two correlations were presented involving height or flow rates of the two phases along with operating variables and physical properties of the liquids. These correlations had AARE values of about 8.5 and 7.8%, respectively.     

Liquid Jet Stability in a Laminar Flow Field

The breakup of a Newtonian liquid jet into droplets injected horizontally into another flowing immiscible Newtonian fluid was studied experimentally under creeping flow conditions. Different breakup mechanisms take place in different flow regions. No filament is generated at very low velocities of the continuous phase when the droplets peel off directly at the nozzle tip. As soon as the flow rate of the continuous phase exceeds a critical value, a filament of a characteristic length begins to grow. The filament breaks up due to instabilities in terms of developing interfacial waves. The laminar breakup length of the filament is found to correlate with the flow rates of both phases and their viscosity ratio. The impact of the capillary diameter, through which the disperse phase is injected, on the filament length was investigated and the maximum droplet size was estimated.     

Dispersion of water into oil in a rotor–stator mixer. Part 2: Effect of phase fraction

In Part 1 (Rueger and Calabrese, 2013), we monitored dilute water-in-oil dispersions in a batch Silverson L4R rotor–stator mixer to establish breakage mechanisms and develop a mechanistic basis for correlation of equilibrium mean drop size. In this study (Part 2) we consider the effect of water phase fraction under similar processing conditions, thereby requiring consideration of coalescence. Most of the work on the effect of phase fraction in stirred vessels was done with a low-viscosity continuous phase in turbulent flow with inertial subrange scaling (d > η). For that case drop size increases linearly with phase fraction, ?. In this study, viscous oils comprised the continuous phase, with water as the drop phase. The equilibrium DSD was measured in both laminar and turbulent flow conditions. The diameter of the largest drops was always less than the Kolmogorov microscale (d < η). A much greater increase (than the aforementioned linear relationship) in drop size with phase fraction was observed for ? ≤ 0.05; including cases where an oil soluble surfactant was present and where metal mixing head surfaces were rendered hydrophobic by treatment with silane functional groups. It is argued that this significantly greater dependence on ? is due to the flow field being locally laminar near the drops with coalescence rate being strongly affected by the collision efficiency, which depends on the viscosity of both phases. The presence of surfactant decreased drop size. The silane treatment decreased drop size; possibly by altering water drop interactions with mill head surfaces. Additional experiments were performed at higher phase fraction, where surfactant was required to stabilize the emulsion. The equilibrium drop size was found to plateau for 0.10 < ? < 0.50. The high phase fraction behavior is attributed to the competing rates of coalescence and breakage and their dependence on ? and drop size.     

Synthesis and characterization of pH/temperature-sensitive block copolymers via atom transfer radical polymerization

In order to prepare well-defined pH-sensitive block copolymers with a narrow molecular weight distribution (MWD), we synthesized a pH-sensitive block copolymer via atom transfer radical polymerization (ATRP) of sulfamethazine methacrylate monomer (SM) and amphiphilic diblock copolymers by the ring-opening polymerization of d,l-lactide/?-caprolactone (LA/CL), and their sol-gel phase transition was investigated. SM, which is a derivative of sulfonamide, was used as a pH responsive moiety, while PCLA-PEG-PCLA was used as a biodegradable, as well as a temperature sensitive one, amphiphilic triblock copolymer. The pentablock copolymer, OSM-PCLA-PEG-PCLA-OSM, was synthesized using Br-PCLA-PEG-PCLA-Br as an ATRP macroinitiator. The number average molecular weights of SM were controlled by adjusting the monomer/initiator feed ratio. The macroinitiator was synthesized by the coupling of 2-bromoisobutyryl bromide with PCLA-PEG-PCLA in the presence of triethyl amine catalyst in dichloromethane. The resultant block copolymer shows a narrow polydispersity. The block copolymer solution shows a sol-gel transition in response to a slight pH change in the range of 7.2-8.0. Gel permeation chromatography (GPC) and NMR were used for the characterization of the polymers that were synthesized.     

Synthesis and characterization of well-defined hydrophilic block copolymer brushes by aqueous ATRP

Homopolymer brushes of poly(N,N-dimethylacrylamide) (PDMA), poly(methoxyethylacrylamide) (PMEA) and poly(N-isopropylacrylamide)(PNIPAM) grown on atom transfer radical polymerization (ATRP) initiator functionalized latex particles were used as macroinitiators for the synthesis of PDMA-b-PNIPAM/PMEA, PMEA-b-PDMA/PNIPAM and PNIPAM-b-PDMA block copolymer brushes by surface initiated aqueous ATRP. The grafted homopolymer and block copolymer brushes were analyzed for molecular weight, molecular weight distribution, chain grafting density, composition and hydrodynamic thickness (HT) using gel permeation chromatography-multi-angle laser light scattering, ¹H NMR, particle size analysis and atomic force microscopy (AFM) techniques. The measured graft molecular weight increased following the second ATRP reaction in all cases, indicating the second block had been added. Chain growth depended on the nature of the monomer used for block copolymerization and its concentration. Unimodal distribution of polymer chains in GPC with non-overlap of molar mass-elution volume curves implied an efficient block copolymerization. This was supported by the increase in HT measured by particle size analysis, equilibrium thickness observed by AFM and the composition of the block copolymer layer by ¹H NMR analysis, both in situ and on cleaved chains in solution. ¹H NMR analysis of the grafted latex and cleaved polymers from the surface demonstrated that accurate determination of the copolymer composition by this method is possible without detaching polymer chains from surface. Block copolymer brushes obey the same power law dependence of HT on molecular weight as homopolymer brushes in good solvent conditions. The NIPAM-containing block copolymer brushes were sensitive to changes in the environment as shown by a decrease in HT with increase in the temperature of the medium.     

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.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part I: Droplet dispersion and coalescence—a review

The theoretical and experimental data on the breakup of droplets are reviewed. Several factors influence development of droplets: flow type and its intensity, viscosity ratio, elasticity of polymers, composition, thermodynamic interactions, time, etc. For Newtonian systems undergoing small, linear deformation, both the viscosity ratio and the capillary number control deformability of drops. On the other hand, the breakup process can be described by the dimensionless breakup time and the critical capillary number. Drops are more efficiently broken in elongational flow than in shear, especially when the viscosity ratio λ ? 3. The drop deformation and breakup seems to be more difficult in viscoelastic systems than in Newtonian ones. There is no theory able to describe the deformability of viscoelastic droplet suspended in a viscoelastic or even Newtonian medium. The effect of droplets coalescence on the final morphology ought to be considered, even at low concentration of the dispersed phase, ?_d ? 0.005. Several drop breakup and coalescence theories were briefly reviewed. However, they are of little direct use for quantitative prediction of the polymer blend morphology during compounding in a twin-screw extruder. Their value is limited to serving as general guides to the process modeling.     

Segregation and conformational transitions in triblock copolymers in dilute solution: 3. Viscometric investigations in solvent mixtures

Viscometric measurements were carried out on a triblock copolymer PMMA/PS/PMMA at two temperatures in two binary solvent mixtures, in order to establish to what extent segregation between the two kinds of blocks is maintained as the composition of the solvent mixture i.e. its preferential affinity to one of the blocks, changes. From the variation of the limiting viscosity number of the polymer versus composition of the solvent mixture, taking into account the corresponding plots for the two homopolymers, it was established: that at relatively low temperature the molecular dimensions of the block copolymer are very close to those calculated neglecting the heterocontact interactions, i.e. assuming segregation, and that at higher temperatures the dimensions observed for the block copolymer are higher than the values calculated by assuming segregation, thus showing that the heterocontacts exert some influence, inducing the chain to expand. A comparison with a PS/PMMA random copolymer of the same composition showed, however, that in the same solvent mixtures the number of heterocontacts was far lower in the case of the block copolymer than in the case of the random copolymer, even at elevated temperatures.     

Phase separation of polystyrene-b-(ethylene-co-butylene)-b-styrene (SEBS) deposited on polystyrene thin films

Phase separation of a triblock copolymer, polystyrene-b-(ethylene-co-butylene)-b-styrene (SEBS) on the thin films of a homopolymer, polystyrene (PS), was studied by atomic force microscopy (AFM) and transmission electron microscopy (TEM). The final morphology after phase separation was found to be greatly dependent on the relation between the molecular weight of the PS block and homo-PS. Dispersed spherical and worm-like micelles of SEBS were observed when the molecular weight of homo-PS is smaller than the PS block in SEBS, while large structures with inner micro-phase separation of SEBS was found when the molecular weight of homo-PS was much higher than that of the PS block. The origin of such a change in morphology is attributed to the difference of structure and interfacial tension at the interface between the matrix homo-PS and the PS block in SEBS triblock copolymer assembly.