Drop deformation in polymer blends during uniaxial elongational flow

The deformation in uniaxial elongational flow of dispersed droplets in immiscible molten polymer blends was studied for negligible interfacial tension and for viscosity ratio p = η(drop)/η(matrix) between 0.005 and 13, with an original method based on quenching elongated specimens. Although drop deformation (drop major axis over initial diameter) was in the range 1 < λ_d < 5, a good overall agreement was found with the small deformation Newtonian theory, which predicts that the drop versus matrix deformation ranges from 5/3 to 0 when p increases from 0 to infinity. The theoretical prediction that for p lower than 1, the droplet should deform more than the faraway surrounding matrix, with a limiting ratio of 5/3 at vanishing droplet viscosity, was experimentally verified.     

Comparative study of monomer droplet nucleation in the seeded batch and semibatch miniemulsion polymerisation of styrene

Monomer droplet nucleation in the seeded miniemulsion polymerisation of styrene under monomer-flooded and monomer-starved conditions was studied. The miniemulsion feeds were added to the reactor either batchwise or semibatchwise. The droplets preserved longer under flooded conditions. As a result, the batch operation led to a larger number of particles (N_p) than the semibatch operation. For the miniemulsion droplets containing predissolved polymer, the final N_p was independent of the way that the feed was added to the reactor and was equivalent to the number of monomer droplets in the original miniemulsion feed. The size distribution of the final latexes, however, was influenced by the operation type. For the batch operation, the rate of polymerisation (R_p) with the miniemulsion feeds was higher than that with the conventional monomer emulsion feed because of the monomer droplet nucleation. But for the semibatch operation, the opposite was true because of R_p controlled by the rate of monomer diffusion from rather stable miniemulsion droplets to the growing polymer particles.     

A combined CFD modeling with population balance equation to predict pressure drop in venturi scrubbers

A venturi scrubber is one of the most important devices for air pollution control. Although there are different models for predicting the pressure drop in venturi scrubbers, most of them have some defects and cannot predict the pressure drop correctly. In this study, for the first time, an Eulerian–Eulerian computational fluid dynamics (CFD) model is combined with a population balance equation to predict the pressure drop in venturi scrubbers. This simulation takes into account a multiple size group model for droplet dispersion and droplet size distribution, which is based on a population balance equation. Flow field has been calculated by solving the time averaged continuity and Navier–Stokes equations along with the standard k–ε turbulence model. The equations included drag, turbulent dispersion, and buoyancy forces. The calculated pressure drop with and without considering the population balance equation was compared with the experimental data to evaluate the accuracy of the CFD modeling. The size distribution of droplets in the venturi scrubber was studied at different points for different liquid to gas ratios and throat gas velocities. The results show that the maximum break-up of droplets happens at the liquid injection point. Finally, the effects of nozzle diameter and nozzle arrangement on pressure drop in venturi scrubbers were investigated.     

On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

Coalescence in quiescent polymer blends with a high content of the dispersed phase

Coalescence in molten quiescent polymer blends induced by van der Waals forces is studied theoretically. Interaction between a droplet and its nearest neighbor keeping spherical shape during drainage of the matrix trapped between them is considered. It is assumed that droplets with time dependent radius R or effective droplets with radius R + h_c/2, where h_c is the critical inter-droplet distance for breakup of the matrix trapped between them, are randomly distributed in the blend through the whole course of the coalescence. Various approaches to calculation of the average time of coalescence, t_c (calculation with preaveraged distance between a droplet and its nearest neighbor at the start of coalescence, h₀, direct averaging of t_c and averaging coalescence frequency, 1/t_c) are compared. Calculated dependence of R on the time of coalescence, t, is compared with experimental results for polypropylene/ethylene–propylene rubber (PP/EPR) blends with EPR content from 15 to 30 wt.%. Calculations using average h₀ and direct averaging of t_c lead to more-less linear dependence of R³ on t. Bare averaging of 1/t_c leads to a steeper than linear dependence of R³ on t and to unreasonably high rate of the coalescence; averaging of 1/t_c with exclusion of pairs with elapsed coalescence time leads to decreasing rate of R³ growth but unreasonably low rate of coalescence. Theories based on the concept of effective droplet radius give smaller differences among various methods of calculations of t_c than the theories assuming random distribution of the droplets. Experimental results show decreasing slope of R³ vs. t dependence, especially for a higher content of dispersed EPR. Theories using average h₀ or direct averaging of t_c predict somewhat smaller rate of coalescence than that experimentally determined for PP/EPR blends. Reasons of these differences are discussed.     

Evidence of Molecular Fragmentation inside the Charged Droplets Produced by Electrospray Process

The behavior of the analyte molecules inside the neutral core of the charged droplet produced by the electrospray (ES) process is not unambiguously known to date. We have identified interesting molecular transformations of two suitably chosen analytes inside the ES droplets. The highly stable Ni(II) complex of 1,8-dimethyl-1,3,6,8,10,13-hexaazacyclotetradecane (1) that consists of a positive charge at the metal center, and the allyl pendant armed tertiary amine containing macrocycle 3,4,5:12,13,14-dipyridine-2,6,11,15-tetramethyl-1,7,10,16-tetraallyl-1,4,7,10,13,16-hexaazacyclooctadeca-3,13-diene (M _4p ) have been studied by ESI mass spectrometry as the model analytes. We have shown that these two molecules are not representatively transferred from solution to gas phase by ESI; rather, they undergo fragmentation inside the charged droplets. The results indicated that a charged analyte such as 1 was possibly unstable inside the neutral core of the ES droplet and undergoes fragmentation due to the Coulombic repulsion imparted by the surface protons. Brownian motion of the neutral analyte such as M _4p inside the droplet, on the other hand, may lead to proton attachment on interaction with the charged surface causing destabilization that leads to fragmentation of M _4p and release of resonance stabilized allyl cations from the core of the droplet. Detailed solvent dependence and collision-induced dissociation (CID) studies provided compelling evidences that the fragmentation of the analytes indeed occurs inside the charged ES droplets. A viable model of molecular transformations inside the ES droplet was proposed based on these results to rationalize the behavior of the analyte molecules inside the charged ES droplets.     

Studies on droplet size distributions during coalescence in immiscible polymer blends filled with silica nanoparticles

The effect of silica nanoparticles on the morphology of （10/90 wt%） PDMS/PBD blends during the shear induced coalescence of droplets of the minor phase at low shear rate was investigated systematically in situ by using an optical shear technique. Two blending procedures were used： silica nanoparticles were introduced to the blends by pre-blending silica particles first in PDMS dispersed phase （procedure 1） or in PBD matrix phase （procedure 2）. Bimodal or unimodal droplet size distributions were observed for the filled blends during coalescence, which depend not so much on the surface characteristics of silica but mainly on blending procedure. For pure （10/90 wt%） PDMS/PBD blend, the droplet size distribution exhibits bimodality during the early coalescence. When silica nanoparticles （hydrophobic and hydrophilic） were added to the blends with procedure l, bimodal droplet size distributions disappear and unimodal droplet size distributions can be maintained during coalescence; the shape of the different peaks is invariably Gaussian. Simultaneously, coalescence of the PDMS droplets was suppressed efficiently by the silica nanoparticles. It was proposed that with this blending procedure the nanoparticles should be mainly kinetically trapped at the interface or in the PDMS dispersed phase, which provides an efficient steric barrier against coalescence of the PDMS dispersed phase. However, bimodal droplet size distributions in the early stage of coalescence still occur when incorporating silica nanoparticles into the blends with procedure 2, and then coalescence of the PDMS droplets cannot be suppressed efficiently by the silica nanoparticles. It was proposed that with this blending protocol the nanoparticles should be mainly located in the PBD matrix phase, which leads to an inefficient steric barrier against coalescence of the PDMS dispersed phase; thus the morphology evolution in these filled blends is similar to that in pure blend and bimodal droplet size distributions can be observed during the early coalescence. These results imply that exploiting non-equilibrium processes by varying preparation protocol may provide an elegant route to regulate the temporal morphology of the filled blends during coalescence.     

Generation of Water-In-Oil-In-Water (W/O/W) Double Emulsions by Microfluidics

Novel compartment microparticles prepared with double emulsion droplets as templates provide a protected internal space for material encapsulation. The effect of three-phase flow rate on the micro-droplet generation of double emulsion mechanism is available for reference to produce precise size and highly monodisperse particles. The influence of three-phase flow rate on the formation mode and size of the emulsion droplets is investigated by combination of experiment and numerical simulation. The size of compound droplets decreases and frequency increases with the increasing outer fluid flow rate. The monodispersity of the double emulsion reduces due to transition from dripping to narrowing jetting regime. Outer droplet size increases with the increasing flow rate of the middle fluid, whereas inner droplet size is the opposite. The frequency increases and then stabilizes, which leads to a widening regime. When Q₂/Q₁ > 6, the multi-core type double emulsion droplets are produced. Droplet coalescence occurs when surfactants is not involved. As Q₁ increases, there is an increasing tendency for inner drop size. The outer drop size is proportional to the sum of the inner and middle flow rate, and that is irrelevant to Q₁/Q₂. For drop size, the ratio of core-shell and internal structure is precisely controlled by adjusting three-phase flow rate respectively.     

Effect of droplet size on the phosphine depression of calcium atomic emission signals in flame spectrometry

The effect of the droplet size on the magnitude of the phosphine depression of calcium signals is discussed. The droplet size governs the time required for droplet desolvation in the flame. It is during the desolvation process that the combustion products of phosphine, PO_x, diffuse into the droplet and form a refractory compound with the analyte. The longer the desolvating droplet resides in the PO_x-contaminated flame, the more severe the depression. A uniform droplet generator, a pneumatic nebulizer spray chamber system, and a glass-frit nebulizer spray chamber system were the sample introduction systems studied. Droplet sizes of (55 μm, 0.5–10 μm (2 μm mean), and <0.1–2 μm (0.1 μm mean) were produced by these systems, respectively, and depressions of the calcium signals of 57%, 55%, and 4% were noted. These results suggest that the phosphine depression on calcium signals may be alleviated by using a glass-frit nebulizer (or modifying a commercial nebulizer) to remove droplets greater than 2 μm in diameter.     

Surface tension of different sized single-component droplets,according to macroscopic data obtained using the lattice gas model and the critical droplet size during phase formation

Size dependences of the surface tension of spherical single-component droplets are calculated using equations of the lattice gas model for 19 compounds. Parameters of the model are found from experimental data on the surface tension of these compounds for a macroscopic planar surface. The chosen low-molecular compounds satisfy the law of corresponding states. To improve agreement with the experimental data, Lennard-Jones potential parameters are varied within 10% deviations. The surface tensions of different sized equilibrium droplets are calculated at elevated and lowered temperatures. It is found that the surface tension of droplets grows monotonically as the droplet size increases from zero to its bulk value. The droplet size R ₀ corresponding to zero surface tension corresponds to the critical size of the emergence of a new phase. The critical droplet sizes in the new phase of the considered compounds are estimated for the first time.     

Master curves for elastic and plastic properties of highly concentrated emulsions

Critical comparison of dependences of elastic and plastic properties of highly concentrated emulsions (so-called “compressed” emulsions) on the concentration and droplet sizes is performed. The studied emulsions of water-in-oil type are so-called “liquid explosives.” They are characterized by different mean sizes and different droplet size distributions of the dispersed phase. Different average values (D _av, D ₃₂, and D ₄₃) are used as characteristics of droplet sizes. Experiments are carried out with emulsions of two concentrations. Aqueous phase (dispersed droplets) is presented by supercooled solutions of inorganic salt in water in a metastable state. The concentration limit of the existence of highly concentrated emulsions is determined by the condition of the closest packing of liquid droplets, which lies in the φ* = 0.77–0.80 range. In addition, there is a limiting value of the maximal size of droplets. This limiting value depends on the concentration and meets the requirement that droplets should be small enough for the solution to exist in a supercooled state. The elastic modulus and the yield stress of emulsions studied are proportional to the square of the reciprocal linear size of droplets, which contradicts some theoretical models, according to which these parameter should be proportional to the reciprocal size of droplets. Using the obtained experimental data, we constructed generalized dependences of the elastic modulus and the yield stress on the concentration and size of droplets. These characteristics are in good agreement with the experimental data.     

Correlation of the viscosity of pure liquids at high pressures based on an equation of state

A novel model has been presented for correlating the dynamic viscosity of Newtonian liquids at high pressures. The proposed model was started with the activation volume, which could simultaneously be influenced by temperature and pressure. The core of the model was based on Hu and Liu's work to calculate the compressibility factor. The final expression may contain two adjustable parameters, namely κ₁ and κ₂, which had been determined by fitting literature viscosity data. The results show that the agreement between experimental data of viscosity and the calculated ones with the proposed model was reasonably good for the selected systems. It was found that the logarithm of parameter κ₁ was a linear function of the reciprocal of the temperature, and κ₁ was approximately equal to viscosity of liquid at 0.1 MPa. Besides, for linear chain hydrocarbons, the logarithm of the parameter κ₁ was completely a linear function of the number of the carbon atoms under certain temperature. A comparison between model with two-parameter and one with one-parameter had been given to show their applicability. The results calculated by not only two-parameter but also one-parameter were superior to corresponding ones by previous pressure equation for estimating viscosity.     

Electrical actuation of dielectric droplets by negative liquid dielectrophoresis

This paper presents an electrical actuation scheme of dielectric droplet by negative liquid dielectrophoresis. A general model of lumped parameter electromechanics for evaluating the electromechanical force acting on the droplets is established. The model reveals the influence of actuation voltage, device geometry, and dielectric parameter on the actuation force for both conductive and dielectric medium. Using this model, we compare the actuation forces for four liquid combinations in the parallel-plate geometry and predict the low voltage actuation of dielectric droplets by negative dielectrophoresis. Parallel experimental results demonstrate such electric actuation of dielectric droplets, including droplet transport, splitting, merging, and dispending. All these dielectric droplet manipulations are achieved at voltages < 100 V_rms. The frequency dependence of droplet actuation velocity in aqueous solution is discussed and the existence of surfactant molecules is believed to play an important role by realigning with the AC electric field. Finally, we present coplanar manipulation of oil and water droplets and formation of oil-in-water emulsion droplet by applying the same low voltage.     

Effect of viscosity ratio on the morphology of PET microfibrils in uncompatibilized and compatibilized drawn PET/PP/TiO2 blends

Uncompatibilized and compatibilized (polypropylene‐grafted maleic anhydride (PP‐g‐MA) as compatibilizer) PET (polyethylene terephthalate)/PP (polypropylene)/TiO₂ drawn strands were prepared by extrusion of the blends and cold drawing of the extrudates. In the uncompatibilized drawn strand, the generated PET microfibrils show large aspect ratio and wide distribution in diameter; whereas in the compatibilized drawn strand numbers of short needle‐like PET formations appear and demonstrate uniform diameter distribution. Derived from PET droplets, the microfibril morphology is greatly influenced by the size of PET droplets in the extrudates: small droplet deforms into needle‐like shape and large one becomes microfibril. In the compatibilized PET/PP/TiO₂ extrudate, the size of PET droplet is much smaller than that in the uncompatibilized one. The reduction of droplet size is attributed to the low viscosity ratio between dispersed phase and matrix, which facilitates the break up of the dispersed PET droplets. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 555–562, 2009     

<Superscript>2</Superscript>H-NMR investigation after a polymerisation-induced phase separation process*

Polymer-dispersed liquid crystals (PDLC) are composite materials consisting of micron-sized droplets of liquid crystal dispersed in a polymer matrix. The easiest method to obtain a PDLC film is the polymerisation-induced phase separation process (PIPS). The liquid crystal is mixed with a monomer of low molecular weight and polymerisation is induced by heat or UV light. The increasing molecular weight of the polymer causes the phase separation of liquid crystal from the polymer matrix as micron-sized droplets. In this work, we have studied the structural changes induced in the polymer matrix of a PDLC after the PIPS process by deuterium nuclear magnetic resonance. Two different selectively deuterated monomers have been synthesized and investigated: isobutyl methacrylate (IBMA-d₂) and methyl methacrylate (MMA-d₃). The main results were the disappearance of the characteristic two-site hop in poly-IBMA, due to liquid crystal molecules, and the lack of unreacted MMA molecules in the liquid crystal droplets. In this last case, we found that it is possible to confine temporarily the unreacted MMA molecules within liquid crystal droplets.Abbreviations MMA Methyl methacrylate - IBMA Isobutyl methacrylate - PDLC Polymer-dispersed liquid crystal - PIPS Polymerisation-induced phase separation - ²H-NMR Deuterium nuclear magnetic resonance*Dedicated to Professor V. Bertini for his 70^th birthday     

Growth and motion of heterogeneous water droplets in laminar diffusion chambers: 2. High nanoparticle concentrations

The heterogeneous condensation of water vapor on nanoparticles and the growth of formed droplets are numerically studied under conditions of laminar diffusion chamber (LDC) of a new type with a hot porous wall. The main attention is focused on the growth of heterogeneous droplets in the gas flow at high number densities of nanoparticles exceeding 10⁸ droplet/m³. Under these conditions, there is an interrelation between the growth of droplets and processes of heat and mass transfer in LDC due to vapor depletion and the release of latent heat of phase transition on growing droplets. The efficiency of the coverage of nanoparticles with water film is studied under LDC nonuniform conditions. It is shown that, at initial number densities of nanoparticles (N _d > 10¹¹ droplet/m³), heterogeneous droplets do not grow to optically detected sizes.     

Kinetics of droplet growth in the metastable region in cellulose acetate/acetone/nonsolvent system

The kinetics of droplet growth in the metastable region were investigated in cellulose acetate/acetone/nonsolvent system. The results obtained by the dynamic light scattering apparatus indicated that the droplet diameter d increased with time t in the relation of d³∝t in all cases. From the detailed consideration on the slope values in these relations, it was concluded that the droplet growth mechanism in this system was coalescence mechanism rather than Ostwald ripening mechanism. The direct observation of the freeze-dried polymer solution by SEM was not contradictory to this conclusion. The initial stage of droplet growth was investigated by the stopped-flow apparatus. The experimental results on the turbidities showed that the droplets grew in the relation of d³∝t as well as the results by the light scattering.     

A real-time AFM study on crystal nucleation and growth in nanodroplets of isotactic polypropylene

Isotactic polypropylene (iPP) nanodroplets were prepared by using the classical droplet method in this study. The formation of nanodroplets allowed the controlled observation of polymer nucleation as well as access to crystal growth at exceptionally high supercooling in iPP. Three cases including the heterogeneous nucleation and fast crystallization in iPP droplets, the formation of multiple independent homogeneous nuclei within a single droplet and a single nucleus within a single droplet were detected by using atomic force microscopy (AFM) during gradually cooling after remelting the nanodroplets. Moreover, it is found that when the volume of droplet is larger than the value of ca. 130000 nm3, the first case was observed. Otherwise, the latter two cases appeared. The temperature at which the onset of nucleation was observed in individual droplets was found to be mainly dependent on height of the droplets when the size scale of the droplet is comparable to the size of the critical nucleus in at least one dimension, which indicates the nucleation behavior under confinement.     

FRAGMENTATION OF PRIMARY FLOCS IN EMULSIONS AND THE SUBSEQUENT REDUCTION OF COALESCENCE

In existing theories emulsion desiabilization is considered as the combined processes of irreversible flocculation and coalescence of dispersed droplets. This approach can be justified when the potential pit characterizing the energy of droplet interaction is sufficiently deep, i.e. excluding small droplet dimensions, strong electrosiatic repulsion and low electrolyte concentrations. For smaller droplet dimensions and stronger electrostatic repulsions the emulsion instability must be considered as a combined process of reversible flocculation and coalescence. In this paper a mathematical model that couples the kinetics of flocculation, coalescence and floe fragmentation is developed in order to quantify the kinetic instability of emulsions with charged submicron droplets. The characteristic limes for flocculation (Smoluchowski's time τ_c) for coalescence (coalescence time τ_c) and for disaggregation (doublet lifetimeτ_d) are considered model parameters. The mathematical model applies to the case when and τ_d<< τ_c, which corresponds to a situation with a small multiplet concentration compared to the concentration of doublets and a singlet-doublet quasi-equilibrium. It is established that at singlet-doublet quasi-equilibrium the rate of the decline in the total droplet concentration is described by second order kinetics in distinction to the exponential time dependence valid for coalescence at irreversible flocculation. The double disintegration reduces the entire coalescence rate, expressed as τ_sm/ τ_d. This reduction is very large at small values of Td. The mathematical model presented can hased on the spontaneous disintegration of doublets predict changes in emulsion stability for model systems and also for technologically important emulsions.