Drop Deformation and Breakup Mechanisms in Viscoelastic Model Fluid Systems and Polymer Blends

This paper reviews the dispersion mechanisms in viscoelastic systems under relatively high shear rate conditions. In particular, two non‐Newtonian deformation and breakup mechanisms were revealed by flow visualization in a transparent Couette shearing setup. The first one is the dispersed droplet elongation perpendicular to the flow direction. This was observed only for viscoelastic drops and had been associated to normal force buildup in the droplet. The second deformation/breakup mechanism was observed in very high viscosity ratio polymer systems. It consists in erosion at the drop surface. Clouds of very small ribbons and sheets were developed around the drop then stretched and finally broken into very small droplets, rapidly distributed in the matrix.     

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     

Modeling of polymer melting,drop deformation,and breakup under shear flow

Polyethylene (PE) or polycarbonate (PC) drop deformation and the breakup mechanism in a PE melt under shear flow were investigated using numerical simulations. The volume of fluid (VOF) method in FIDAP was used to track the dynamic interface. Two models were built for the investigation of a PE/PE system and a PE/PC system. Experimental data of polymer properties, such as specific heat capacity, viscosity, and heat conductivity, were incorporated in the simulations. For the PE/PE system, a temperature‐dependent viscosity model was used for the matrix PE and the dispersed PE. For the PE/PC system, generalized viscosity models were used for PE and PC with time‐dependent moving boundaries. An erosion mechanism similar to that observed in previous experiments was found for deformation and breakup of both PE and PC in the PE melt under simple shear flow. Local flow information, such as temperature, shear rate, viscosity, and shear stress, was obtained from the simulation results. The shear stress at the interface was much higher than the shear stress either in the dispersed phase or in the matrix phase, which could explain the erosion breakup mechanism. Polym. Eng. Sci. 44:1258–1266, 2004. © 2004 Society of Plastics Engineers.     

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.     

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.     

Prediction of dispersed phase drop diameter in polymer blends: The effect of elasticity

This paper discusses the prediction of the dispersed phase drop diameter in polymer blends considering the viscoelastic properties of polymers. The prediction is based on a simple force proportionality. Polymers are viscoelastic, and thus the elasticity of the matrix and the elasticity of the dispersed phase affect the drop size. The forces that deform a polymer droplet in a polymer matrix are the shear forces, η_mγ, and the matrix first normal stress, T_11,m. This deformation is resisted by the interfacial forces, 2 Γ/D and the drop's first normal stress, T_11,d. As a first approximation, the forces were balanced to predict the particle size in polymer blends. The diameter of the dispersed phase was predicted reasonably well for several systems at different operating conditions. It was observed for some systems (PS/PP, PS/EPMA, PS/PA330) that, as the shear rate increased, the diameter of the dispersed phase initially decreased. At a critical shear rate, the diameter reached a minimum value, and beyond it, the diameter increased with shear. This critical value was found to be between 100 to 162.5 s⁻¹ for a PS/PP system. The force balance predicts this minimum drop diameter at a similar critical shear rate. The specific energy input (the amount of energy input into the blend) could not explain the phenomenon of a minimum drop diameter with increase in shear. This minimum is not observed for the high concentration systems, such as the 20% PP dispersed in PS, since the effects of coalescence become significant. In reactive blends, the predicted drop diameter was closer to the experimentally determined diameter, and there was less variation in diameter with changes in shear rate.     

Transient and steady-state deformations and breakup of dispersed-phase droplets of immiscible polymer blends in steady shear flow

Transient and steady-state deformations and breakup of viscoelastic polystyrene droplets dispersed in viscoelastic high-density polyethylene matrices were observed in a simple steady shear flow between two transparent parallel disks. By separately varying the elasticities of the individual blend components, the matrix shear viscosity, and the viscosity ratio, their effects on the transient deformation, steady-state droplet size, and the breakup sequence were determined. After the startup of a steady shear flow, the viscoelastic droplet initially exhibits oscillations of its length in the flow direction, but eventually stretches preferentially in the vorticity direction. We find that at fixed capillary number, the oscillation amplitude decreases with increasing droplet elasticity, while the oscillation period depends primarily on, and increases with, the viscosity ratio. At steady-state, the droplet length along the vorticity direction increases with increasing capillary number, viscosity ratio, and droplet elasticity. Remarkably, at a viscosity ratio of unity, the droplets remain in a nearly undeformed state as the capillary number is varied between 2 and 8, apparently because under these conditions a tendency for the droplets to widen in the vorticity direction counteracts their tendency to stretch in the flow direction. When a critical capillary number, Ca_c, is exceeded, the droplet finally stretches in the vorticity direction and forms a string which becomes thinner and finally breaks up, provided that the droplet elasticity is sufficiently high. For a fixed matrix shear stress and droplet elasticity, the steady-state deformation along the vorticity direction and the critical capillary number for breakup both increase with increasing viscosity ratio.     

Nonlinear rheological behavior of a novel oil displacing agent

In this work, the shear and elongational rheologies have been investigated for a newly developed oil displacing agent, polymeric surfactant‐PSf. It was found that the PSf solutions exhibited Newtonian, shear‐thinning, and shear‐thickening behavior, respectively, depending on the polymer concentration and shear rate, and Cox–Merz rule was not applicable to these systems. The first normal stress difference (N₁) versus shear rate plots for PSf were complicated, which varied with the composition of the solutions. The uniaxial elongation in capillary breakup experimental results indicated that Exponential model could be used to fit the experimental data of the PSf solutions at lower polymer concentrations. In addition, it was found that PSf was more effective in improving shear viscosity than partially hydrolyzed polyacrylamide, but not in the case of elongational viscosity. The experimental results indicated that the microstructural mechanisms are responsible for the rheological behavior of the polymers. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40813.     

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.     

BUOYANCY-DRIVEN MOTION OF DROPS AND BUBBLES IN A PERIODICALLY CONSTRICTED CAPILLARY

Buoyancy-driven motion of viscous drops and air bubbles through a vertical capillary with periodic constrictions is studied. Experimental measurements of the average rise velocity of buoyant drops are reported for a range of drop sizes in a variety of two-phase systems. The instantaneous drop shapes at various axial positions within the capillary are also quantitatively characterized using digital image analysis. Periodic corrugations of the capillary wall are found to have a substantial retarding effect on the mobility of drops in comparison with previous experimental results in a straight cylindrical capillary. For systems characterized by small Bond numbers, drop deformations are found to be periodic. In large Bond number systems, however, drop breakup eventually occurs as the drop size is increased beyond a critical limit. The observed mode of breakup is a tail-pinching process similar to that observed by Oibricht and Leal (1983) for pressure-driven motion of low viscosity ratio drops through a sinusoidally constricted capillary. In contrast to their results, however, the same mode of breakup was also observed for systems with O (1) viscosity ratios,     

Capillary breakup extensional rheometry of associative and hydrolyzed polyacrylamide polymers for oil recovery applications

High molecular weight polymers used for heavy oil recovery exhibit viscoelasticity that can influence the oil recovery during chemical enhanced oil recovery. Different polymers having similar molecular weight and shear rheology may have different elongation flow behavior depending on their extensional properties. Displacing slugs are more likely to stretch than shear in tortuous porous media. Therefore, it is critical to seek an analytical tool that can characterize extensional parameters to improve polymer selection criteria. This article focuses on the extensional characterization of two polymers (hydrolyzed polyacrylamide and associative polymer) having identical shear behavior using capillary breakup extensional rheometer to explain their different porous media behavior. Maximum extensional viscosity at the critical Deborah number and Deborah number in porous media classified the associative polymer as the one having high elastic‐limit. Extensional characterization results were complemented by significantly higher pressure drop, marginally increased oil recovery of associative polymer in porous media. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46253.     

Effects of shear rate,viscosity ratio and liquid crystalline polymer content on morphological and mechanical properties of polycarbonate and LCP blends

Studies were conducted on the effects of shear rate, viscosity ratio and liquid crystalline polymer (LCP) content on the morphological and mechanical properties of polycarbonate (PC) and LCP blends. The LCP (LC5000) used was a thermotropic liquid crystalline polymer consisting of 80/20 of parahydroxybenzoic acid and poly(ethylene terephthalate) (PHB/PET). The viscosity ratio (viscosity of LCP: viscosity of matrix) was varied by using two processing temperatures. Due to the different sensitivity of materials to temperature, variation in the processing temperature will lead to varying viscosity of the components in the blends. Based on this principle, the processing temperature could be manipulated to provide a favourable viscosity ratio of below unity for fibre formation. To study the effect of shear rate, the flow rate of the blend and the mould thickness were varied. The shear rate has a significant effect on the fibrillation of the LCP phase. The effect was more prominent when the viscosity ratio was low and the matrix viscosity was high. At 5 wt% LCP, fibrillation did not occur even at low viscosity ratios and high shear rates. It was also observed that the LCP content must be sufficiently high to allow coalescence of the dispersed phase for subsequent fibrillation to occur. © 2002 Society of Chemical Industry     

Rheological study of mixing in molten polymers: 1-mixing of low viscous additives

A new mixing device has been designed and developed in order to investigate complex mixing situations encountered in polymer blends and formulations. This mixing device called here rheo-mixer has been adapted on a classical rheometer and calibrated in terms of shear/stress that both permanent and dynamic regimes may be quantitatively run. The ability of the mixer to bring interesting information about complex polymeric systems was demonstrated by following the process of incorporation of a miscible liquid or partially miscible into a high viscosity polymer. As examples, EVA/diethyl 2-hexyl phtalate, poly(ε-caprolactone)/ε-caprolactone, and EVA/ε-caprolactone systems were tested.It was demonstrated that the viscosity ratio is not the predominant parameter for mixing process control because the mixing is mainly controlled by the diffusion for these low viscosity ratio systems (λ<10⁻⁵) as miscible systems (EVA/DOP and PCL/ε-CL) and partially miscible systems (EVA/ε-CL) are concerned. Actually, the mixing efficiency of these fluids is poor because the shear migration diminishes the rate of mixing due to a decrease of the deformation in the high viscous media. The mixing by thick striation is only effective when the viscosity ratio becomes, by the diffusion process, typically higher than 10⁻³. Furthermore, the discussion based on the mutual diffusion coefficient agrees well with the experimental finding, at least qualitatively.     

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.     

Melt flow behavior in capillary extrusion of nanosized calcium carbonate‐filled poly(L‐lactic acid) biocomposites

Nanosized calcium carbonate (nano‐CaCO₃)‐filled poly‐L ‐lactide (PLLA) biocomposites were compounded by using a twin‐screw extruder. The melt flow behavior of the composites, including their entry pressure drop, melt shear flow curves, and melt shear viscosity were measured through a capillary rheometer operated at a temperature range of 170–200°C and shear rates of 50–10³ s^?1. The entry pressure drop showed a nonlinear increase with increasing shear stress and reached a minimum for the filler weight fraction of 2% owing to the “bearing effect” of the nanometer particles in the polymer matrix melt. The melt shear flow roughly followed the power law, while the effect of temperature on the melt shear viscosity was estimated by using the Arrhenius equation. Hence, adding a small amount of nano‐CaCO₃ into the PLLA could improve the melt flow behavior of the composite. POLYM. ENG. SCI., 52:1839–1844, 2012. © 2012 Society of Plastics Engineers     

Effect of the dispersed phase fraction on particle size in blends with high viscosity ratio

It has been reported that for polymer blends with high viscosity ratio (>1), the size of the dispersed particles decreases with increasing volume fraction of the dispersed phase. In order to explain this effect, an equation was derived for the affine deformation of an imaginary plane of the dispersed phase in stratified two‐phase steady, simple, shear flow. The model predicts that for viscosity ratio >1, the deformation rate increases with volume fraction of the dispersed phase, and the shear stress also increases, leading to an increase of the breakup time. Therefore, the total deformation of the dispersed phase, before breakup, increases with increase of volume fraction, resulting in a decrease of the size of the dispersed phase particles. Accordingly, one can expect that in industrial mixers, the particle size of the blends should decrease as the volume fraction increases, if coalescence is suppressed. Experiments were carried out in a Haake batch mixer, using polyethylene/polyamide‐6 blends compatibilized by adding maleic anhydride grafted polyethylene. Particle size decreased up to 20 wt% polyamide‐6, at 100, 150, and 200 RPM, and increased between 20 and 30 wt%. The decrease of the particle size is mainly due to increased deformation of the dispersed phase. The increase of the particle size above 20 wt% is due to coalescence at high fractions.     

Influence of normal stress difference on polymer drop deformation

Polypropylene drops of varying viscosity and elasticity were sheared in a polystyrene matrix. Two transparent, counter-rotating parallel disks provided simple shear flow. By adjusting the speed of one disk the drop center was fixed in the laboratory frame and deformation followed via high magnification video camera. It was found that with high matrix elasticity drops of the minor phase stretched perpendicular (x₃) to the flow direction (x₁). This is the first report of widening of drops in shear flow. An analytical relation was established between the second normal stress differences of the phases and degree of widening. The formation of sheets and the phenomena of widening results in a larger than affine area generation.     

Shear and extensional properties of short glass fiber reinforced polypropylene

Shear and extensional properties of a commercial short glass fiber reinforced polypropylene were carefully investigated using commercial rheometers and a novel on‐line rheometer. This on‐line slit rheometer, installed on an injection molding press, has been designed to measure the steady shear viscosity, the first normal stress difference, and the apparent extensional viscosity of polymer melts and composites for high strain rates up to 10⁵ s⁻¹ in shear and 200 s⁻¹ in extension. Our results show that the steady‐state viscosity measurements using the on‐line rheometer are in excellent agreement with those obtained using commercial rheometers. The steady‐state and the complex viscosities of the composites were found to be fairly close to that of the matrix, but the Cox‐Merz rule was not verified for the composites at high rates. The elasticity of the composites was found to be equal to that of the polypropylene matrix. The apparent extensional viscosity was obtained from the pressure drop in the planar converging die of the slit rheometer using the analyses proposed by Cogswell [1] and Binding [2]. The extensional viscosity of the polypropylene was found to be much larger than the shear viscosity at low strain rates with a Trouton ratio of about 40 that decreased rapidly with increasing strain rate down to the value of 4 at 200 s⁻¹. The extensional viscosity of the composites was also found to be close to that of the matrix, with values 35 and 5% larger for the 30 and 10 wt% reinforced polypropylenes, respectively. These results are compared with the predictions of the Goddard model [3], which are shown to overpredict our experimental results. POLYM. COMPOS. 26:247–264, 2005. © 2005 Society of Plastics Engineers.     

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.     

Morphology evolution of a bisphenol A polycarbonate/poly (styrene-co-acrylonitrile) blend under shear and after shear cessation

The deformation, breakup and morphology relaxation of a commercially important polycarbonate (PC)/poly(styrene-co-acrylonitrile) (SAN) blend under and after steady shear flow have been studied in situ by combined phase contrast optical microscopy (PCOM), small angle light scattering (SALS) and rheometry. Under steady shear flow, the morphology of PC/SAN blends evolves via repeated deformation, breakup and finally string-like morphology. The data can be qualitatively interpreted with the mode-coupling renormalization group (MCRG) model. At high shear rate, shear-induced mixing effect is found to be saturated and no further shear-induced homogenization can be observed, which may be due to the fact that the experimental conditions (T, C) is far from the critical region and the shear suppression of concentration fluctuations is limited. Upon cessation of shear, different relaxation mechanisms are found. For low shear rate, the anisotropic ellipsoids retract to isotropic domains after shear cessation; while for higher shear rate, the string-like pattern breaks into necklace-like structure first and then the aligned structure relaxes to an isotropic distribution via diffusion process. The slow coarsening process upon cessation of shear is attributed to high viscosity of PC matrix and viscoelastic effects.