Particle-induced bridging in immiscible polymer blends

Pickering emulsions are emulsions whose drops are stabilized against coalescence by particles adsorbed at their interface. Recent research on oil/water/particle systems shows that particles can sometimes adsorb at two oil/water interfaces. Such “bridging particles” can glue together drops of oil in water or vice versa. We hypothesize that the same effect should apply in immiscible polymer blends with droplet-matrix morphologies, viz., added particles should glue together drops and give rise to particle-bridged drop clusters. We test this hypothesis in PIB-in-PDMS blends [PIB, poly(isobutylene); PDMS, poly(dimethylsiloxane)] with fumed silica particles. Direct visualization shows that the particles can indeed induce clustering of the drops, and the blends appear to show gel-like behavior. Such gel-like behavior is confirmed by dynamic oscillatory experiments. However, we are unable to conclusively attribute the gel-like behavior to droplet clustering: Association of the fumed silica particles in the bulk, which itself causes gel-like behavior, confounds the results and prevents clear analysis of the gluing effect of the particles. We conclude that PIB/PDMS/fumed silica is not a good model system, for studying particle-containing polymer blends. We instead propose that spherical monodisperse silica particles can offer a far more convenient model system, and provide direct visual evidence of gluing of PIB drops in a PDMS matrix.     

Effect of fumed silica nanoparticles on the morphology and rheology of immiscible polymer blends

We examined the effect of interfacially active particles on the morphology and rheology of droplet/matrix blends of two immiscible homopolymers. Experiments were conducted on polybutadiene/polydimethylsiloxane (10/90) blend and the inverse system. The effects of fumed silica nanoparticles, at low particle loadings (0.1–2.0 wt%), were examined by direct flow visualization and by rheology. Fumed silica nanoparticles were found to significantly affect the morphology of polymer blends, inducing droplet cluster structure and decreasing the droplet size, regardless of which phase wets the particles preferentially. This is surprising in light of much past research that shows that particles are capable of bridging and thus induce droplet cluster structure in droplet/matrix systems only when they are preferentially wetted by the continuous phase. Therefore, there should exist other possible mechanisms responsible for these droplet cluster structures except for the bridging mechanism. We proposed a particle-flocculating mechanism based on the fact that fumed silica particles readily flocculate due to their high aspect ratio, fractal-like shape, or interparticle attractions. Optical microscopy also reveals that the clustering structure becomes more extensive, and the droplet sizes in the clusters become smaller when the particle loading is increased. Rheologically, the chief effect of particles is to change the flow behavior from a liquid-like rheology to gel-like behavior. This gel-like behavior can be attributed to droplet clustering. Moreover, it should be emphasized that such gel-like behavior can be seen in the blends regardless of which phase wets the particles preferentially, suggesting that, once again, bridging is not the only cause of droplet clustering.     

Interfacially active particles in droplet/matrix blends of model immiscible homopolymers: Particles can increase or decrease drop size

Particles have been shown to adsorb at the interface between immiscible homopolymer melts and to affect the morphology of blends of those homopolymers. We examined the effect of such interfacially active particles on the morphology of droplet/matrix blends of model immiscible homopolymers. Experiments were conducted on blends of polydimethylsiloxane and 1,4-polyisoprene blended in either a 20:80 or 80:20 weight ratio. The effects of three different particle types, fluoropolymer particles, iron particles, and iron oxyhydroxide particles, all at a loading of 0.5 vol.%, were examined by rheology and by direct flow visualization. Particles were found to significantly affect the strain recovery behavior of polymer blends, increasing or decreasing the ultimate recovery, slowing down or accelerating the recovery kinetics, and changing the dependence of these parameters on the applied stress prior to cessation of shear. These rheological observations were found to correlate reasonably well with particle-induced changes in drop size. The particles can both increase as well as decrease the drop size, depending on the particle type, as well as on which phase is continuous. The cases in which particles cause a decrease in drop size are analogous to the particle stabilization of “Pickering emulsions” well-known from the literature on oil/water systems. We hypothesize that cases in which particles increase drop size are analogous to the “bridging–dewetting” mechanism known in the aqueous foam literature.     

Particle-stabilized polymer blends

The effect of low-volume fractions of nanoparticles on the morphological processes and the rheological properties of immiscible blends are dis cussed. For blends of poly-isobutylene and poly-dimethylsiloxane stabilized by silica particles, particles help to suppress coalescence. Yet, particle bridging of different droplets has also been reported and leads to a slow build up of a gel-like structure, which could interfere with the morphology evolution under flow. We first investigated the importance of this effect under relevant conditions. To further assess the relative importance of the different processes in technically relevant polymer–polymer blends, the effect of carbon black particles on morphological processes—coalescence and break-up—in polyamide and ethylene–ethylene–metylacrylate copolymers will be studied using rheological methods. It will be shown that particles affect coalescence and break-up, suggesting that the effect of particles is linked to their effect on interfacial dynamics.     

Investigation of liquid–liquid drop coalescence using tomographic PIV

High-speed tomographic PIV was used to investigate the coalescence of drops placed on a liquid/liquid interface; the coalescence of a single drop and of a drop in the presence of an adjacent drop (side-by-side drops) was investigated. The viscosity ratio between the drop and surrounding fluids was 0.14, the Ohnesorge number (Oh = μ_d/(ρ_dσD)^1/2) was 0.011, and Bond numbers (Bo = (ρ _d  − ρ _s )gD ²/σ) were 3.1–7.5. Evolving volumetric velocity fields of the full coalescence process allowed for quantification of the velocity scales occurring over different time scales. For both single and side-by-side drops, the coalescence initiates with an off-axis film rupture and film retraction speeds an order of magnitude larger than the collapse speed of the drop fluid. This is followed by the formation and propagation of an outward surface wave along the coalescing interface with wavelength of approximately 2D. For side-by-side drops, the collapse of the first drop is asymmetric due to the presence of the second drop and associated interface deformation. Overall, tomographic PIV provides insight into the flow physics and inherent three-dimensionalities in the coalescence process that would not be achievable with flow visualization or planar PIV only.     

A parameter investigation of shear-induced coalescence in semidilute PIB–PDMS polymer blends: effects of shear rate, shear stress volume fraction, and viscosity

In this work, drop coalescence of polymer blends under shear flow in a parallel flow apparatus was investigated by optical sectioning microscopy. In each experiment, shear rate was set at values low enough to avoid any break-up phenomena. The time evolution of the drop size distribution was determined by motorized sample scanning and iterative acquisition of stacks of images along sample depth. Drop size and location in the acquired images was found by automated image analysis techniques. A systematic experimental campaign to investigate the effects of shear rate (in the range 0.1–0.5 s⁻¹), volume fraction (2.5–10%), and viscosity of the two phases (3–63 Pa s) at different viscosity ratio (0.1–2.3) was carried out. By comparing data from different experiments, it was found that at any strain value, the average drop size decreases monotonically with the shear stress, calculated as the product of shear rate and matrix viscosity. Furthermore, the coalescence rate slowed down with increasing viscosity ratio. Overall, these results provide an extensive set of data, which can be used as a benchmark for modeling shear-induced coalescence in polymer blends.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Instability of entangled polymers in cone and plate rheometry

Flow instability in three entangled polymer systems including a 10 wt% 1,4-polybutadiene (PBD) solution, an 11.4 wt% polyisobutylene (PIB) solution, and a long chain branched polyethylene melt (LD 146) was investigated in both stress-controlled and rate-controlled experiments in the cone–plate geometry. It was found that flow instability occurred for experiments in both rate- and stress-controlled modes. The effects of cone angle or rim gap and shearing time on flow instability were studied. The smaller cone angle and shorter shearing time delay (in terms of stress or shear rate) the occurrence of severe instability and mass loss of the PBD solution but not for the PIB. Our data are consistent with the dramatic shear rate jump for the flow curve constructed from the stress-controlled experiments being associated with mass loss after the severe instabilities. We also find that the Cox–Merz representation gives a powerful tool for investigation of flow instability. Finally, another interesting result in this work is that it seems that the stress overshoot can be related to the onset of flow instability in the present system.     

Dissipative particle dynamics simulation of polymer drops in a periodic shear flow

The steady-state and transient shear flow dynamics of polymer drops in a microchannel are investigated using the dissipative particle dynamics (DPD) method. The polymer drop is made up of 10% DPD solvent particles and 90% finite extensible non-linear elastic (FENE) bead spring chains, with each chain consisting of 16 beads. The channel’s upper and lower walls are made up of three layers of DPD particles, respectively, perpendicular to Z-axis, and moving in opposite directions to generate the shear flow field. Periodic boundary conditions are implemented in the X and Y directions. With FENE chains, shear thinning and normal stress difference effects are observed. The “colour” method is employed to model immiscible fluids according to Rothman–Keller method; the χ-parameters in Flory–Huggins-type models are also analysed accordingly. The interfacial tension is computed using the Irving–Kirkwood equation. For polymer drops in a steady-state shear field, the relationship between the deformation parameter (D_def) and the capillary number (Ca) can be delineated into a linear and nonlinear regime, in qualitative agreement with experimental results of Guido et al. [J. Rheol. 42 (2) (1998) 395]. In the present study, Ca<0.22, in the linear regime. As the shear rate increases further, the drop elongates; a sufficiently deformed drop will break up; and a possible coalescence may occur for two neighbouring drops. Dynamical equilibrium between break-up and coalescence results in a steady-state average droplet-size distribution. In a shear reversal flow, an elongated and oriented polymer drop retracts towards a roughly spherical shape, with a decrease in the first normal stress difference. The polymer drop is found to undergo a tumbling mode at high Schmidt numbers. A stress analysis shows that the stress response is different from that of a suspension of solid spheres. An overshoot in the strain is observed for the polymer drop under extension due to the memory of the FENE chains.     

Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Effects of coalescence and breakup on the steady-state morphology of an immiscible polymer blend in shear flow

The steady-state morphology of an immiscible polymer blend in shear flow has been investigated by optical microscopy techniques. The blend is composed by poly-isobutylene (PIB) and poly-dimethylsiloxane (PDMS) of comparable viscosity. Experiments were performed by means of a home-made transparent parallel plate device. The two plates can be independently counterrotated, so that sheared droplets of the dispersed phase can be kept fixed with respect to the microscope point of view, and observed for long times. The distribution of drops and their average size were measured directly during flow at different shear rates and for different blend compositions. It was found that the average drop size in steady-state conditions is a decreasing function of the applied shear rate, and does not depend on blend composition for volume fractions up to 10%. Experiments have proved that, in the shear rate range which could be investigated, the stationary morphology is controlled only by coalescence phenomena, droplet breakup playing no role in determining the size of the dispersed phase. More generally, it has been shown that the steady-state morphology is a function not only of the physical parameters of the blend and of the shear rate, but also of the initial conditions applied to the blend. The steady-state results reported in this paper constitute the first direct experimental confirmation of theoretical models which describe the mechanisms of shear-induced drop coalescence.     

Effect of solidification on drop fragmentation in liquid–liquid media

 This paper presents results of experimental and analytical investigation on molten alloy drop fragmentation in water pool. Emphasis is directed towards delineating the roles which melt to coolant heat transfer and melt solidification play in the fragmentation process. The strong impact of coolant temperature upon fragmentation process is addressed. A set of 23 drop fragmentation experiments were performed, in which 8 experiments employed a low melting point alloy, cerrobend-70 and 15 experiments using Pb–Bi eutectic alloy as drop fluid. The results show strong impact of coolant temperature on particle size distribution of the fragmented drops. A linear stability analysis of the interface between the two liquid fluids with thin crust growing between them, is performed. A modified dimensionless Aeroelastic number, for Kelvin–Helmholtz instability, is obtained and used as a criteria for fragmentation of molten drops penetrating into another liquid coolant media with lower temperature. The nondimensionalized mean diameter of the fragmented particles is correlated with the Aeroelastic number. Received on 26 March 2000     

Long-term aging effects on the rheology of neat laponite and laponite–PEO dispersions

We observe aging behavior of neat laponite systems over the course of 1,000 or more days. Under basic conditions, low laponite concentrations (1 wt%) slowly evolve from a viscoelastic liquid to a glass made of clusters acting as constituent elements interacting via long-range repulsion. Higher concentrations of laponite (3 wt%) quickly form a glass of individual particles. Intermediate concentrations of laponite form a glass that is a combination of clusters and individual particles. The aging rheological response and upturn of the loss modulus at low frequencies are well predicted by models of soft glassy systems (Fielding et al., J Rheol, 44(2):323–369, 2000; Sollich, Phys Rev E, 58(1):738–759, 1998). If low amounts of high-molecular-weight (M _n ≥ 163 kg/mol) poly(ethylene oxide) (PEO) are added, the aging behavior follows the dynamical response of the clay. Above a critical ratio, φ, of the free polymer chains in solution to the total laponite surface area, the PEO dynamics dominate at high frequencies. It appears that the dynamics of these complex laponite-PEO systems are governed by the parameter φ.     

An experimental study of two-phase flow in simulated reduced-gravity condition: dispersed droplet to slug flow transition and slug flow

The results from an experimental study of reduced-gravity two-phase flows are reported in this paper. The experiments were conducted in simulated reduced-gravity conditions in a ground-based test facility with a circular test section of 25 mm inner diameter. The flow conditions for which data were acquired lie in the dispersed droplet to slug flow transition and slug flow regime. Local data were acquired for 17 different flow conditions at three axial locations. The acquired data complement and extend those discussed in an earlier paper by the authors (Vasavada et al. in, Exp Fluids 43: 53–75, 2007). The radial profiles and axial changes in the local data are analyzed and discussed in this paper. The area-averaged data, in conjunction with the local data, are discussed to highlight important interaction mechanisms occurring between fluid particles, i.e., drops. The data clearly show the effect of progressive coalescence leading to formation of slug drops. Furthermore, the shape of slug drops in reduced-gravity conditions was observed to be different from that in normal-gravity case. The analyses presented here show the presence of drop coalescence mechanisms that lead to the formation of slug drops and transition from dispersed droplet flow to the slug flow regime. The most likely causes of the coalescence mechanism are random collision of drops driven by turbulence eddies in the continuous phase and wake entrainment of smaller drops that follow preceding larger drops in the wake region. Data from flow conditions in which the breakup mechanism due to impact of turbulent eddies on drops illustrate the disintegration mechanism.     

Application of the PIV technique to measurements around and inside a forming drop in a liquid–liquid system

A particle image velocimetry (PIV) method has been developed to measure the velocity field inside and around a forming drop with a final diameter of 1 mm. The system, including a microscope, was used to image silicon oil drops forming in a continuous phase of water and glycerol. Fluorescent particles with a diameter of 1 μm were used as seeding particles. The oil was forced through a 200 μm diameter glass capillary into a laminar cross-flow in a rectangular channel. The velocity field was computed with a double-frame cross-correlation function down to a spatial resolution of 21 × 21 μm. The method can be used to calculate the shear stress induced at the interface by the cross-flow of the continuous phase and the main forces involved in the drop formation process.     

Bread dough rheology: an improved damage function model

We describe an improved damage function model for bread dough rheology. The model has relatively few parameters, all of which can easily be found from simple experiments as discussed in this paper. Small deformations in the linear region are described by a gel-like power-law memory function. Then, we consider a set of large non-reversing deformations—stress relaxation after a step of shear, steady shearing and elongation beginning from rest and biaxial stretching. With the introduction of a revised strain measure which includes a Mooney–Rivlin term, all of these motions can be well described by the damage function described previously. For reversing step strains, larger amplitude oscillatory shearing and recoil we present a discussion which shows how the damage function model can be applied in these cases.     

Effect of poly(ethylene oxide) on the rheological behavior of silica suspensions

The steady-shear viscosity, dynamic viscoelasticity, and sedimentation behavior were measured for silica suspensions dispersed in aqueous solutions of poly(ethylene oxide) (PEO). For suspensions prepared with polymer solutions in which the transient network is developed by entanglements, the viscosity at a given shear rate decreases, shows a minimum, and then increases with increasing particle concentration. Because the suspensions are sterically stabilized under the conditions where the particle surfaces are fully covered with by a thick layer of adsorbed polymer, the viscosity decrease can be attributed to the reduction of network density in solution. But under the low coverage conditions, the particles are flocculated by bridging and this leads to a viscosity increase with shear-thinning profiles. The polymer chains with high molecular weights form flexible bridges between particles. The stress-dependent curve of storage modulus measured by a stress amplitude sweep shows an increase prior to a drastic drop due to structural breakdown. The increase in elastic responses may arise from the restoring forces of extended bridges with high deformability. The effect of PEO on the rheological behavior of silica suspensions can be explained by a combination of concentration reduction of polymer in solution and flocculation by bridging.     

Particle velocimetry inside Newtonian and non-Newtonian droplets impacting a hydrophobic surface

A particle velocimetry technique is described which enables the measurement of the fluid velocity inside impacting drops. Using high speed photography of 2 μm fluorescent tracer particles suspended in the fluid, the velocity field was measured as a function of time and radial position. The potential of the technique is illustrated using velocimetry measurements of drops of pure water and aqueous solutions of 200 ppm poly-(ethylene oxide) (PEO). Dilute solutions of PEO have been known for some time to suppress the rebound of water from hydrophobic surfaces. The dissipation has traditionally been attributed to an increased extensional viscosity as the polymers stretch in the extensional flow of the droplet. Our results enable us to infer that the extensional viscosity of PEO drops, during both the spreading and retraction phase, is similar to that of pure water. The data suggest that the true source of dissipation lies at the droplet edge. We also show, by analysing the spreading of water drops, that the Roisman-Yarin theory for a droplet spreading on a surface is valid in the bulk of the droplet prior to the final stages of spreading.     

Dynamic simulation of non-spherical particulate suspensions

Particle-level simulation has been employed to investigate rheology and microstructure of non-spherical particulate suspensions in a simple shear flow. Non-spherical particles in Newtonian fluids are modeled as three-dimensional clusters of neutrally buoyant, non-Brownian spheres linked together by Hookean-type constraint force. Rotne–Prager correction to velocity disturbance has been employed to account for far-field hydrodynamic interactions. An isolated rod-like particle in simple shear flow exhibits a periodic orientation distribution, commonly referred to as Jeffery orbit. Lubrication-like repulsive potential between clusters have been included in simulation of rod-like suspensions at various aspect ratios over dilute to semi-dilute volume fractions. Shear viscosity evaluated by orientation distribution qualitatively agrees with one obtained by direct computation of shear stress.     

Investigation of binary drop rebound and coalescence in liquids using dual-field PIV technique

Experiments on binary drop collisions within an index-matched liquid were conducted for Weber numbers (We) in the range of 1–50. Drop pairs of water/glycerin mixture were injected horizontally into silicone oil and, due to gravitational effects, travelled on downward trajectories before colliding. A dual-field high-speed PIV measurement system was employed to quantify drop trajectories and overall collision conditions while simultaneously examining detailed velocity fields at the collision interface. Sequences of velocity and vorticity fields were computed for both larger and smaller fields of view. In the We range examined, both rebounding and coalescing behavior occurred. Coalescence was found to result from a combination of vortical flow within drops and strong drop deformation characteristic of higher We. Flow through the centers of opposing ring vortices, strengthened by drop deformation, enhanced drainage of the thin film in the impact region, leading to film rupture and coalescence. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

In situ observations of unusual drop deformation and wobbling in simple shear flow

Deformation and wobbling of a liquid drop immersed in a liquid matrix were studied under mild shear conditions for various viscosity ratios. In situ visualization experiments were conducted on a homemade transparent Couette cell incorporated to the Paar Physica MCR500 shear rheometer. The effect of drop or matrix elasticity was examined and was found to play a major role in both deformation and wobbling processes. Experimental results were compared to Jackson and Tucker (J Rheol 47:659–682, 2003), Maffettone and Minale (J Non-Newton Fluid Mech 78:227–241, 1998) and Yu and Bousmina (J Rheol 47:1011–1039, 2003) ellipsoidal models. It was found that the agreement between the Newtonian models and the experimental results required an increase in the drop viscosity. Such increment in viscosity was found to scale with the first normal stress difference.