Capillary Breakup Extensional Rheometry Research Articles

Shear and extensional rheological characterization of poly(acrylonitrile)/halloysite nanocomposite solutions

The shear and extensional flow properties of polyacrylonitrile (PAN) solution in the presence of halloysite nanotubes (HNTs) were investigated at an industrially relevant concentration of the polymer. In dynamic shear rheology, the elasticity and relaxation time of PAN solutions and the availability of heterogeneous PAN domains were found to increase with HNT content. Extensional flow behavior of PAN solutions were characterized using the capillary breakup extensional rheometry and increasing the amount of HNT content in the solution was found to increase the life-time of the filament and suppress strain hardening at high strains.

Studying the effects of elongational properties on atomization of weakly viscoelastic solutions using Rayleigh Ohnesorge Jetting Extensional Rheometry (ROJER)

The extensional rheological properties of dilute polymer solutions play a dominant role in many commercial processes such as air-assisted atomization. This is a high deformation rate process important in application of diverse materials such as paints, fertilizer sprays and delivery of airborne drugs. Dilute polymeric solutions which have identical values of high shear-rate viscosity (HSV) often exhibit different values of Sauter Mean Diameter (SMD) in their spray size distributions as a result of differing extensional rheological properties. We explore the atomization of a series of model Poly(ethylene oxide) (PEO) solutions dissolved in water/glycerol mixtures. Each solution is sprayed with an air-assisted spray gun under similar conditions and imaged with a commercial spray measurement system. The values of HSV for PEO solutions are close to the solvent viscosity and matched to those of typical ink or paint samples. The surface tensions of the fluids are also tuned to be very similar, however both the SMD and the droplet size distribution change considerably. For the highest molecular weight PEO systems, interconnected beads-on-string structures are observed at different positions of the spray fan. Capillary Break-up Extensional Rheometry (CaBER) can be used to measure the extensional properties of the more viscous solutions, but the well-known limitations of this approach include inertially-induced asymmetries, gravitational sagging and the very short filament lifetimes of low viscosity samples all of which constrain the range of relaxation times that can be probed. Consequently we also explore the use of Rayleigh Ohnesorge Jet Elongational Rheometry (ROJER) to probe the extensional response of these viscoelastic solutions at realistic timescales and deformation rates. A cylindrical liquid jet is excited by a piezo-actuator at a known frequency as it exits a micromachined nozzle, and stroboscopic imaging provides high temporal and spatial resolution in the break-up process. Analyzing the evolution in the jet diameter before break-up enables meaningful measurement of relaxation times down to values as small as 60μs, and these values can be directly correlated with the differences in the final spray size distributions and the mean diameters. We outline a simple model for the fluid dynamics of the thinning filaments close to breakup that accurately describes the variation of the average droplet diameter as a function of the elongational relaxation time measured for each fluid.

Probing hydrogen bond interactions in a shear thickening polysaccharide using nonlinear shear and extensional rheology

Mamaku gum is a polysaccharide extracted from the fronds of the black tree fern found in New Zealand. The cooked pith has traditionally been used for various medicinal purposes and as a food source by the Ma¯ori people of New Zealand. It has potential applications as a thickener in the food industry and as a palliative for patients with dysphagia. Studies on the shear rheology of Mamaku gum have revealed that the gum exhibits shear thickening at a critical shear rate due to a transition from intra- to inter-molecular chain interactions upon shear-induced chain elongation. In this paper, we demonstrate that these interactions are primarily due to hydrogen bonding. We perform extensional rheology on mixtures of Mamaku gum and urea (a known disruptor of hydrogen bonds) to quantify the nature of these interactions. Capillary Breakup Extensional Rheometry (CaBER) performed on the pure Mamaku gum solutions yield plateau values of the Trouton ratio as high as ∼104, showing that the viscoelasticity of the gum in uniaxial elongation is much higher than in shear. For all Mamaku concentrations tested, the extensional viscosity decreases upon increasing urea concentration. Furthermore, the relaxation time decreases exponentially with increasing urea concentration. This exponential relationship is independent of the Mamaku concentration, and is identical to the relationships between urea concentration and characteristic timescales measured in nonlinear shear rheology. We show using the sticky reptation model for polymers with multiple sticker groups along the backbone how such a relationship is consistent with a linear decrease in the free energy for hydrogen bond dissociation. We then demonstrate that a time-concentration superposition principle can be used to collapse the viscoelastic properties of the Mamaku-gum/urea mixtures.

Microdroplet formation of polyvinylpyrrolidone/carbon nanotube by ultrasonic atomization

Ultrasonic atomization is conducted to produce composite particles of polyvinylpyrrolidone (PVP) and multi-walled carbon nanotube (MWCNT) from an aqueous suspension. The rheological properties of the suspensions are varied in a systematic manner by changing the molecular weight of the polymers, the polarity, and the concentration of MWCNT in the given composite system. A particular interest of this study is to investigate how the ultrasonic atomization of PVP/MWCNT suspensions is affected by their shear and extensional properties. As a characteristic of the fluid under extensional flow, the fluid relaxation time is measured from capillary breakup extensional rheometry. It is found that the average size of the composite droplets is increased as the relaxation time in the capillaries of PVP/MWCNT increases, while the number of available particles is mainly limited by the shear viscosity of the suspension. With the available materials and analyses adopted in this study, the observed trends are explained in terms of two dimensionless groups: the Deborah and Ohnesorge numbers, which encompass the material parameters (viz, relaxation time, shear viscosity, density, and surface tension) associated with the atomization process of viscoelastic fluids.

Experimental study on the capillary thinning of entangled polymer solutions

The transient elongation behavior of entangled polymer and wormlike micelles (WLM) solutions has been investigated using capillary breakup extensional rheometry (CaBER). The transient force ratio X = 0.713 reveals the existence of an intermediate Newtonian thinning region for polystyrene and WLM solutions prior to the viscoelastic thinning. The exponential decay of X(t) in the first period of thinning defines an elongational relaxation time λ x which is equal to elongational relaxation time λ e obtained from exponential diameter decay D(t) indicating that the initial stress decay is controlled by the same molecular relaxation process as the strain hardening observed in the terminal regime of filament thinning. Deviations in true and apparent elongational viscosity are discussed in terms of X(t). A minimum Trouton ratio is observed which decreases exponentially with increasing polymer concentration leveling off at Trmin = 3 for the solutions exhibiting intermediate Newtonian thinning and Trmin ≈ 10 otherwise. The relaxation time ratio λ e/ λ s, where λ s is the terminal shear relaxation time, decreases exponentially with increasing polymer concentration and the data for all investigated solutions collapse onto a master curve irrespective of polymer molecular weight or solvent viscosity when plotted versus the reduced concentration c[ η], with [ η] being the intrinsic viscosity. This confirms the strong effect of the nonlinear deformation in CaBER experiments on entangled polymer solutions as suggested earlier. On the other hand, λ e ≈λ s is found for all WLM solutions clearly indicating that these nonlinear deformations do not affect the capillary thinning process of these living polymer systems.

Correlation of Elongational Fluid Properties to Fiber Diameter in Electrospinning of Softwood Kraft Lignin Solutions

Viscoelastic properties of N,N-dimethylformamide (DMF) solutions of softwood kraft lignin (SKL) containing small amounts of poly(ethylene oxide) (PEO) were investigated. Of interest is the relationship between viscoelastic properties of the spinning solutions and their corresponding electrospinning behavior. Although it is well established that fiber diameter is critical in determining the material properties of nanofibers, lignin solutions have been observed to display poor electrospinnability in many instances. Thus, the motivation behind this work was to understand and exert control over the relevant fluid properties that control the fiber diameter of SKL/PEO fibers, The results of dynamic shear and capillary breakup extensional rheometry (CaBER) experiments indicated that SKL solutions were weakly elastic in shear and Newtonian in elongational flow. SKL solutions were not electrospinnable at concentrations of 25–45 wt % but form fibers at 50 wt % concentration. The addition of PEO to SKL solutions led to an increase in shear moduli and pronounced strain hardening in elongational flow. The characteristic time scales of tensile stress growth (λ) measured with CaBER were dependent on the SKL concentration, PEO concentration, and PEO molecular weight. In contrast to SKL solutions, SKL/PEO solutions are electrospinnable over the concentration range of 25–45 wt % SKL depending on the combination of SKL concentration, PEO concentration, and PEO molecular weight. Correlation between the fiber diameters obtained during electrospinning and the measured value of λ are discussed.

Determination of axial forces during the capillary breakup of liquid filaments – the tilted CaBER method

The capillary breakup extensional rheometry (CaBER) is a versatile method to characterize the elongational behavior of low-viscosity fluids. Commonly, data evaluation is based on the assumption of zero normal stress in axial direction ( $\upsigma_{\rm zz}=0$ ). In this paper, we present a simple method to determine the axial force using a CaBER device rotated by 90° and analyzing the deflection of the filament due to gravity. Forces in the range of 0.1–1,000 μN could be assessed. Our study includes experimental investigations of Newtonian fructose solutions and silicon oil mixtures (viscosity range, 0.9–60 Pa s) and weakly viscoelastic polyethylene oxide (PEO, $M_{\rm w}=10^{6}$ g/mol) solutions covering a concentration range from c ≈ c* (critical overlap concentration) up to c > c e (entanglement concentration). Papageorgiou’s solution for the stress ratio $\upsigma_{\rm zz}/\upsigma_{\rm rr}$ in Newtonian fluids during capillary thinning is experimentally confirmed, but the widely accepted assumption of vanishing axial stress in weakly viscoelastic fluids is not fulfilled for PEO solutions, if c e is exceeded.

Effects of weak elasticity on the stability of high Reynolds number co- and counter-rotating Taylor-Couette flows

This study examines the impact of dilute polymer solutions on the unique isolated secondary flows between concentric, rotating cylinders, namely Taylor-Couette (TC) flow. We mapped the stability of flow states using Newtonian and dilute polyethylene oxide (PEO) solutions over the Reynolds number range of − 100 < Reo < 500 and 0 < Rei < O(103), where subscripts ‘o’ and ‘i’ refer to outer and inner cylinders, respectively. Elasticity number (El) of the PEO fluids, defined as the ratio of elastic to inertial forces, ranges from O(10− 4) to O(10− 2). This work expands on previous studies by (a) significantly expanding the range of Rei, Reo, and El examined, (b) use of a consistent, conservative protocol for reaching flow states, and (c) rheological characterization of the solutions via shear and capillary breakup extensional rheometry. Using spectral analysis of flow visualization of the r-z or z-θ planes, we find the effect of El on the critical conditions for laminar and chaotic axisymmetric and nonaxisymmetric flow states is nonmonotonic and mode-dependent, with greater modification of higher order transitions involving small-scale features. While the critical conditions are modified by low El for all transitions, the flow states vary from those for Newtonian fluids at higher Rei and for the more elastic fluids.

Effect of extensional properties of polymer solutions on the droplet formation via ultrasonic atomization

AbstractUltrasonic atomization was conducted using 2.4 MHz ultrasound generator to produce polymeric particles from the solutions of water‐soluble polymers like poly (ethylene oxide) (PEO), poly(vinyl alcohol) (PVA), and poly(vinyl pyrrolidone) (PVP). In the series of solutions containing these polymers of various molecular weights, the shear viscosity and surface tension were varied; such differences, however, could not account for the observed trends in the atomization behavior. It was found that the availability of droplet formation and size of the droplets depend strongly on the extensional characteristics of polymer solutions along with the apparent extensional viscosities and the longest relaxation times. The extensional properties of polymer solutions were effectively measured by capillary breakup extensional rheometry (CaBER) and provided a rational basis to understand the essential role of fluid viscoelasticity in ultrasonic atomization. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers

Capillary breakup extensional rheometry (CaBER) on semi-dilute and concentrated polyethyleneoxide (PEO) solutions

Semi-dilute (\(c^\ast ce) solutions of PEO yield uniformly thinning, cylindrical filaments in capillary breakup extensional rheometry (CaBER) experiments. Up to c ≈ ce thinning can be characterized by a single elongational relaxation time λE. Comparison with the longest shear relaxation time, λS reveals that λE/λS decreases with increasing concentration or molecular weight according to (c[η]) − 4/3. This is attributed to the large deformation the solutions experience during filament thinning. A factorable integral model including a single relaxation time and a Soskey or Wagner damping function accounting for the large deformation in CaBER experiments is used to calculate λE/λS and provides good agreement with experimental results. Irrespective of concentration or molecular weight a beads-on-a-string structure occurs prior to filament breakup at a diameter ratio D/D0 ≈ 0.01. This instability is supposed to be closely related to a flow-induced phase separation.

The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary breakup extensional rheometry experiments

Abstract We monitor the capillary thinning and breakup of low viscous liquid filaments with high speed imaging to determine the relaxation time of dilute polymer solutions in extension. The induction of filament thinning by a slow extension of a liquid bridge beyond the static stability limit enables one to create axially symmetric thinning profiles with minimized inertial oscillations from acceleration of the liquid. The minimized disturbance of the capillary thinning process by this slow retraction method (SRM) allows the observation and quantitative fitting of the visco-capillary and inertio-visco-capillary balance as well as the potential flow regime for a series of Newtonian liquids covering a viscosity range from 350 to 27 mPa s. For dilute solutions of polyethylene oxide in water the SRM allows the reliable determination of relaxation times in extension of as low as 240 μs. A lower limit for the polymer concentration c l o w below which an elasto-capillary balance cannot be observed is introduced, based on the finite extensibility limit L 2 of the polymer chain.

INCREASING THE EXTENSIONAL VISCOSITY OF SILICONE OIL REDUCES THE TENDENCY FOR EMULSIFICATION

The purpose was to study the emulsification of silicone oil tamponade agents that cause clinical complications. This study aimed to increase the emulsification resistance of silicone oil 1,000 to be at least as resistant as silicone oil 5,000 while maintaining the shear viscosity <5,000 mPa/s to aid injection and removal. High-molecular-weight (423 kDa) poly(dimethyl siloxane) was added to silicone oil 1,000 at 5% and 10% w/w concentration. The shear and extensional viscosity of 1,000 and 5,000, a 50:50 mixture of 1,000 and 5,000 and 5% and 10% w/w additive blends, respectively, of silicone oil were measured using capillary breakup extensional, rotational shear, and capillary extrusion rheometry. In vitro emulsification was assessed qualitatively after agitation using Pluronic F68 or a protein solution as the emulsion stabilizer. The addition of high-molecular-weight polymer increased the extensional viscosity of the blends at high strain rates to levels equal to or greater than silicone oil 5,000. In all cases, the shear viscosity of the blends was lower than that of silicone oil 5,000. The additive blends were qualitatively as emulsification-resistant as silicone oil 5,000. The addition of low concentrations of very-high-molecular-weight polymers of the same chemistry as the bulk oil has the potential to increase the emulsification resistance of the tamponade agents while maintaining ease of injection and removal.

Extensional rheology of a shear-thickening cornstarch and water suspension

A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.

Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHVN, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHVT, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ 21, the first normal stress difference N 1, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate $\dot{\gamma}$ for solutions of varying concentrations and molar masses (3–10 × 105 g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M w–c– $\dot{\gamma}$ for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N 1 could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.

Extensional flow of wormlike micellar solutions

Abstract We consider the inhomogeneous extensional response of a new constitutive model, the VCM model [Vasquez, et al., 2007. A network scission model for wormlike micellar solutions I: model formulation and homogeneous flow predictions. J. Non-Newt. Fluid Mech. 144, 122–139] that has been developed to describe concentrated solutions of wormlike micelles. The time dependent numerical analysis is carried out in a simplified slender filament formulation appropriate for transient elongational flows of complex fluids. The simulations show that, beyond a critical extension rate, elongating filaments of a micellar fluid described by the VCM model exhibit a dramatic and sudden rupture event as a result of the scission of the entangled wormlike chains. The computations capture many of the features of the high-speed rupture process observed experimentally [Bhardwaj, et al., 2007. Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions. J. Rheol. 51, 693–719] in filament stretching experiments with wormlike micelle solutions. The highly localized rupture predicted by the VCM model and the corresponding evolution in the tensile force within the filament is contrasted with the familiar and more gradual necking responses predicted by the upper convected Maxwell and Giesekus models under equivalent kinematic boundary conditions.

Filament stretching and capillary breakup extensional rheometry measurements of viscoelastic wormlike micelle solutions

A filament stretching extensional rheometer and capillary breakup extensional rheometer are used to measure the extensional rheology of a series of wormlike micelle solutions experiencing a uniaxial elongational flow. The experiments are performed using a series of wormlike micelle solutions of both cetylpyridinium chloride and sodium salicylate (NaSal) in an aqueous sodium chloride solution and cetyltrimethylammonium bromide and NaSal in de-ionized water. The linear viscoelasticity of all the wormlike micelle solutions is well described by a Maxwell model with just one or two relaxation times while the steady shear measurements all demonstrate characteristics of shear banding at large shear rates. In transient homogeneous uniaxial extension imposed by a filament stretching rheometer, each of the wormlike micelle solutions demonstrate significant strain hardening. At large extension rates, the wormlike micelle solution filaments are all found to fail through a dramatic rupture near the axial midplane at a constant stress independent of imposed extension rate. The result is an extensional viscosity that decays linearly with increasing extension rate. This filament failure likely stems from the local scission of individual wormlike micelle chains. For the more concentrated solutions, as the imposed extension rate is reduced, a critical extension rate is found below which the filament does not rupture, but instead elastocapillary pinch off is recovered and the elastic tensile stresses achieved in the fluid filament grow far beyond the value observed at rupture. This dramatic upturn in the elastic tensile stress and the extensional viscosity at low extension rates is not intuitively expected and is most likely a result of structural changes to the entangled wormlike micelle solution. Strain hardening is also observed in capillary breakup rheometry experiments, however, when the results of filament stretching and capillary breakup rheometry measurements at nominally the same extension rate are superimposed, the results do not agree; the extensional viscosity measurements from filament stretching are in some instances more than an order of magnitude larger. This result calls into question the use of capillary breakup rheometry for quantitatively measuring the extensional viscosity of wormlike micelle solutions.