Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005     

Slip velocity and slip layer thickness in flow of concentrated suspensions

The rheological characterization of highly filled suspensions consisting of a Newtonian matrix (hydroxyl-terminated polybutadiene), mixed with two different sizes of aluminum powder (30% and above by volume) and two different sizes of glass beads (50% and above by volume), was performed using a parallel disk rheometer with emphasis on the wall slip phenomenon. The effects of the solid content, particle size, type of solid particle material, and temperature on slip velocity and slip layer thickness were investigated. Suspensions of small particles of aluminum (mean diameter of 5.03 μm) did not show slip at any concentration up to the maximum packing fraction. However, suspensions of the other particles exhibited slip at the wall, at concentrations close to their maximum packing fraction. In these suspensions, the slip velocity increased linearly with the shear stress, and at constant shear stress, the slip velocity increased with increasing temperature. The slip layer thickness increased proportionally with increasing size of the particles for the glass beads. Up to a certain value of (filler content/maximum packing fraction), ϕ/ϕ_m, the slip layer thickness divided by the particle diameter, δ/D_P, was 0, but it suddenly increased and reached a value that was independent of ϕ/ϕ_m and the temperature. On average, the ratio of δ/D_P was 0.071 for aluminum and 0.037 for glass beads. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 515–522, 1998     

Wall slip of concentrated suspension melts in capillary flows

The effects of wall slip of concentrated suspension melts in capillary flows were investigated at elevated temperature. The modeled material is a mixture of polymer EVA (Ethylene Vinyl Acetate) and non-colloidal spherical powder (glass microspheres) with mean particle size within 53∼63 μm. The effect of particle concentration on wall slip was studied experimentally in a capillary rheometer. For suspensions with different particle loadings (35%, 40%, and 45% by volume), the slip velocity V_s increased with an increase of particle concentration at the same testing temperature. A master slip curve can be obtained by plotting slip velocity versus the product of wall shear stress and square root of particle concentration. As such, a new particle concentration-dependent slip model is proposed. A theoretical approach coupled with the new slip model and flow equation is employed to characterize the flow behavior of concentrated suspension in a capillary rheometer, with reasonable agreement obtained with experimental observations.     

Viscoelastic properties of suspensions with weakly interacting particles

Rheological characterization of a model suspension containing hydroxyl-terminated polybutadiene and glass beads with filler concentration up to 30% by volume was performed by using a Haake parallel disk rheometer. The rheological tests conducted were the measurement of the storage modulus, G′, loss modulus, G′, and complex viscosity, η*, as functions of the frequency and the steady shear viscosity as a function of the shear rate. The linear viscoelastic region was determined to extend up to 50% strain by measuring G′, G′, and η* as functions of strain amplitude. By using multiple gap separations between the disks, it was found that the suspension did not exhibit slip at the walls of the rheometer. G′ and G′ were used to determine the relaxation times distribution, G_i(λ_i, ⊘) as functions of the relaxation time, λ_i, and the filler content, ⊘. The relaxation moduli, G_i(λ_i, ⊘), decreased with the relaxation time, but increased with the filler content. The Cox–Merz rule was also observed to be valid for these suspensions. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 507–514, 1998     

Sharkskin mechanism of high‐impact polystyrene (HIPS) and rheological behavior of HIPS/TiO2 composites

The rheological behaviors of high‐impact polystyrene (HIPS) and HIPS/TiO₂ composites were investigated by use of a rheometer in the present article. HIPS exhibited a constant critical stress of the sharkskin in various temperatures, and the analysis indicated that the mechanism of sharkskin of HIPS was wall–slip and its special temperature dependency was determined by weak wall–melt adsorption. The experimental results also showed that the introduction of TiO₂ into HIPS only slightly influenced the apparent viscosity (η_a) of the composites. Moreover, TiO₂ exhibited an unusual effect on the non‐Newtonian index of the composites at high shear rate. Both phenomena indicated the increase of inner free volume induced by TiO₂ in molecularly rigid HIPS. Moreover, it was noteworthy that a featured stress could be used to label the dispersion of TiO₂ in the HIPS matrix, and the numeric affinity of this featured stress and the critical stress of sharkskin revealed that both processes were relevant to the same molecular relaxation. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 802–807, 2005     

Viscosity corrections for concentrated suspension in capillary flow with wall slip

Corrections for viscosity measurements of concentrated suspension with capillary rheometer experiments were investigated. These corrections include end effects, Rabinowitsch effect, and wall slip. The effects of temperature, particle concentration, and contraction ratio on the end effects were studied and their effects were accounted for using an entrance and exit losses model. The non‐Newtonian effect and the nonlinearity of slip velocity against wall shear stress were described using a slip model. The true viscosity of a concentrated suspension with glass powder suspended in a non‐Newtonian binder system was calculated as a function of shear rate and effective particle concentration, taking into consideration particle migration, which is calculated by a diffusive numerical model. Particle size was found to affect significantly the viscosity of the suspension with viscosity decreasing with increasing particle size, which can be reflected by a decrease in the value of the power‐law index in the Krieger model. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Experimental study and modeling of wall slip of polymethylmethacrylate considering different die surfaces

Wall slip of polymethylmethacrylate (PMMA) was studied on different flow channel surfaces using a rheological slit die and a high pressure capillary rheometer. As die surfaces polished steel, ground steel, and Si doped Diamond like carbon (DLC) were used. A new wall slip model is presented in this paper which assumes a lubricating film between the polymer melt and the die surface. The slip velocity has a power law dependency on wall shear stress. In the double logarithmic plot the wall slip curves are linear and can be parallel shifted to higher values with increasing temperature. The predicted dependencies of the wall slip velocity could be confirmed with experiments conducted with PMMA on polished steel. Furthermore, the die surface influences the flow behavior of PMMA. No wall slip was found on ground steel and on DLC. No complete film could be established by the lubricant on the ground steel die wall. The DLC‐coating exhibits a similar surface roughness and surface energy to polished steel, but the chemical composition is different. It is a metastable form of amorphous carbon containing sp² and sp³ bonds. As a consequence slip additives have a low ability to bond to this material. POLYM. ENG. SCI., 58:1391–1398, 2018. © 2017 Society of Plastics Engineers     

Study on viscosity of polymer melt flowing through microchannels considering the wall‐slip effect

For polymers with long, complicated, branched chains, it is difficult to measure the real shear viscosity and slip velocity, using the capillary rheometer based on the adsorption–desorption mechanism. In this study, a double‐barrel capillary rheometer was used to investigate the viscosities of four polymers including polypropylene, high‐density polyethylene, polystyrene, and polymethylmethacrylate in a microchannel. A general model of polymer viscosity based on the entanglement–disentanglement was presented. The proposed model is important in understanding the mechanism of wall slip. This general model can be transferred to the other different models when changing the parameters. Actually, the entanglement–disentanglement model can also be transformed to the adsorption–desorption model. Using the model, it was found that the viscosities of polystyrene and polymethylmethacrylate were reduced with decreasing die diameter, and the slip velocities were increased with the increase of shear stress which agrees well with polymer microrheology based on the microscale effect. For polymers with long, complicated, branched chains, the proposed model improves the accuracy of the calculated viscosity and gains the real slip velocity when polymer melt flows through a microchannel. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Single screw extrusion of viscoplastic fluids subject to different slip coefficients at screw and barrel surfaces

Commonly encountered viscoplastic fluids including concentrated suspensions of polymeric and ceramic composites, foams, gels, concrete, food products, and energetic compounds exhibit wall slip during their flow and processing. For some viscoplastics fluids, especially highly filled suspensions, wall slip may dominate the flow and deformation and hence the processing behavior of the suspension. The wall slip velocity is generally a function of the wall shear stress and temperature. Various factors including the materials of construction i.e., chemical nature and the roughness of the wall surface affect the wall slip behavior of viscoplastic fluids. In this study an analytical model of the extrusion of viscoplastic fluids under isothermal and fully-developed conditions in shallow channels is developed. The model accommodates the use of different slip coefficients at barrel and screw surfaces. It thus permits the investigation of effects of introducing different materials of construction for the barrel and screw surfaces and development of design expressions.     

Porous Ni/ZrO2 Cermet from Highly Concentrated Composite Colloid

Rheology and shaping of concentrated cermet suspensions consisting of nickel (Ni) and yttria‐stabilized zirconia (YSZ) nanoparticles in water have been examined over a broad range of volumetric solids concentration (? = 0.1–0.4) and Ni fraction (f_Ni = 0.15–0.45). Preferential adsorption of pyrogallol‐poly(ethylene glycol) polymer (i.e., Gallol‐PEG) on surface of the Ni and YSZ particles imparts steric hindrance between the suspending particles so that fluidity can be obtained under shear stress. The cermet suspensions exhibit shear‐thinning flow behavior under steady‐shear measurement over shear rates of 10⁰–10³ s^?1. Yield stress and yield strain of the suspensions appear to vary pronouncedly with ? and f_Ni under oscillatory shear over a shear‐strain range of 10^?1–10³%. With the Gallol‐PEG adsorption, an apparent viscosity less than 6 × 10^?1 Pa.s at a shear rate of 10² s^?1 has been obtained for the highly concentrated composite suspension with ? of 0.40 and f_Ni of 0.25. A high solids concentration effectively prohibits phase segregation during wet‐shaping processes. Uniform green compacts have been obtained from slip casting of the concentrated cermet mixture (? = 0.30) without use of binder and are then fired at 1200°C under reducing atmosphere to form porous Ni/YSZ compacts. Relative sintered density increases from 65% to 75% of the theoretical value when f_Ni was increased from 0.15 to 0.45, due mainly to the lower sintering temperature required for the Ni phase.     

Experimental investigation of the rheological behaviors of polypropylene in a capillary flow

The rheological characterization of polymer melts is strongly related to their material properties. In this study, we focused on the rheological behaviors of a polypropylene (PP) melt through a capillary die. With an advanced twin‐bore capillary rheometer with dies measuring 1.0, 0.5, and 0.25 mm in diameter, experiments were performed over a shear‐rate range of 3 × 10² to 5 × 10³ s^?1 at three temperatures, 210, 220, and 230 °C. The results demonstrate that the geometry dependence of the PP viscosity relied on the die diameter and the temperature of the PP melt. The viscosity values of the PP melt in the 0.25‐mm diameter die were higher than were those in the 0.5‐ and 1.0‐mm dies at 220 and 230 °C. However, the viscosity values in all of the tested dies were similar at 210 °C. The tendency for the viscosity to decrease as the temperature of the polymer melt increased weakened in the 0.25‐mm diameter die. As a result, the pressure applied to the PP melt in the 0.25‐mm diameter die increased; this caused a decrease in the free volume between molecules. On the basis of the Barus equation, the contribution of pressure to the changed viscosity in each die at each of the tested temperatures was calculated and was found to be as high as 32.86% in the 0.25‐mm die at 230 °C. Additionally, the effect of the wall slip on the geometry dependence of the PP viscosity in the tested dies was investigated with a modified Mooney method. The values of the slip velocity revealed that wall slip occurred only in the 0.25‐mm die at 210 °C. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43459.     

Time‐dependent rheological behavior of low‐density polyethylene white color masterbatches under dynamic stress field

The time‐dependent behavior of low‐density polyethylene (LDPE) white color masterbatches (WCMBs), which were concentrated suspensions filled with titanium dioxide (TiO₂), was found using dynamic stress rheometer. The viscosity first decreased slightly with time then continuously increased with time, and T_g(δ) (δ was the angle of loss) decreased with time, which meant the time‐dependent behavior of the elastic contribution was more pronounced than that of the viscous contribution. The higher the experimental frequency and temperature, the more pronounced the viscosity increase. However, the higher experimental stress did not lead to pronounced viscosity increase, which was attributed to the existence of small defects at higher stress. The 30 wt % of TiO₂ content was critical to obvious time‐dependent behavior. The viscosity increase with time was related to the formation of a hard shell around the melt sample during the test. It was verified by thermogravimetric analysis that the TiO₂ concentration at the outer surface was higher than that at the core of the sample and, because the outer surface contained more TiO₂, a hard shell was formed, which impeded further deformation of the sample. This was completely different from the other reported systems with time‐dependent behavior. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2793–2799, 2002     

The effect of temperature and moisture on the rheology of black coal-oil suspensions

Rheological properties of black coal-KC220 oil suspensions have been investigated using a Contraves rheometer over a temperature and coal volume fraction range of 18–200°C and 0.247-0.385, respectively. The suspensions behaved as Newtonian fluids. Variation of viscosity with temperature does not follow any regular trend and peak viscosity values occur in the temperature range of 80–140°C for dry coal and 70–130°C for moist coal, depending upon the concentrations of coal in the suspension. Freshly prepared suspensions of moist coal exhibit viscosity peaks at a temperature lower than that of the corresponding suspension with dry coal. However, when aged, the suspensions of moist coal exhibit very small peak viscosity and follow an Arrhenius type behavior. For both dry and moist coal, the maximum volume fraction, ?_m, continues to decrease with an increase in temperature.     

Dimensional Analysis of Crossflow Microfiltration Data

Abstract

A new approach to correlating crossflow microfiltration (CFMF) data based on dimensional analysis is presented. The steady state flux was assumed to be a function of the trans‐membrane pressure (ΔP), the crossflow velocity (u), the particle concentration (c), filtrate viscosity (μ), and membrane resistance (R _m). Correlations of the form J/u=K(ΔP/cu ²) ^a (ΔP/μuR _m) ^b were tested on three sets of published data: one for CFMF of dried yeast suspensions in a laminar flow hollow fiber module, one for dried yeast suspensions in a turbulent flow tubular module and one for suspensions of latex particles in a laminar flow flat sheet module. The R ² values for the fits of the correlations to the data were 0.98, 0.94, and 0.91 respectively.     

Dilatancy of concentrated suspensions with Newtonian matrices

Suspensions filled close to their maximum packing fraction present special challenges in their processing and in their rheological characterization. In this report, the literature in the area of dilatancy of concentrated suspensions is reviewed. Furthermore, the shear viscosity of a Newtonian polymeric liquid filled with 60 vol. percent of ammonium sulfate has been investigated. Both capillary and parallel disk torsional flows, were employed, spanning three decades in shear stress. Upon correction for slip, the suspension exhibited shear thinning at low shear stresses and shear thickening at higher shear stresses. Above a critical wall shear stress, the shear viscosity of the suspension increased unboundedly and the flow became pluglike with apparent slip at the wall. These findings have important ramifications in the processing of composites from such concentrated suspensions.     

Gas‐Liquid Mass Transfer in Fibrous Bed Reactor with Counter‐Current Liquid Recycle

In this work, the gas‐liquid mass transfer in a lab‐scale fibrous bed reactor with liquid recycle was studied. The volumetric gas‐liquid mass transfer coefficient, k_La, is determined over a range of the superficial liquid velocity (0.0042–0.0126 m.s^–1), gas velocity (0.006–0.021 m.s^–1), surface tension (35–72 mN/m), and viscosity (1–6 mPa.s). Increasing fluid velocities and viscosity, and decreasing interfacial tension, the volumetric oxygen transfer coefficient increased. In contrast to the case of co‐current flow, the effect of gas superficial velocity was found to be more significant than the liquid superficial velocity. This behavior is explained by variation of the coalescing gas fraction and the reduction in bubble size. A correlation for k_La is proposed. The predicted values deviate within ± 15 % from the experimental values, thus, implying that the equation can be used to predict gas‐liquid mass transfer rates in fibrous bed recycle bioreactors.     

A novel rheometer design for yield stress fluids

An inexpensive, rapid method for measuring the rheological properties of yield stress fluids is described and tested. The method uses an auger that does not rotate during measurements, and avoids material and instrument‐related difficulties, for example, wall slip and the presence of large particles, associated with yield stress fluids. The method can be used for many types of yield stress fluids, including concentrated lignocellulosic biomass. Sample preparation prior to measurement is minimal, reducing, or eliminating disruption of the sample. We show that measurements using this technique compare well with measurements obtained with a vane rheometer. A variation of the described method is proposed that would make it easier to measure time‐dependent rheological properties. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1523–1528, 2014     

Compression molding of glass reinforced thermoplastics: Modeling and experiments

The shearing and extensional behavior of glass mat‐thermoplastic (GMT) material under compression molding was investigated with a special model being developed for the case of non‐lubricated mold‐plate surfaces. Mathematical expressions for the radial and through‐thickness flow velocities were derived that enabled the derivation of extensional and shear strain rates. The GMT non‐lubricated (no‐slip wall conditions) compression molding was modeled as a combination of extensional and shearing flow and the two extensional and shear viscosities were determined. Scott's approach was used in this work to determine the radial velocit in the r‐direction, which depends on the shear power‐law expression. The velocity component in the z‐direction was then calculated using the continuity equation. The velocity profiles were used to calculate the shear and extensional strain rates. Scott's shear viscosity did not satisfy the constitutive equation for the extensional part, but a power‐law expression with new parameters depending on the deformation tensors was successfully used to calculate an independent extensional viscosity using the same non‐lubricated squeezing experiment. Lubricated squeezing flow was carried out for the same material to achieve a pure extensional flow, and the extensional viscosity calculated using this approach agreed with the extensional viscosity determined using the non‐lubricated experiment. GMT material used in this study is confirmed to have two layers of continuous long fibers orientated randomly inplane, separated by short chopped fibers in the middle, which suggests that the material can be treated as an isotropic material, and the fiber‐matrix separation is seen to be high at the extremities of the flow.     

Rheology of highly filled natural CaCO3 composites. I. Effects of solid loading and particle size distribution on capillary rheometry

The rheology of poly(di‐methyl siloxane) suspensions containing various loadings of natural CaCO₃ particles, of several particle size distributions, was studied using capillary rheometry. Highly loaded suspensions were investigated, emphasizing the unique behavior of high filler loaded compositions. Mild shear thinning was observed for most suspensions, whereas shear thickening was observed for suspensions containing nearly maximal possible solid loadings. The dominancy of particle size distribution was demonstrated by studying the relative suspensions viscosity as function of shear rate. It was further illustrated by the influence of the filler specific surface area on the flow properties. A seemingly slight changes in the particles‐specific surface area caused significant changes in the viscosity of maximal solid loaded unimodal suspensions. Fair agreement with the Chong and Krieger and Dougherty models was found for unimodal suspensions, while the combined Farris–Chong model showed an improved fit for the bimodal suspensions. Evidence for wall slip was demonstrated, using scanning electron microscopy and energy dispersive spectrometry, as a clear difference in the extrudate outer and bulk compositions; although no influence on the flow data was observed. POLYM. COMPOS., 28:512–523, 2007. © 2007 Society of Plastics Engineers     

Better characterization of raw natural rubber by decreasing the rotor speed of Mooney viscometer: Role of macromolecular structure

The objective of our work was to characterize natural rubber (NR) samples with different macromolecular structures by measuring Mooney viscosities (V_R) at variable rotor speeds ≤2 rpm, called variable speed Mooney viscosity (M_VS). Model samples of technically specified rubbers of constant Mooney viscosity (TSR5CV) were prepared with chosen specific clones. The structures of the samples were characterized by size‐exclusion chromatography coupled with an online multi‐angle light‐scattering detector (SEC‐MALS). Rheological properties of the samples were also characterized by a dynamic moving die rheometer. Measuring monoclonal model samples by M_VS showed three types of V_R flow curves. The V_R at high rotor speed (2 rpm) was correlated with number‐average molar mass (M_n), whereas V_R at low rotor speed (0.05 rpm) was correlated with weight‐average molar mass (M_w). Measuring M_VS revealed the rheological behaviors of samples and enabled discrimination between samples with different macromolecular structures and should thus help in predicting processability. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers