Wall slip velocity measurement of molten polypropylene in capillary flow based on length‐corrected Mooney technique

In this study, to measure wall slip velocity of molten polypropylene (PP) by using different length‐to‐diameter (L/D) ratios of capillary dies with fixed diameter, a length‐corrected Mooney technique was proposed. Moreover, the effects of pressure, temperature, and L/D ratio were considered to better represent wall slip mechanism. To verify the feasibility of the length‐corrected Mooney technique, a series of capillary rheological experiments for molten PP were carried out. Meanwhile, the power‐law quantitative equations of slip velocity were established by shear stress. Moreover, the effects of L/D ratio and temperature on rheological properties of PP were investigated. In addition, numerical simulations for slip velocity and rheological properties of PP were performed. Numerical results validated that the length‐corrected Mooney technique, and the power‐law quantitative equations of slip velocity were available. Results showed that wall slip velocity of molten PP decreased with the capillary die's L/D ratio, but increased with the temperature and shear rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44589.     

Surface tearing and wall slip phenomena in extrusion of highly filled HDPE/wood flour composites

The extrudate surface tearing of highly filled high‐density polyethylene (HDPE)/wood flour composites has been investigated in relation to the rheological properties and the wall slip phenomenon in capillary dies. Rotational and capillary rheometers were employed to measure the rheological properties. Mooney analysis was used for determination of wall slip velocity. The results showed considerable increase of storage modulus, dynamic and shear viscosity with increasing wood flour loading. It was also found that all wood filled composites did not obey the Cox–Merz rule. The wall slip velocity depends on wood filler content and shear rate. Generally, with increasing shear rate the slip velocity sharply increases leading to plug‐like flow. It was observed that the surface of the extrudates becomes smoother with increase in shear rate and wood flour content. POLYM. ENG. SCI., 46:1204–1214, 2006. © 2006 Society of Plastics Engineers     

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.     

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     

Rheological characterisation of hydroxyapatite filled polyethylene composites. Part 2 – Isothermal compressibility and wall slip

Abstract

Rheological characterisation of hydroxyapatite–high density polyethylene (HA–HDPE) composites has been performed in terms of isothermal compressibility and wall slip. Addition of HA to the polymer melt decreases the compressibility of the melt. The unfilled HDPE was found to exhibit wall slip at shear stresses as low as 0·10 MPa. The flow curves of the composites showed three distinct regions: a gradient at low shear rates; a plateau region; and a gradient at higher shear rate. An increase in rheometer pressure seems to suppress the slip in composites. The 40 vol.-% HA–HDPE composite exhibited two critical shear stresses, one corresponding to wall slip, which occurs in the lower shear rate region of the flow curve, and the other corresponding to a plateau, which is identified with the stick–slip behaviour of unfilled HDPE reported in the literature. The plateau shear stress increased with filler volume fraction and this effect is attributed to the decreased compressibility of the melt. A good correlation with a negative correlation coefficient was found to exist between compressibility and shear stress in the plateau region. The slip observed in unfilled HDPE and at low shear rates in the 40 vol.-% HA–HDPE systems has been explained in terms of a low molecular weight polymer layer formed at the melt/wall interface. The large interfacial slip observed in the plateau region is attributed to complete disentanglement of adsorbed chains from free chains at the melt/wall interface at and beyond the plateau region.     

Capillary flow of low‐density polyethylene

The capillary flow of a commercial low‐density polyethylene (LDPE) melt was studied both experimentally and numerically. The excess pressure drop due to entry (Bagley correction), the compressibility, the effect of pressure on viscosity, and the possible slip effects on the capillary data analysis have been examined. Using a series of capillary dies having different diameters, D, and length‐to‐diameter L/D ratios, a full rheological characterization has been carried out, and the experimental data have been fitted both with a viscous model (Carreau‐Yasuda) and a viscoelastic one (the Kaye—Bernstein, Kearsley, Zapas/Papanastasiou, Scriven, Macosko, or K‐BKZ/PSM model). Particular emphasis has been given on the pressure‐dependence of viscosity, with a pressure‐dependent coefficient β_p. For the viscous model, the viscosity is a function of both temperature and pressure. For the viscoelastic K‐BKZ model, the time‐temperature shifting concept has been used for the non‐isothermal calculations, while the time–pressure shifting concept has been used to shift the relaxation moduli for the pressure‐dependence effect. It was found that only the viscoelastic simulations were capable of reproducing the experimental data well, while any viscous modeling always underestimates the pressures, especially at the higher apparent shear rates and L/D ratios. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

“SPURT FRACTURE” IN CAPILLARY FLOW

The critical conditions under which flow curves in capillary flow abruptly change their slope to zero (spurt) and the influence of solvent additive and solvent power on this phenomenon have been investigated. Based on a forced high elastic state concept an expression for the so-called spurt phenomenon, i.e. fracture-induced slip at the wall in a capillary of a capillary rheometer, is deduced. It is found that the spurt fracture stress, τ^s _cr, and the spurt fracture shear rate, γ^s _cr, can be represented by the master curve log (τ ^s _crr ((p/M_c)PE(M_c/p))^2/3 against log (a_T γ^s _cr), where a_T is the WLF shift factor, M_c the molecular weight between entanglements and p the density.

Estimation of slip rates at the wall and measurements on slightly crosslinked high density polyethylene supports the assumption that spurt results from melt fracture at the capillary wall.

Only addition of the non-solvent calcium stearate (with high density polyethylene) results in flow behavior which significantly deviates from that found for samples containing good solvents. Gel permeation chromato-graphy indicates that if chain scission resulting in lower molecular weight takes place, it will be limited to thin layers near the capillary wall.

melt fracture in the capillary cannot be reached. The flow behavior is influenced by addition of the non-solvent calcium stearate. The slopes of the flow curves is changed at relatively low shear rates but the high molecular weight polymer DMDS 5140 never the less shows spurt behavior at the same stress as for the pure sample.

This behavior may tentatively be interpreted as being caused by the formation of a boundary layer of non-solvent at low shear rate the thickness of which depends on the polymer and flow field. At stresses corresponding to the critical conditions, fracture in the polymer takes place. The interface between the non-solvent layer and the polymer matrix must according to Han61 be expected to be unstable     

Kinematics of the stick-slip capillary flow of high-density polyethylene

A study of the kinematics of the stick-slip capillary flow of high-density polyethylene has been carried out in this work by using particle image velocimetry (PIV). The experiments covered a wide range of shear rates and the velocity maps and profiles across the die were obtained for the different regimes of the discontinuous flow curve. In the low shear rate region, the melt exhibited shear thinning without slip. In the unstable stick-slip regime, an alternating behavior between full adhesion and slip was observed, whereas both, the maximum velocity and the slip velocity of the melt, changed continuously during pressure oscillations. In addition, non-homogenous slip, characterized by regions with and without slip at the die wall, was occasionally observed during the oscillations. In contrast to the general assumption, the flow in the high shear rate region was found to be unstable, and characterized by high frequency pressure oscillations. A steep rise of the slip velocity took place from the onset of the stick-slip regime and reached values higher than 70% of the maximum velocity for the profiles in the high shear rate branch. However, a true plug flow was never observed due to shear thinning of the melt. Finally, a direct proof of the Mooney hypothesis to account for slip in polymer melts is given on the basis of the comparison of velocity profiles measured in the low and high shear branch.     

Geometrical dependence of viscosity of polymethylmethacrylate melt in capillary flow

The shear viscosity of polymethylmethacrylate (PMMA) melt is particularly investigated by using a twin‐bore capillary rheometer at four temperatures of 210, 225, 240, and 255°C with different capillary dies. Experimental results show that the geometrical dependence of shear viscosity is significantly dependent on melt pressure as well as melt temperature. The measured shear viscosity increases with the decrease of die diameter at lower temperatures (210 and 225°C) but decreases with the decrease of die diameter at higher temperatures (240 and 255°C). Based on the deviation of shear viscosity curves and Mooney method, negative slip velocity is obtained at low temperatures and positive slip velocity is obtained at high temperatures, respectively. Geometrical dependence and pressure sensitivity of shear viscosity as well as temperature effect are emphasized for this viscosity deviation. Moreover, shear viscosity curve at 210°C deviates from the power law model above a critical pressure and then becomes less thinning. Mechanisms of the negative slip velocity at low temperatures are explored through Doolittle viscosity model and Barus equation, in which the pressure drop is used to obtain the pressure coefficient by curve fitting. Dependence of pressure coefficient on melt temperature suggests that the pressure sensitivity of shear viscosity is significantly affected by temperature. Geometrical dependence of shear viscosity can be somewhat weakened by increasing melt temperature. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 3384–3394, 2013     

Rheological behavior of zirconia feedstock flowing through various channels considering wall-slip

The existence of wall slip for ZrO₂ feedstock flow in micro powder injection molding was investigated based on capillary rheometer experiments using dies of three dimensions. A power law function was derived by data fitting to determine the wall slip velocity based on which numerical simulation was carried out to explore the influence of wall slip on micro injection molding. Experimental results indicate that the feedstock is less sensitive to temperature fluctuation at higher shear rates. Power-law model can provide higher accuracy than the modified Cross model to depict the rheological behavior of the feedstock in capillary flows with different channels. Numerical simulation results show that in case of steady flow higher dynamic viscosity of the feedstock and higher pressure losses of the flow appeared when the wall slip boundary was included as compared to no-slip assumption in micro powder injection molding. This is because that when the wall slip boundary was included the shear rate distribution of the feedstock was lower than that of the feedstock assuming no-slip boundary.     

Rheological properties and morphology of compatibilized poly(butylene terephthalate)/linear low‐density polyethylene alloy

The rheological behavior of PBT/LLDPE and PBT/LLDPE‐g‐AA blends [where PBT is poly(butylene terephthalate), LLDPE is linear low‐density polyethylene, and AA is acrylic acid] under a capillary flow was investigated with a capillary rheometer. The Utracki equation was used to describe the viscosity–composition dependence of PBT/LLDPE and PBT/LLDPE‐g‐AA blends at low shear stresses. However, at high shear stresses, this equation was not suitable for these blending systems. There existed a maximum on the curves of the entrance pressure drop versus the blending compositions, and the interlayer slip factor β in the Utracki equation was related not only to the shear stress but also to the elasticity difference of the two blending components. Morphological observations indicated that at high shear rates, there existed two different morphologies at different positions of the extrudates, and this was the reason that the Utracki equation failed. Near the wall of the capillary, low‐viscosity PBT stratified, and this resulted in an additional decrease in the viscosities of the blending systems. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 206–213, 2003     

Relationship between shear stress and shear strain of polymer melt under vibrating force field

Abstract

When a sinusoidal vibration was superimposed in parallel on the flow direction of a polymer melt being extruded through a capillary, the shear stress and shear rate of the polymer melt were analysed with a constant velocity type dynamic rheometer of capillary (CVDRC) devised by the authors. By measuring the instantaneous data of capillary entry pressure, capillary volume flux (or absolute velocity of piston rod) and their phase difference in a vibrating force field, it was found that the relationship between the pulsating amplitude value coefficient of entry pressure and that of volumetric flowrate was an approximate power series; the wall shear stress and wall shear rate of low density polyethylene (LDPE) melt extruded dynamically under various amplitudes and frequencies also exhibited a non-linear proportional relationship.     

Comparisons of the rheological behaviors of polypropylene and polymethyl methacrylate in a capillary die

In this study, the rheological characteristics of polypropylene (PP) melt at 210, 220, and 230 °C and polymethyl methacrylate (PMMA) melt at 230, 240, and 250 °C in a micro die were investigated. The experiments were performed over a shear rate range of 3 × 10² to 5 × 10³ s^?1 using an advanced twin‐bore capillary rheometer. Dies with diameters of 1.0, 0.5, and 0.25 mm were used. The results indicated that the geometric dependences of the PP and PMMA viscosities were not identical at different shear rates and temperatures and that the micro size effect had a profound influence on the PP viscosity. The analysis demonstrated that the variations in the shear viscosity of the PP and PMMA melts in the micro die were partially attributed to the contribution of the pressure applied to the polymer melts. Additionally, the effect of wall slip on the PP and PMMA viscosities in the tested dies was investigated based on the modified Mooney method. The results implied that wall slip easily occurred in the PP melt flowing through the 0.25 mm die at 210 °C due to the distinct size effect. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134 , 44617.     

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.     

Slip flow of coal water slurries in pipelines

Experiments were carried out on a pilot scale slurry transport apparatus to investigate slip flow behavior of coal water slurries (CWSs) in pipes with various diameters (25, 32, 40 and 50 mm). The effects of volume concentration, particle size and slurry temperature on wall slip behavior (wall slip velocity, critical wall shear stress and slippage contribution) were investigated. A numerical technique based on Tikhonov regularization was applied to determine the wall slip behavior. As the slurry temperature or the particle size increased, the critical wall shear stress was observed to decrease and the wall slip velocity was observed to increase significantly, while when the solid concentration was very close to the maximum packing fraction, a slight increase in volume concentration would lead to a rapid decrease in wall slip velocity and a sharp increase in critical wall shear stress. The temperature influence on critical wall shear stress and yield stress increased as volume concentration increased. At low wall shear stress, the slippage contribution was mainly dependent on the difference between yield stress and critical shear stress. While at high wall shear stress, it was dependent on both of the shear viscosity of the bulk slurries and the wall slip velocity.     

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     

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride)

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride) has been studied using a capillary rheometer. The elongational viscosity was evaluated based on Cogswell's method with two types of capillaries: capillary length (L)/capillary diameter (D) = 10 mm/1 mm and L/D = 0 mm/1 mm. We used the ratio P₀/P_L that indicates the contribution of elongational flow to the total flow involving both the shear and elongational flows. P_L and P₀ are the pressure losses in the capillary and the converging flows, respectively. P₀/P_L increased with molecular weight and shear rate. This corresponds to decreasing the number of entanglements of molecular chain under a large displacement, especially high shear. Thus, we suggest using P₀/P_L as the parameter of the entanglement interaction on the molecular chain under a large displacement. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2381–2384, 1999     

The rheology of homogeneously gas-fluidized solids,studied in a vertical standpipe

The rheology of homogeneously gas-fluidized cracking of catalyst held at various porosities has been studied in a vertical standpipe. It was found that the rheology can be described by means of a Bingham-plastic model with the inclusion of slip at the wall.Yield stress and viscosity could both be correlated with linear functions of the porosity.The wall slip velocity v_w could be described by a relation ?μ_wv_w = τ_w ? τ_w0 in which μ_w is some kind of wall slip viscosity, τ_w the wall shear stress and τ_w0 a wall yield stress. Both μ_w and τ_w0 depend again on porosity. τ_w0 also depends on the wall roughness.     

温度和固相粒径与浓度对水煤浆管内流动壁面滑移的影响

通过改变管径、温度、煤粉粒度和浓度,在中试规模的输送装置上研究水煤浆直管内的滑移流动规律,联合采用Mooney滑移修正方法和Tikhonov正则化方法确定浆体壁面滑移特性。结果表明,随温度和固相粒径的增大,临界剪切应力降低,壁面滑移速度显著增加;浓度越高,临界剪切应力及产生相同滑移速度所需的壁面剪切应力越大,温度升高对临界剪切应力和屈服应力的降低越显著;低壁面剪切应力下的滑移贡献率主要取决于临界剪切应力及屈服应力的相对大小,高壁面应力下主要取决于壁面滑移速度和浆体真实流变特性。     

Melt Flow Properties During Capillary Extrusion of Linear Low-Density Polyethylene

Abstract

The melt flow properties of a linear low-density polyethylene (LLDPE) were measured by means of a capillary rheometer under the experimental conditions of temperatures from 220° to 260°C and apparent shear rates varying from 12 to 120 s^?1. The end pressure drop (ΔP _end) was determined by employing the Bagley's plotting method. The results showed that ΔP _end increased nonlinearly with increasing shear stress. The end pressure fluctuation phenomenon was observed at lower shear stress level, and several plateau regions were generated in the end pressure drop-shear stress curves, suggesting onset of the wall-slip phenomenon during die extrusion of the resin melt. The critical shear stress with onset end pressure fluctuation phenomenon increased with a rise of temperature. Furthermore, the melt shear flow did not strictly obey the power law. The melt shear viscosity decreased nonlinearly with increasing shear stress and with a rise of temperature, whereas the dependence of the melt shear viscosity on the test temperature accorded with a formula similar to the Arrhenius expression.