EVALUATION OF POLYMER ADSORPTION-GEL FORMATION AND SLIP IN POLYMER SOLUTION FLOWS

A superposition model for evaluation of the effects of polymer adsorption-gel formation and slip of polymer solutions exhibiting both phenomena has been applied to the capillary flow of aqueous solutions of two molecular weight grades of hydroxyethyl cellulose (Natrosol 250, types G and HR, supplied by Hercules Powder Company). The flow behaviour of the solutions investigated was non-Newtonian. Evaluations are presented of the effective thicknesses of polymer adsorption-gel formation and pure solvent layers, as a function of the wall shear stress, tube radius and polymer concentration, corresponding to the determinations of the effective velocity at the wall.

The results of the analysis indicate the surface characteristics undergo a dramatic change from polymer adsorption-gel formation at the tube surface to the phenomenon characterized by slip in a narrow tube radius interval which has important implications in enhanced oil recovery by polymer solution floods. It also provides an explanation for the contrasting behaviours observed in the flow of aqueous Natrosol solutions through packed beds (Sadowski, 1963) and filter cakes (Kozicki et al., 1972).     

田菁冻胶在毛细管及多孔介质中滑移效应研究

本文用实验方法研究了田菁冻胶压裂液在毛细管和多孔介质中的流动特性,求得相应的滑移效应,提出本构方程及C·H.B.模型,并得以验证.     

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.     

Thickness uniformity of HDPE blown film: Relation to rheological properties and density

Previous work has elucidated that the wall slip velocity and viscosity of polymer melts influence the thickness uniformity of blown film. The present study investigates the effects of the stress dependence of wall slip, the shear thinning and the density on the uniformity. We have prepared high‐density polyethylenes with a variety of molecular weight distributions, which have different rheological properties. Examination of the thickness uniformity of their blown film has shown that the uniformity is correlated with wall slip velocity, the stress dependence of the velocity, melt viscosity, shear thinning and density; the coefficient of the correlation is determined to be 0.990. The reason why the stress dependence of wall slip and the shear thinning affect the uniformity is explained in terms of polymer melt flow behavior in a die, while the effect of density is interpreted considering bubble fluctuation in the blow‐up process. Polym. Eng. Sci. 44:965–972, 2004. © 2004 Society of Plastics Engineers.     

Experimental and Numerical Analysis of the Viscous Fingering Instability of Shear‐Thinning Fluids

Miscible flow displacements in a rectilinear Hele‐Shaw cell of Newtonian as well as rheologically well‐characterized shear‐thinning fluids are examined through experimental measurements and numerical modelling. Water is used as a displacing fluid while the displaced fluid consists of either a reference Newtonian glycerol solution or shear‐thinning solutions of Alcoflood? polymers of different molecular weights. The experimental measurements revealed that the shear‐thinning behaviour of the non‐Newtonian solutions resulted in more complex instability patterns and new finger structures not previously observed in the case of Newtonian displacements are identified and characterized. An analysis of the effects of the rheological behaviour of the shear‐thinning fluids on instability characteristics such as the finger width and finger tip velocity is presented. Numerical simulations using a pseudo‐spectral method are conducted and allowed to compare the predictions of the mathematical model based on an effective Darcy's law with the experimental measurements.     

Scherfließen und Wandgleiten von Massen für den Pulverspritzguss

This contribution presents coupling of laws for shear flow and wall slipping by the shear stress at the slipping interface. It includes the special case of Coulombian friction postulated by Uhland as well as the assumption of a constant sliding velocity along the flow channel according to Mooney. As an example, Ostwald and de Waele's law of shear thinning flow is combined with a shear stress of sliding depending on internal pressure by a power law. Examined feedstocks for metal injection molding showed a rheological behavior according to the model presented.     

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     

Interfacial stress in non-Newtonian flow through packed bed

This study investigates the pressure drop characteristics, shear stress in packed bed with shear thinning power law type non-Newtonian liquid. A mechanistic model has also been developed to analyze the pressure drop and interfacial stress in packed bed with non-Newtonian liquid by considering the loss of energy due to wettability. The Ergun's and Foscolo's equations were used for comparison with the experimental data. The Ergun equation was modified to account for the effect of flow behavior index of non-Newtonian fluid in the column. The intensity factor of shear stress and the friction factor were analyzed based on energy loss due to wettability effect of liquid on the solid surface.     

Pipe flow of a dense emulsion: Homogeneous shear‐thinning or shear‐induced migration?

The flow field of a 70% concentrated noncolloidal o/w emulsion in a pipe has been investigated by means of Particle Image Velocimetry in a matched refractive index medium. At steady state and in laminar regime, the shape of axial velocity profiles is not parabolic and exhibits a shear‐thinning behavior of the dense emulsion, with a flow index of 0.5 and a negligible yield stress (less than 1 Pa). However, instead of a square root law, the pressure drop increases linearly with U_m. To explain this apparent inconsistency, two mechanisms of different nature are considered. The first originates from a possible relation between the consistency factor and the drop mean diameter. The second mechanism is shear‐induced migration and leads to the development of a concentration gradient in the pipe cross section. Both mechanisms considered reconcile the experimental data, the apparent local shear‐thinning behavior and the linear evolution of the pressure drop with the flow rate. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Modelling of gas interstitial velocity radial distribution over cross-section of a tube packed with granular catalyst bed; effects of granule shape and of lateral gas mixing

The previously presented [Zió?kowska, I., Zió?kowski, D., 1993. Modelling of gas interstitial velocity radial distribution over a cross-section of a tube packed with granular catalyst bed. Chemical Engineering Science 48, 3283-3292] mathematical model of gas flow field within a tube packed with a bed of spherical elements has been modernised. The modernisation consists in more rigorous treating of the radial gas dispersion within the bed voids in the fluid dynamic equations and in involving the formulae correlating the flow resistance in beds packed with various non-spherical elements (Raschig rings, cylinders) with their characteristics. The model solution relates the gas interstitial and superficial radial distributions with an empirical parameter—the local effective viscosity or corresponding Reynolds number, dependent on the geometric, aerodynamic and physical properties of the system which are usually known. The effective viscosity is associated with the kinetic energy dissipation due to the interface friction, the shear stresses in molecular and turbulent motion and the radial dispersion in the gas stream. Its knowledge makes possible the evaluation of the radial profiles of the gas interstitial velocity, as well as the dispersion coefficient, or corresponding Péclet number and the drag coefficient for individual element within the bed. The effective viscosity has been determined experimentally for beds of Raschig rings and cylinders by the method presented previously [Zió?kowska, I., Zió?kowski, D., 2001. Experimental analysis of isothermal gas flow field in tubes packed with spheres. Chemical Engineering and Processing 40, 221-233] and the results have been correlated with the system characteristics. Then the correlations have been used, according to the model, in evaluation of the radial distributions of the gas interstitial velocity, the radial dispersion coefficient and the drag coefficient for individual element within the bed.     

Lattice‐Boltzmann simulation of sago (Metroxylon sagu) starch solutions in porous media

From rheological experiments in gelatinized sago starch solution already reported in the literature and a Lattice‐Boltzmann simulation, we provide some insight into the understanding of the non‐Newtonian fluid dynamics of sago‐starch‐type solutions in porous media. In this paper, permeability and wall shear stress in arbitrarily generated and randomly generated porous media are predicted in the range of the modified Darcy's law. Additional results on flow paths, velocity, shear‐stress tensor, and pressure fields are provided. We prove that our LBE model for sago starch solutions reproduces Blake‐Kozeny and Ergun laws. The model presented in this paper is intended to be used for simulating packed beds.     

Creeping flow of non-Newtonian liquids through fluidized beds of spherical particles

Fluidization of spherical particles beds by shear thinning polymer solutions in creeping flow region was investigated. The fall of the expansion rate was observed with the increasing shear thinning behaviour of polymer solutions tested. Simultaneously, the maximum bed porosity reached in the expanded beds and the stability of the particulate fluidization decreased. The comparison of the experimental and calculated bed expansion data showed that the capillary and cell models of the beds are not correct for describing the flow of shear thinning polymer solutions through fluidized beds. An empirical criterial equation was suggested for this purpose.     

Electrodiffusion characterization of non-Newtonian flow through packed beds

The limiting current technique, involving the cathodic controlled reduction of ferricyanide ions, has been used in order to characterize the axial dispersion and the solid-liquid mass transfer for a non-Newtonian shear thinning power-law fluid flowing through fixed beds of spherical and parallelepipedal particles. For each of the two phenomena, results corresponding to Newtonian and non-Newtonian power-law flow at low Reynolds numbers can be described by the same dimensionless equation for beds packed with particles of the same shape.This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

Effect of Wood Fibers on the Rheological and Mechanical Properties of Polystyrene/Wood Composites

The effects of wood fibers on the rheological and mechanical properties of polystyrene/wood (PS/wood) composites were investigated. The composites with different ratios of PS and wood were prepared by means of internal mixer and, additionally, two different sizes of the wood particles were used, such as ～100 and ～600 µm. The rheological properties were studied using capillary rheometer, apparent shear rate, apparent shear stress, apparent viscosity, power law index, and flow activation energy at a constant shear stress were determined. The rheological results showed that the shear stress–shear rate variations obeyed a power law equation, and the composites exhibited shear thinning. The flow activation energy of the composites increased with the addition of wood particles. Mechanical results showed that stress at break of the composites was higher than that of pure PS, whereas the strain at break and impact strength of the composites were lower than that of PS. In addition, the mechanical properties of the present composites were improved when the small size of wood particles were incorporated.     

Velocity profiles and frictional pressure drop for shear thinning materials in lid-driven cavities with fully developed axial flow

A finite element numerical study has been carried out on the isothermal flow of power law fluids in lid-driven cavities with axial throughflow. The effects of the tangential flow Reynolds number (Re_U), axial flow Reynolds number (Re_W), cavity aspect ratio and shear thinning property of the fluids on tangential and axial velocity distributions and the frictional pressure drop are studied. Where comparison is possible, very good agreement is found between current numerical results and published asymptotic and numerical results. For shear thinning materials in long thin cavities in the tangential flow dominated flow regime, the numerical results show that the frictional pressure drop lies between two extreme conditions, namely the results for duct flow and analytical results from lubrication theory. For shear thinning materials in a lid-driven cavity, the interaction between the tangential flow and axial flow is very complex because the flow is dependent on the flow Reynolds numbers and the ratio of the average axial velocity and the lid velocity. For both Newtonian and shear thinning fluids, the axial velocity peak is shifted and the frictional pressure drop is increased with increasing tangential flow Reynolds number. The results are highly relevant to industrial devices such as screw extruders and scraped surface heat exchangers.     

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     

Thermal and flow effects during adsorption in conventional,diluted and annular packed beds

Previous investigations have shown a complex combination of thermal and flow effects during adsorption in highly loaded, narrow packed beds. Respective conditions were realized by packing relatively large zeolite particles in a narrow tube (which causes wall channelling) and adsorbing water vapour from air on the particles (which is highly exothermic). The present work extends the investigation to novel column configurations with purposely altered conditions of heat generation and flow—namely to diluted beds, annular beds and beds consisting of coated particles. Experimental results obtained by near infrared tomography are compared with the results of breakthrough experiments in conventional columns and with numerical calculations. The latter are conducted with a non-isothermal, two-dimensional model that not only considers the increase of porosity and flow velocity near the tube wall, but also expresses the effective transport coefficients as functions of the radial coordinate. The model provides reasonable accuracy under conditions for which the usual plug-flow assumption is questionable.     

Computational Modeling of Die Swell of Extruded Glass Preforms at High Viscosity

Computational simulations of glass extrusion are performed to quantify the effects of material behavior and slip at the die/glass interface on the die swell. Experimental data for three glass types are used to guide the computational study, which considers glass material to be viscous with and without shear thinning and viscoelastic using the Maxwell upper‐convected model. The study starts with assuming no‐slip at the glass/die interface to see if material behavior alone can explain the die swell results, and then considers slip using the Navier model where interface shear is directly proportional to the relative slip speed at the interface. Consistent with the possibility of slip and intended high viscosity applications, viscosity ranging from 10^7.4–10^8.8 Pa·s was used. Based on optimization of the various input parameters required to achieve the measured die swell and ram force values, the study concludes that interface slip occurred as only extreme values of the shear thinning parameters provided an alternative.     

CFD investigation of the pipe transport of coarse solids in laminar power law fluids

A numerical parametric study of the laminar pipe transport of coarse particles in non-Newtonian carrier fluids of the power law type has been conducted using an Eulerian-Eulerian computational fluid dynamics (CFD) model. The predicted flow fields have been successfully validated by experimental measurements of particle velocity profiles obtained using a positron emission particle tracking technique, whilst solid-liquid pressure drop has been validated using relevant correlations gleaned from the literature. The study is concerned with nearly-neutrally buoyant particles flowing in a horizontal or vertical pipe. The effects of various parameters on the flow properties of such mixtures have been investigated over a wide range of conditions. The variables studied are: particle diameter (2-9 mm), mean solids concentration (5-40% v/v), mean mixture velocity (25-125 mm s⁻¹), and rheological properties of the carrier fluid (k=0.15-20 Pa sⁿ; n=0.6-0.9). A few additional runs have been conducted for shear thickening fluids, i.e. n>1. Whilst the effects of varying the power law parameters and the mixture flowrate for shear thinning fluids are relatively small over the range of values considered, particle size and solids concentration have a significant bearing on the flow regime, the uniformity of the normalised particle radial distribution and of the normalised velocity profiles of both phases, and the magnitude of the solid-liquid pressure drop. The maximum particle velocity is always significantly less than twice the mean flow velocity for shear thinning fluids, but it can exceed this value in shear thickening fluids. In vertical down-flow, particles are uniformly distributed over the pipe cross-section, and particle diameter and concentration have little effect on the normalised velocity and concentration profiles. Pressure drop, however, is greatly influenced by particle concentration.