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.     

Effect of dispersant on the rheological properties and slip casting of concentrated sialon precursor suspensions

The ability of Hypermer KD1 to disperse high solids loading reaction sialon suspensions for slip casting has been characterised. It has been found to be a very effective dispersant in organic media of 60-vol.% MEK and 40-vol.% Ethanol, yielding fluid and highly homogeneous suspensions. The effects of added amounts of KD1 have been observed through adsorption data, sedimentation tests and rheology measurements. KD1 imparts low viscosity and stability to the suspension. It has been found that 3-wt.% addition of KD1, based on the weight of reaction sialon powders, results in a very stable and high flowable suspension with near Newtonian flow behavior. Less amounts of dispersant lead to unstable suspensions with obvious shear thinning flow behaviors, while adding excessive dispersant leads to high viscosities, especially at high solids loading. Measuring the pore size distribution of green bodies from different suspensions has proved the effects of dispersant amounts on dispersing the slurries and on slip casting performance.     

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.     

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.     

A mechanism for extrusion instabilities in polymer melts

A mechanism for explaining some of the instabilities observed during the extrusion of polymer melts is further explored. This is based on the combination of non-monotonic slip and elasticity, which permits the existence of periodic solutions in viscometric flows. The time-dependent, incompressible, one-dimensional plane Poiseuille flow of an Oldroyd-B fluid with slip along the wall is studied using a non-monotonic slip equation relating the shear stress to the velocity at the wall. The stability of the steady-state solutions to one-dimensional perturbations at fixed volumetric flow rateis analyzed by means of a linear stability analysis and finite element calculations. Self-sustained periodic oscillations of the pressure gradient are obtained when an unstable steady-state is perturbed, in direct analogy 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     

EXTRUSION AND LUBRICATION FLOWS OF VISCOPLASTIC FLUIDS WITH WALL SLIP

The simplest model flow which approximates the extrusion (shallow screw channels) and lubrication flow is the steady, laminar flow occurring between two infinitely long parallel plates i.e., the generalized plane Couette flow. Here we develop an analytical model of the generalized plane Couette flow of viscoplastic fluids. The deformation and flow behavior of viscoplastic fluids can be realistically represented with the Herschel-Bulkley constitutive equation, which we have utilized as the basis for the development of our analytical model. Furthermore, as also demonstrated here, the deformation behavior of viscoplastic fluids is generally complicated by the presence of wall slip at solid walls, which occurs as a function of the wall shear stress. The wall slip versus the wall shear stress behavior of viscoplastic fluids can be experimentally characterized using viscomelric flows, including steady torsional and capillary flows. Thus determined Navier's wall slip coefficient can then be utilized in modeling of processing flows. In our analytical model of the generalized plane Couette flow of viscoplastic fluids the Navier's wall slip boundary condition was included. This model should be an important engineering tool, which provides design expressions for the extrusion and lubrication flows of viscoplastic fluids, with or without wall slip occurring at the walls. @KEYWORDS:Extrusion, lubrication, flow, viscoplastic, slip.     

Rheology and applications of highly filled polymers: A review of current understanding

This paper reviews current knowledge about the rheology and applications of highly concentrated molten polymers, focusing on hard particles with sizes ranging from several 100 s nm to a few microns. Understanding the rheological properties should assist the formulation and processing of such polymeric materials. The main factors affecting the rheological behavior of these composites are discussed, such as size distribution, nature and shape of the particles, interactions, maximum packing fraction and matrix viscosity. The matrix viscosity is a key parameter that has to be optimized to be low enough to enable the material processing and high enough to improve the dispersion. The size polydispersity of the fillers facilitates higher filling levels and decreases the melt mixture viscosity for a given filler content. The different types of interactions (viz. particle-particle, particle-matrix) are described to interpret the phenomena arising during processing better. On the other hand, mixing is of particular importance to reach high-quality dispersion and distribution of the particles in the matrix in order to obtain a homogenous mixture and desirable properties. The mixing methods and tools to characterize the degree of mixing are reviewed. The use of organic dispersants is generally necessary to improve and control the dispersion degree and flow properties. Mathematical models relating the viscosity as a function of the filler content for unimodal and bimodal highly filled suspensions are summarized. Constraints and flow instabilities often lead to non-linear rheological behavior such as wall slip, particle-binder segregation, swelling and surface instabilities phenomena; these are discussed. Finally, the latest applications for highly filled systems (such as solid propellants, flame retardancy, magnetic materials, ceramic materials, batteries, etc.) are presented as a source of inspiration for industrial improvements.     

Couette grain flow experiments: The effects of the coefficient of restitution, global solid fraction, and materials

Granular flows are complex flows of solid granular material which are being studied in several industries. However, it has been a challenge to understand them because of their non-linear and multiphase behavior. The present experimental work investigates granular flows undergoing shear, by specifically studying the interaction between rough surfaces and granular flows when the global solid fraction and the material comprising the rough shearing surface are varied. A two-dimensional annular shear cell, with a stationary outer ring and inner driving wheel, and digital particle tracking velocimetry (DPTV) technique were used to obtain local granular flow properties such as velocity, local solid fraction, granular temperature, and slip. A customized particle drop test apparatus was built to experimentally determine the coefficient of restitution (COR) between the granular and surface materials using high-speed photography. Results showed that wheel surface materials that produce higher COR values exhibit higher velocity and granular temperature values near the wheel, and lower slip velocities. The local solid fraction appears inversely related to the COR values. The global solid fraction seemed to correspond with velocity and granular temperature, while displaying an inverse relationship to slip. Results also showed an initial decrease in the kinetic energy of the flow as the global solid fraction increased, due to the formation of a distinct contact region. This was followed by a rise in kinetic energy as the global solid fraction continued to increase, based on the increase of particles present in the kinetic region of the flow.     

Rheological behavior of two- and three-phase fiber suspensions

The rheology of two polyamide 6.6 systems filled with long glass fibers, as well as at of a three-phase polyamide 6.6-glass fiber-gas bubble system, was studied using capillary rheometry, To investigate the influence of fiber concentration, the shear and extensional viscosities were determined for both 30 and 40 vol% fiber filled suspensions as well as for the base polymer. Comparison revealed a modest increase in both the shear and extensional viscosities with increased fiber fraction. The shear viscosities, η_s, of both suspensions are shown to be close to one order of magnitude greater than the base matrix fluid viscosity, η. However, the extensional viscosities, η_E, of the suspensions are determined to be approximately four orders of magnitude greater than the shear viscosity of the matrix fluid for strain rates from 10⁰ s⁻¹ to 10² s⁻¹. The addition of a gas bubble phase to the neat polymer and polymer-fiber suspensions was accomplished through the decomposition of various percentages of an azodicarbonamide blowing agent. The presence gas bubbles resulted in reduced shear and extensional viscosities for both the neat and fiber-filled polyamide with greater reductions observed for the neat polyamide. Greater viscosity reductions were observed as the blowing agent centration was increased.     

Flow Channel Boundaries in Silos

The critical slip planes at the silo filling state are compared with the flow channel boundary during silo discharge for semi‐mass flows. The static critical slip planes are determined by using the dynamic programming method based on the stress field of granular solids stored in silos at the filling state. The flow channel boundary is estimated through the finite element analysis of the silo discharge. The results indicate that the critical slip line lies above the flow channel boundary. This characteristic can be attributed to the changeover of major principal stress directions of granular solids from the silo filling to the silo discharge. The analysis demonstrates that the silo wall friction tends to lift up the critical slip plane and flow boundary. A simple correlation is developed between the positions of critical slip planes and flow boundaries and is experimentally verified.     

Numerical study of flow at a liquid-porous medium interface

The problem of the two-dimensional creeping flow of a viscous incompressible liquid in a flat channel partially filled with a model fibrous porous medium that is represented by a regular system of square cylinders (prisms) located across the flow is solved. Two types of flows are considered: a shear flow due to the motion of the upper wall of the channel and a gradient flow due to the presence of a pressure drop along the channel. The hydrodynamic microscopic fields of velocity are numerically found. The macroparameters such as the rate of filtration, the permeability of a system of cylinders, the flow rate of the liquid through the channel, tangential stresses on the upper wall of the channel and the porous boundary, and a slip coefficient, the use of which in the Saffman slip boundary condition makes it possible to considerably simplify the solution of the original problem, are obtained as a result of averaging.     

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     

Analysis on the apparent slip and depleted layer of polymer flow in narrow-bore capillaries

Polymer solutions flowing through small-diameter capillaries of which length scale is much larger than that of polymers were experimentally demonstrated to have the enhanced flow rate as compared to in bulk flow. Thisapparent slip phenomenon was analyzed by obtaining theslip velocity and concentrationdepleted layer thickness. Hydrolyzed polyacrylamide (HPAM) of highly flexible polymer and Xanthan of rigid rodlike polymer were made to flow through stainless steel capillaries having the diameter range of about 100 to 250 μm. The results showed that both slip velocity and depleted layer thickness decreased markedly with increasing polymer concentration. This behavior can be interpreted as being due to the reduction of diffusion coefficient and flexibility of polymer chains as the concentration is increased. The depleted layer thickness of HPAM was much larger than the polymeric length scale and was shown to increase with increasing wall shear stress. This is considered as an evidence of thestress-induced diffusion of polymer chains being a dominant factor for the apparent slip of flexible polymer solution. On the other hand, the depleted layer thickness of Xanthan solution was almost constant with the wall shear stress, which can not be explained by the stress-induced diffusion mechanism alone.     

Gas flow regime changes in a bubble column filled with a fibre suspension

Gas flow characteristics in opaque fibre suspensions have been captured on film using a stop‐motion X‐ray imaging technique called flash X‐ray radiography (FXR). Gas flows in a bubble column filled with various cellulose fibre suspensions from 0% (an air–water system) to 5% by mass have been observed. The gas flow regime changes from vortical to churn‐turbulent as the fibre concentration increases for a fixed superficial gas velocity. Two new gas flow regimes, identified as surge churn‐turbulent and discrete channel flow, have also been recorded at high fibre concentrations.     

水煤浆的滑移速度修正模型

在煤水混合物的流动过程中存在着滑移效应,但是在用传统的Mooney方法和Jastr- zebski方法对高浓度水煤浆的滑移特性进行分析时,没能得出一致的结果。笔者基于前人对滑移的假设,通过多管径管流试验。研究了高浓度水煤浆管内流动的滑移现象,分析了滑移引起的附加流量对总流量的影响,提出了选取最佳滑移指数确定水煤浆真实流变特性的本构模型和方程。指出高浓度浆态非牛顿流体存在屈服应力。     

Highly swirling transient flows in spray dryers and consequent effect on modeling of particle deposition

Cotton turf and hotwire measurements were used to experimentally assess the highly swirling flow characteristics in a spray dryer fitted with a rotary disc atomizer. The numerical simulation captured key features of the flow field. Analysis revealed that rapid rotation of an atomizing disc tends to centrifugally split the central inlet jet. The flow field exhibited significant long time-scale transient behaviour. However, this centrifugally split jet resulted in a balanced upward recirculation region in the chamber as expected by the jet-feedback mechanism. Detailed analysis using a ‘transient air-steady particle’ approach revealed that this approach is applicable for such highly swirling transient flows as well. However, caution should be exercised when interpreting the deposition results, particularly in regions of low particle velocities. This is anticipated be an important consideration in future attempts to simulate the predominantly transient flows in spray dryers.     

Rheology of concentrated suspensions

The dependence of the viscosities of highly concentrated suspensions on solids concentrations and particle size distributions is investigated by using an orifice viscometer. Based on the extensive amount of data on pertinent systems, an empirical equation which correlates the relative viscosities of suspensions (or relative moduli of filled polymeric materials) as a function of solids concentrations and particle size distributions is proposed. The equation has a constant which characterizes size distributions of spherical particles and can be determined experimentally without measuring viscosities. For uniform-size spherical particles, it reduces to the well-known Einstein equation at dilute solids concentrations.     

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