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     

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.     

Effect of the surface roughness and construction material on wall slip in the flow of concentrated suspensions

Recent studies on polyethylene, elastomers, and thermoplastics have revealed that the construction material and surface roughness are two important factors affecting wall slip. In this study, to determine the true rheological behavior of model concentrated suspensions, a multiple‐gap separation method was used in a parallel disk rheometer. The model suspensions studied were poly (methyl methacrylate) particles with an average particle size of 121.2 μm in hydroxyl‐terminated polybutadiene. The aim of this study was to investigate the effect of disk R_a in the range of 0.49–1.51 μm and disk construction material on the wall slip and the true viscosity of the model concentrated suspensions. The wall slip velocity and the viscosity were found to be independent of R_a for particle size‐to‐disk R_a ratios of 80–247. Also, the true viscosity was found not to be affected by the rheometer surface construction material. Glass surfaces resulted in the highest slip velocity, whereas aluminum surfaces resulted in the lowest slip velocity. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3341–3347, 2007     

Retention of Liquid by Solids in Suspensions and Sediments

Abstract

The effects of associated immobile liquid on the settling behavior of particles in solid-liquid suspensions are investigated. The effects are studied with respect to such sedimentation parameters as suspension porosity ?, final sediment volume fraction u_s, internal void fraction of the flow unit u_i, Steinours parameter A, and McKay's packing factory which corrects for the effective volume and density of the flow units in a sedimenting suspension. It is shown that the degree of liquid association with the settling particles is a function of their physicochemical characteristics. Suspensions containing clays and carbonates, owing to their ionic nature and loose packing behavior, absorb large amounts of liquids and result in larger settled sediments of a compressible nature. On the other hand, systems like glass beads-liquid suspensions absorb little associated liquid and virtually result in noncompressible settled sediments due to their rigid spherical shapes and close packing. The addition of hydrocolloids (such as natural gums) provides ionic stability to suspensions by giving them low cmpressibility and low values of u_s, u_i, A, and p.     

Concentrated suspension-based additive manufacturing – viscosity,packing density,and segregation

This paper describes the influence of particle size distribution (PSD) of refractory silica on the suspension viscosity, packing density, and segregation in layers solidified by ceramic stereolithography (CerSLA). Using bimodal PSD displays most significant decrease of suspension viscosity than suspension made of mono-modal PSD. Given the Krieger-Dougherty model and packing density experiment, the lower viscosity results from the higher maximum volume fraction, φ_m, reached through the closely packed particles. Furthermore, from the differential sedimentation of coarser or denser particles in suspensions, particle size segregation in layers is detected. To determine the distribution of particle size within each layer, a linear intercept method is used, which demonstrates the vertical changes in PSD. Mono–modal PSD case show severe segregations in solidified layers in which the population of larger or denser particles is greater near the bottom. However, much less segregation occurs with bimodal PSD due to suppressed segregation.     

Rheological behavior and microstructure of bimodal suspensions of core‐shell structured swollen particles

The rheological behavior and microstructure of bimodal suspensions of core‐shell structured swollen particles have been examined with changing volume ratio of two different sized particles. As the volume fraction of large particles increases, the viscosity, degree of shear‐thinning, and the critical shear stress σ_c decreases, while the interparticle distance ξ of the microstructure increases. The suspensions exhibit single mode rheological behavior and have a single diffraction peak in the SAXS profiles. These results suggest that the bimodal suspensions of the core‐shell structured swollen particles behave likely to unimodal suspensions of hard spheres with alloy like single mode microstructure composed of hypothetical intermediate size particle. The relationship between σ_c and ξ can be represented as σ_c = 3kT/4πξ³, which corresponds to the dynamics of the Brownian hard sphere model with ξ being the particle diameter. These findings indicate that the shear‐thinning of the suspensions can be attributed to dynamical competition between the thermal motion and the hydrodynamic motion under shear flow and that the mechanism can be applied to bimodal suspensions of the swollen particles as well as unimodal suspensions of hard spheres. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 102: 2212–2217, 2006     

Effect of air flowrate on particle velocity profile in a circulating fluidized bed

The research was conducted in a cold flow circulating fluidized bed (CFB). The diameter and height of riser are 5 and 200 cm, respectively. The objective is to study effect of gas velocity on hydrodynamic of glass beads having mean diameter of 547 micron and density of 2,400 kg/m³. The measurement of particle velocity profile was achieved by using a high-speed camera and an image processing software. A probe of 0.5 cm in diameter was inserted into the riser at the height of 110 cm from gas distributor and was set at 3 positions along the radius of the riser; 0, 0.6, and 1.8 cm from center. Transport velocity (U _tr ), core-annulus velocity (V _CA ) and minimum pneumatic velocity (V _mp ) were employed in determining solid flow pattern in the riser. It was observed that the flow regimes changed from fast fluidization to core-annulus and to homogeneous dilute bed when the gas velocities increased from 7, 8 and 9 m/s, respectively. The results from high-speed camera showed that glass beads velocity existed a maximum value at the center of the riser and gradually decreased toward the wall for all three gas velocities. It was also found that most of solid traveled upward in the core of the riser, however, solid traveled downward was identified at the wall layer.     

Influence of Polymeric Suspension Characteristics on the Particle Coating in a Spouted Bed

Abstract

The influence of the coating suspensions and particle properties on the coating process in a conventional spouted bed is presented. Glass beads were coated at fixed operating conditions with different formulations of aqueous polymeric coating suspensions in a spouted bed of laboratory scale. The wettability of the solids by the liquid was quantified by the contact angle and surface tension of the coating suspensions. The coating efficiency and particle growth were correlated with the adhesion of the coating suspension to the solid particle, which is a function of the solids and liquid characteristics. The physical properties of the coated particles—particle mean diameter, sphericity, bulk, absolute and apparent densities, porosity and flow velocity—were determined and compared to the properties of uncoated particles.     

The influence of suspended particles on the mass transfer at a rotating disc electrode. Non-conducting particles

The influence of suspended SiC particles on the mass transfer at an RDE (rotating-disc electrode) was investigated for the reduction of K₃Fe(CN)₆ and ZnO in alkaline electrolyte. A model for the increased mass transfer is developed, based on the decrease of the diffusion layer thickness by rotation of the particles in this layer. In experiments with different volume fractions of suspensions a critical value in the rotation speed and in volume fraction is found. The influences of hydrodynamic conditions, gravity, particle size and adhesion between particles and electrode were studied to investigate the origin of both critical values.     

Aqueous and Nonaqueous Colloidal Processing of Difficult‐to‐Densify Ceramics: Suspension Rheology and Particle Packing

Aqueous and nonaqueous colloidal processing of zirconium diboride (ZrB₂) and boron carbide (B₄C) has been investigated. The aqueous and nonaqueous ZrB₂ and B₄C suspension formulations have been optimized. The suspensions were cast into green bodies using slip casting. The correlation between the state of dispersion with the rheological properties of the suspensions and the resulting packing density was observed in both aqueous and nonaqueous processing. The attractive interactions between powder particles in water were difficult to overcome with electrical double layer or electrosteric repulsion. Reasonably low viscosity aqueous ZrB₂ suspensions up to 45 vol% solids could be prepared. It was not possible to produce low viscosity (viscosity below 1 Pa·s at shear rate of 100 s^?1) aqueous B₄C suspensions with solid content above 30 vol%. Slip casting of the weakly aggregated ZrB₂ suspensions resulted in low packing densities (~55% relative density) of the green bodies. On the other hand, dispersion of powder particles in nonaqueous media (cyclohexane and dodecane) enabled suspensions with lower viscosities and a higher maximum solid concentration (up to 50 vol%) to be prepared. The well‐dispersed nonaqueous suspensions promoted an efficient particle packing, resulting in higher green densities (64% and 62% relative density for ZrB₂ and B₄C, respectively) compared to aqueous processing. The significantly high green densities are promising to allow densification of the materials at lower sintering temperature.     

Evaporation of Distilled Water in a Fluidized Bed of Various Types of Fluidizing Particles Under Reduced Pressure

An objective of this study is to continuously obtain dispersed, dry, fine powders from a dilute suspension of heat-sensitive materials at a low temperature and high drying rate. A fluidized bed under reduced pressure was used in this study and, as a first step, only distilled water (without solid powders) was used as a sample. Drying characteristics were examined for various types of fluidizing particles. The diameter of fluidizing particle varied for inert particles (glass beads). Three kinds of hygroscopic porous particles (silica gel beads; 3A, 4B, and 5D) were also used as fluidizing particles. Under reduced pressures, the maximum drying rate was found to be higher than that at atmospheric pressure, while the bed temperature became lower with an increase in the maximum drying rate (i.e., drying at lower temperature with a higher drying rate is possible under reduced pressures. As diameter of the fluidizing particle was increased, the maximum drying rate became higher, although the amount of gas required for fluidization also increased. The maximum drying rates for silica gel beads were found to be almost equal to those of glass beads, with the exception of 3A silica gel beads (having a smaller pore diameter). The bed temperature was lower for silica gel beads compared to glass beads at the same maximum drying rate (i.e., silica gel beads (hygroscopic porous particles) are superior to glass beads (inert particles) with regard to drying at low temperatures at a high drying rate).     

Rheology of Concentrated AP/HTPB Suspensions Prepared at the Upper Limit of AP Content

Due to the requirements for the preparation of an ammonium perchlorate (AP)/hydroxy‐terminated polybutadiene (HTPB) based composite propellant, an upper limit content of AP applicable in the propellant, φ_max (wt%), exists. The rheology of concentrated AP/HTPB suspensions prepared at φ_max is investigated in this study. The relative viscosity, η_rφ(‐), of the suspensions prepared at φ_max is almost constant at approximately 200. For the suspensions prepared at φ_max, the HTPB layer thickness, H_φp (µm), on the AP particle, calculated from the specific surface area measured by the air‐permeability method, is closely related to the void fraction, ε_max(‐), for the loose packing of the AP powder. H_φp decreases with increasing ε_max. By reversal conclusion it was found that the relative viscosity of the suspension, of which the HTPB layer thickness is H_φp, will accordingly be η_rφ.     

Measurements by MRI of the settling and packing of solid particles from aqueous suspensions

This study extends the application of existing magnetic resonance imaging methods to measure the settling of solid particles from aqueous suspensions. The acquisition of one‐dimensional multiecho projections allowed the direct measurement of initial magnetizations (M₀), from which solid volume fractions along the sedimentation column were inferred. For polystyrene beads, it was found that monoexponential curves accurately fitted the transverse relaxation decays. In contrast, for the other four solids investigated (activated carbon, talc, calcium carbonate, and glass beads), the single exponential model did not suffice and additional terms in the fitting function significantly improved the calculation of solid concentrations. Additional information about particle sizes was obtained by comparing volume fractions with the spin–spin relaxation times of the hydrogen protons as a function of the vertical height through the sedimenting suspensions of activated carbon and polystyrene beads. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

A generalized model to predict the viscosity of solutions with suspended particles. IV. Determination of optimum particle-by-particle volume fractions

A new approach has been introduced to establish the optimum composition for all particles within a mixture or suspension to achieve the optimum packing fraction, φ_n, and/or the minimum viscosity, η. The derivation to obtain the optimum particle volume fraction assumed that a previously developed optimum composition for binary particles applied to any two particle volumes V_i and V_j in the mixture. The composition of the maximum packing fraction for a mixture of more than two particles was then assumed to be calculable from the optimized relationship of each separate binary pair of particle volumes V_i and V_i in the mixture. This derived equation was successfully shown to predict the optimum particle-to-particle composition of McGeary's experimentally measured binary, tertiary, and quaternary mixtures. The difference between the calculated and measured volume fractions was no greater than 3.85% and, in most instances, was significantly less than 3.85%. The maximum packing fractions, φ_n, determined experimentally by McGeary, were also successfully predicted to better than 3.26%. Theoretical particle-to-particle volume fractions evaluated for an example pressure-agglomerated latex appeared to predict the particle-size distribution only within a narrow range of particle sizes. However, when the theoretical and experimental results were evaluated as a function of the number of particles for each particle diameter, it was apparent that the agglomerated distribution closely approximated the theoretical optimum distribution above 600 Å. Agreement with theory below 600 Å was unsatisfactory. The decrease in viscosity of the example agglomerated latex appeared to have been enhanced as the optimum theoretical particle-size distribution was approached. © 1994 John Wiley & Sons, Inc.     

Drift flux modelling of CFB risers

Solids inventory is a critical parameter for catalytic reactors: it impacts the geometrical configuration of the reactor, compressor/blower requirements, and the overall economics of the process. Although significant advances have been made for characterizing the hydrodynamic regimes in gas–solid fluidization, empirical relationships for predicting the solids inventory in risers are largely in the developmental stages. Empirical models are either based on the slip velocity, slip factor or the Richardson–Zaki bed expansion relationship. We propose the drift flux model, commonly for gas–liquid hydrodynamic modelling. The drift flux model accounts for radial variations in the axial velocity profile and void fraction with a distribution parameter, C₀, and the relative velocity between the phases with the drift velocity, U_2j: In high density risers, the distribution parameter varies between 1.03 and 1.12. The drift velocity is a function of the product of the particle terminal velocity and varies with solids hold‐up.     

Layer inversion and mixing of binary solids in two- and three-phase fluidized beds

Water fluidization in a 210 mm diameter semi-cylindrical acrylic column of a binary solids mixture of 3.2 mm polymer beads (ρ_s=1280 kg/m³) and 0.385 mm glass beads (ρ_s=2500 kg/m³) at superficial liquid velocities from 18.1 to 43.1 mm/s is shown to generate layer inversion at a superficial liquid velocity, U_L, of 33.1 mm/s. Introduction of air with a superficial velocity, U_g, of 1.92 mm/s yielded a layer inversion velocity at U_L=30.4 mm/s. The latter is explainable if it is assumed that the determinant of layer inversion is the interstitial liquid velocity and that therefore the main function of the gas in this respect is to occupy space.Mixing of the binary solids, as quantified by a mixing index applied to measured particle compositions at different levels of the fluidized bed, is shown to be greatest at the layer inversion velocity for liquid fluidization and, in general, to increase as co-current gas flow increases at a fixed value of U_L.     

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.     

Slot coating flows of non‐colloidal particle suspensions

Slot coating is used in the manufacturing of functional films, which rely on specific particle microstructure to achieve the desired performance. Final structure on the coated film is strongly dependent on the suspension flow during the deposition of the coating liquid and on the subsequent drying process. Fundamental understanding on how particles are distributed in the coated layer enables optimization of the process and quality of the produced films. The complex coating flow leads to shear‐induced particle migration and non‐uniform particle distribution. We study slot coating flow of non‐colloidal suspensions by solving the mass and momentum conservation equations coupled with a particle transport equation using the Galerkin/Finite element method. The results show that particle distribution in the coating bead and in the coated layer is non‐uniform and is strongly dependent on the imposed flow rate (wet thickness). © 2016 American Institute of Chemical Engineers AIChE J, 63: 1122–1131, 2017     

Role of the effective electrical conductivity of nanosuspensions in the generation of TiO2 agglomerates with electrospray

Suspensions with varying volume fraction of TiO₂ nanoparticles and ionic strength were electrosprayed to obtain agglomerates of different characteristics, which were then deposited to produce films with tailored morphology, thickness, and porosity. The role of the nanoparticle volume fraction in both the effective electrical conductivity of TiO₂ nanosuspensions and the control of the size of agglomerates produced by electrospray was investigated. A simple modified equation for the effective electrical conductivity of TiO₂ nanoparticle suspensions was derived. The equation, which accounted for nanoparticles' diffuse ionic layer and their agglomeration in a liquid, showed that the effective electrical conductivity is not only a function of the liquid and particle conductivities, and the particle volume fraction but also a function of both the thickness of the adsorbed ionic layer on the particles and the particle size. Gradual increase of particle volume fraction resulted in an increase in the suspension's effective electrical conductivity, when the initial liquid conductivity was in the range of 10^?4–10^?3 S m^?1. When the liquid conductivity was in the range of 10^?3–10^?2 S m^?1; however, addition of particles did not have any significant effect on the effective electrical conductivity. Control over the size of the TiO₂ nanoparticle agglomerates was achieved by electrospraying suspensions with liquid electrical conductivity of the order of 10^?3 S m^?1 and by varying the particle volume fraction. Electrospray deposition of suspensions with TiO₂ volume fraction=0.04% resulted in a more compact film with lower porosity and showed better water-splitting performance.     

The effect of bed materials on the solid/bubble motion in a fluidised bed

Gas fluidisation provides good mixing and contact of the gas and particle phases as well as good heat transfer. These attractive features are achieved by the high degree of bubble-induced particle circulation within the bed. Bubble and particle motion vary with bed materials and operating conditions, as investigated in the present study, by the use of the non-intrusive positron emission particle tracking (PEPT) technique. The selected materials were spherical polyethylene and glass particles.The data obtained by the PEPT technique are used to determine the particle velocities and circulation pattern. Bubble rise velocities and associated sizes can be inferred from the particle velocity data, since particles travel upwards mostly in the bubble wake. The results indicate that the flow structure and gas/solid motion within the fluidised beds were significantly different, even at the same value of the excess gas velocity, U-U_mf. The solid circulation pattern within the beds differ: if for glass beads, a typical UCDW-pattern existed (upwards in the centre of the bed, downwards near the wall), the pattern in the polyethylene bed is more complex combining a small zone of UWDC movement near the distributor and a typical UCDW-pattern higher up the bed. Transformed data demonstrate that at the same value of excess gas velocity, U-U_mf, the air bubbles in the polyethylene fluidised bed were smaller and rose more slowly than in the fluidised bed of glass beads, thus yielding a longer bubble residence time and improved gas/solid contact. For polyethylene beads, the size and rise velocity of air bubbles did not increase monotonically with vertical position in the bed as would be predicted by known empirical correlations, which however provide a fair fit for the glass beads data. Bubble sizes and solid circulation patterns are important parameters in the design of a fluidised bed reactor, and vary with the bed material used.