The flow of non-Newtonian solutions through packed beds

The rheological behavior of aqueous solutions of Separan AP-30®, polymethylcellulose, and polyvinylpyrrolidone was studied experimentally. These solutions exhibit non-Newtonian flow behavior in simple shear, and are characterized by one of several 2, 3, or 4 parameter rheological equations. The equations used included the power law, the Ellis model, Spriggs equation, the Herschel-Bulkley equation, and Meter's model. The power law model fits the data for each of the solutions over a limited range of shear rates, whereas the other models, which include either a lower shear rate limiting Newtonian viscosity, and/or an upper shear rate limiting Newtonian viscosity, or a yield stress, fit the data well over a wide range of shear rates from 0.00675 to 1076 sec^?1. The pressure drop-flow rate data for the same aqueous solutions flowing through packed beds were correlated well by the Ergun equation using the various rheological models applied in this work to evaluate a modified fluid viscosity. In each case it was found that the rheological model which best fit the viscometric data also gave the best packed bed friction factor correlation, and that no one model, such as the powerlaw, or the Ellis model, is the best one to use in all cases for all solutions. For polyvinylpyrrolidone solutions large deviations between experimental values of friction factor and those from the Ergun equation occurred for modified Reynolds numbers greater than one. A pseudo viscoelastic parameter was used to improve the friction factor correlation empirically at high Reynolds numbers.     

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.     

A unified model for particulate expansion of fluidised beds and flow in fixed porous media

A model is derived for a fluidised bed that enables its steady state particulate expansion to be predicted as a function of superficial velocity from the initial (packed bed) condition to the final fully expanded (single suspended particle) state. These predictions are in good agreement with the empirical correlations and functional dependencies found by Richardson and Zaki[1,2] over the full range of flow conditions. The derivations incorporat revisions in the form of the pressure drop correlations for flow in porous media that are justified on theoretical and empirical grounds.     

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.     

Reduction of hematite with hydrogen in fixed and fluidised beds

Reduction of hematite with hydrogen has been carried out in fixed and fluidised beds at identical gas flow rates. Influence of gas velocity and particle size has been ascertained. The performances of the two types of bed for the reduction of hematite with hydrogen have been compared. The observed difference in performance is considered to be primarily due to the solids movement characteristics of systems studied. This is also influenced by the bubbling phenomena occurring in fluidised systems.     

A general particle stress equation for fixed and fluidised beds

A general constitutive equation is proposed for the solid particle stress in a fluidised bed. This equation reduces in a straightforward manner to describe the particle stress in a fixed bed, and it implies a Mohr-Coulomb yield criterion for the transition from the fixed-bed to the fluidised-bed state. Experimental evidence is given to show that at incipient fluidisation, the particle stress assumes a form agreeing with that predicted by theory.     

The transition from the fixed to the fluidised state of binary-solid liquid beds

A peculiar phenomenon is observed when a binary-solid bed, in which the particle species possessing the larger minimum fluidization velocity is placed initially on top of the other, is brought from the fixed to the fluidised state. Contrary to the well known behaviour of mono-component beds, a single minimum fluidization velocity is not observed in this case and, more importantly, the fluid pressure drop can turn out to be considerably greater than the total effective weight of the particles. Particle–wall interactions are shown to be responsible for this latter effect. The problem is approached by considering differential horizontal slices of the bed with the simplification suggested by Janssen in 1895 that the ratio of vertical to horizontal solid pressure in a slice is constant—the Janssen constant K. Predictions of the model, which contains no adjustable parameters, are shown to be in excellent agreement with experimental measurements.     

An experimental study of non-newtonian fluid flow through fixed and fluidized beds of non-spherical particles

Extensive measurements of pressure drop in fixed beds, minimum fluidization velocity and expansion characteristics for beds of non-spherical particles are reported in the following ranges of conditions: 10^-3 ≤ Re ≤ 20; 0.66 ≤ n ≤ 1 and 0.41 ≤ ? ≤ 0.75. Based on an analysis of these results, it is illustrated that the existing frameworks originally developed for Newtonian fluid flow through beds of spherical particles are also satisfactory for power law fluid flow through beds of non-spherical particles, provided a volume equivalent diameter modified by a sphericity factor and a modified Reynolds number are used instead of their usual definitions.     

Measurement and simulation of bubbling fluidised beds

The effective control of systems requires the formulation of suitably robust models of their behaviour. The work described in this paper describes the simulation and modelling of the behaviour of a bubbling fluidised bed. A simple system is investigated consisting of a vertical planar bed. The performance of the bed is characterised by measuring the proportion of the bed occupied by the voids associated with bubbles. From these measurements it is possible to evaluate the response of the bed to changes in the gas flow rate into it in the time domain and through transformation into the frequency domain. These techniques allow a simulation of the bed based on the work of Clift and Grace [R. Clift, J. Grace, Coalescence of bubbles in fluidised beds, A.I.Ch.E. Symp. Ser. 67 (116) (1970) 23–33.] to be validated. The simulation can then be used to evaluate a simple but effective physical model of a bubbling fluidised bed which treats it as being primarily a temporary store of gas. The model represents the dynamics of the bed well and in the form of a transfer function which can be used successfully as a basis for controlling the bed.     

Aggregate behaviour of liquid fluidised beds

New and long published experimental observations of the onset of aggregate (bubbling) behaviour in liquid fluidised beds are shown to be in agreement with the predictions of a recently published model of the fluidisation process. For a given liquid, the transition from particulate to aggregate fluidisation depends on both the density and size of the suspended particles: the lower the particle density the larger is the size necessary for a transition to occur: thus for fluidisation by ambient water, lead particles larger than 200 μm and soda glass particles larger than 2000 μm will exhibit aggregate behaviour; below a critical particle density no such transition is possible.     

Mechanism of elutriation from fluidised beds

Elutriation can be used as a convenient method for classification of particles. However, it has been observed that complete elutriation is not possible. Elutriation stops when the concentration of the elutriating component in the bed reaches an equilibrium value. The rate equation for elutriation has been found to be analogous to that of a first order reversible chemical reaction. In this paper two correlations—one for evaluating the equilibrium bed concentration and the other for the elutriation rate constant have been proposed by relating these quantities with the relevant system parameters.     

Prediction of bubble behaviour in fluidised beds based on solid motion and flow structure

It has been demonstrated that the non-intrusive positron emission particle tracking (PEPT) could be a potential technique for observing bubble flow pattern, measuring bubble size and rise velocity in bubbling fluidised beds according to the solid motion in bubble and its wake. The results indicate that the behaviour of air bubbles varies greatly with the bed materials and superficial gas velocity. Three types of bubbling patterns (namely A, B and C) have been reported in this study, in which the pattern C is observed when the polyethylene fluidised bed is operated at the superficial gas velocity (U − U_mf) of 0.25–0.5 m/s and the ratio of bed height to bed diameter is unity. After the comparison of the results measured by the PEPT technique with the values calculated by using a number of empirical correlations, two modified correlations are recommended to calculate the bubble size based on the PEPT data.     

Momentum transfer to Newtonian and non-Newtonian fluids flowing through packed and fluidized beds

This paper deals with the flow behaviour of Newtonian and non-Newtonian fluids flowing through packed and expanded beds. With the help of tube-bundle theory a generalized average shear-stress—shear-rate relationship is derived and found to predict the flow behaviour of power law as well as non-power law fluids. Polyvinyl alcohol solutions in water, a representative of power law fluids, and grease in kerosene, a representative of nonpower law fluids, are studied. The present investigation covers the range of Reynolds number from 10^?3 to 10³. An expression for average shear-stress at minimum fluidization velocity is derived and found to agree with that of our experiment. The generalized frictional Reynolds number is defined and a design chart is also presented for the evaluation of fluidizing velocities.     

Liquid flow through aligned fiber beds

The influence of surface properties on the flow of fluids, including epoxy resin, through aligned glass and other fiber beds has been examined. The observed flow rates were higher than those predicted from the Kozeny-Carman equation, and were influenced by the surface properties of the fluid used. This is attributed to variations in the distribution of porosities and to the presence of air bubbles trapped during the initial wetting of the bed. The implications of these findings to the preparation of composites are discussed.     

Resonant and non-linear behaviour in vibrationally fluidised beds

This paper presents an experimental examination of the behaviour of vibrationally fluidised granular materials. This work was principally focused on examining the resonant behaviour of these systems. The harmonic response of a column of various granular materials (Geldart type A and B) was measured using a small apparatus. These materials displayed several non-linear effects such as; a normalised response that was dependent on excitation level, multiple harmonic components in the response to a single excitation frequency, and odd behaviour in terms of the motion of the emulsion.Two resonant peaks were found for each material. The relative magnitudes of these two peaks were heavily dependent on excitation level, so much so that at high levels of excitation only the higher resonant frequency was present. In each case, some correlation was found between this resonant peak and a prediction based on a “granular-gas” estimate of the speed of sound in the fluidised emulsion. This correlation was further examined by studying the resonant of the system under various levels of partial vacuum. The prediction followed the trend correctly.     

Particle-fluid heat transfer and dispersion in fluidised beds

The dynamic response of a gas fluidised bed has been measured for a range of particle sizes of lead glass ballotini and a range of particle Reynolds numbers. A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain. The coefficient of thermal dispersion, the particle-to-fluid heat transfer coefficient and the intraparticle thermal conductivity have been found for the experimental response by non-linear regression. The coefficient of axial dispersion was found to be large and the particle to fluid heat transfer coefficients agreed with an established correlation for fixed and fluidised beds. The intraparticle thermal conductivity agreed with literature values for lead glass, the estimates showed no trend with flowrate, and the standard deviation of the estimate was three times smaller than the deviation found from similar experiments in fixed beds.