Ivan Machač

Flow of non-Newtonian fluids in fixed and fluidised beds

Abstract An attempt has been made to reconcile and to critically analyze the voluminous literature available on the flow of rheologically complex fluids through unconsolidated fixed beds and fluidised beds. In particular, consideration is given to the prediction of macro-scale phenomena of flow regimes, pressure drop in fixed and fluidised beds, minimum fluidisation velocity, dispersion and liquid–solid mass transfer. Available scant results seem to suggest that flow patterns qualitatively similar to that observed for Newtonian fluids, can be expected for the flow of purely viscous non-Newtonian fluids. A Reynolds number based on the effective pore size and pore velocity is seen to be a convenient parameter for the delineation of these flow regimes. Out of the four approaches available, the generalisation of the capillary model, due to Comiti and Renaud ( Chem. Engng. Sci. 44 (1989) 1539–1545), appears to be the best for the estimation of the pressure drop through fixed beds. This method requires the flow rate – pressure drop data for the flow of a Newtonian fluid, such as air or water, through the same bed to evaluate the two key parameters, namely, the tortuosity and the dynamic surface area. While this approach can accommodate non-spherical particle shape and the wall effects and encompasses all possible flow regimes, it is limited to the situations where the polymer–wall interactions are negligible. Similarly, based on a combination of the capillary and drag models, satisfactory expressions have been identified for the prediction of the minimum fluidising velocity and velocity-voidage behaviour of uniformly expanded fluidised beds for power-law liquids and beds of spherical particles. Little is known about the effect of particle shape and column walls on these parameters. Even less work has been reported on dispersion and liquid–solid mass transfer in packed and fluidised beds, and no theoretical or experimental results seem to be available on heat transfer in these systems. Therefore, the expressions for the prediction of Peclet and Sherwood numbers presented herein must be regarded as somewhat tentative at this stage. Finally, little definitive and quantitative information is available on the role of viscoelasticity and of the effects arising from polymer/wall interactions, polymer retention, etc.

Flow of generalized newtonian liquids through fixed beds of nonspherical particles

Abstract The flow of generalized Newtonian liquids through a random fixed bed of particles has been investigated and a universal method of calculation of the creeping flow was suggested. The usefulness of this method has been verified experimentally for the flow of power law, Ellis and Sutterby liquids through fixed beds of different nonspherical particles.

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

Abstract 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.

Fall of non-spherical particles in a Carreau model liquid

Abstract The free fall of short cylinders and rectangular prisms through polymer solutions of different measure of shear-thinning and elasticity has been investigated experimentally in the creeping flow region. The influence of the particle shape and the rheological behaviour of the liquid on the particle terminal velocity have been evaluated. A procedure based on the modification of the Stokes relationship for a Carreau model fluid have been proposed for the prediction of the terminal falling velocity of non-spherical particles. The suitability of the proposed procedure has been documented by good agreement between experimental and calculated terminal falling velocity data.

Terminal falling velocity of spherical particles moving through a Carreau model fluid

Abstract In this paper, the method, which is based on the results of numerical solution of Hills variational principles, is presented for the prediction of the terminal falling velocity of spherical particles moving slowly through a Carreau viscosity model fluid. The suitability of this method is documented by the comparison of calculated data of terminal falling velocity with experimental data measured for the fall of glass, steel, and lead balls through polymer solutions characterised by different measure of shear-thinning and elasticity.

Non-Newtonian fluidization of spherical-particle beds

Abstract Fluidization of spherical-particle beds with viscoelastic shear thinning polymer solutions was experimentally investigated in creeping- and transient-flow regions. The results of measurements show that the course of bed expansion depends on the kind and degree of non-Newtonian anomaly, on the flow region, and on the apparatus wall effect. The limited bed expansion observed during fluidization in the creeping-flow region weakened with the increasing Reynolds number and vanished when a critical value of Reynolds number was exceeded. Empirical equations based on the Carreau viscosity model were suggested for the prediction of minimum fluidization velocity and for bed expansion in both creeping- and transient-flow regions.

Wall effects on terminal falling velocity of spherical particles moving in a Carreau model fluid

Experimental verification of our previous numerical simulation of wall effects on the terminal falling velocity of spherical particles moving slowly along the axis of a cylindrical vessel filled with a Carreau model fluid is presented. Dependences of the wall correction factor FW on the sphere to tube ratio d/D and on the dimensionless Carreau model parameters m, Λ, and ηr were obtained using a finite element method. Calculated data of the wall correction factor were compared with the results of our new falling sphere experiments. The experiments were carried out in six types of cylindrical Perspex columns (16 mm, 21 mm, 26 mm, 34 mm, 40 mm, and 90 mm in diameter) filled with aqueous solutions of polymers exhibiting different degrees of shear thinning and elasticity. Seventeen types of spherical particles (1–8 mm in diameter) made of glass, ceramics, steel, lead, and tungsten carbide were used for the drop tests. Measurements of the liquid flow curves, primary normal stress differences, oscillatory, creep and recovery, stress relaxation, and stress growth tests were carried out on the rheometer Haake MARS (Thermo Scientific). A good agreement between numerically and experimentally obtained FW data was found.

Flow of non-Newtonian fluids through fixed beds of particles: Comparison of two models

Two models based on modifications of the capillary representation of a particle bed are proposed in order to evaluate the pressure gradient for the flow of non-Newtonian purely viscous fluids through fixed beds. In the first model, the ideas of flow around particles are considered simultaneously and the bed factor is used as a dynamic characteristic of the bed. In the second one, the tortuosity factor and dynamic specific area are used as bed structure parameters. The validity and accuracy of the models have been tested using an extensive set of experimental data concerning fixed beds of spherical and various shaped non spherical particles. In these experiments, 19 particle-fluid systems were investigated in the range of Reynolds number including creeping and transition flow regimes; power-law fluid behaviour index was ranged between 0.27 and 1. The mean deviation between pressure drop model predictions and the whole set of experimental data is less than 10% for both models presented. The models are efficient even when important wall effect exists.

Druckverlust bei der strömung einer flüssigkeit durch ein rohr mit schraubeneinbauten

Zusammenfassung Der Einfluss zweier Typen von Schraubeneinbauten in einem Rohr mit kreisrundem Querschnitt auf den Druckverlust wurde bei der Stromung einer Newtonscher Flussigkeit im Reynoldszahlbereich 15 ≲ Re ≲ 5600 untersucht. Die Forschungsergebnisse sind in Form von Ahnlichkeitsgleichungen dargestellt, die die Abhangigkeit des Widerstandsbeiwertes von den Stromungsbedingungen sowie von den physikalischen und geometrischen Eigenschaften beinhalten. Die Gleichungen sind in graphischer und analytischer Form angegeben.

Fluidization of spherical particle beds with non-Newtonian fluids in columns of rectangular cross-section

The results of experimental investigation of expansion of spherical particle beds fluidized with shear-thinning and simultaneously elastic polymer solutions in rectangular (two-dimensional) columns and creeping-flow region are presented.