Norman Epstein

Creeping flow relative to permeable spheres

Abstract The several possible solutions to the problem of creeping flow relative to an isolated permeable sphere are discussed and compared quantitatively. The most satisfactory solutions is that based upon Brinkmans extension of Darcys Law. This solution is generalized, using Happels free-surface model, to cover the practically important problem of flow relative to a swarm of permeable spheres. A physically realistic and mathematically consistent expression for the hydrodynamic resistance experienced by a typical sphere within such a system is derived. This expression is then used to predict the settling rate and the overall permeability of the swarm.

Fine particle deposition in smooth parallel-plate channels

Abstract The effect of electrical double-layer interactions on the rate of deposition of uniform spherical particles from an aqueous suspension in laminar flow through a smooth parallel-plate channel was measured experimentally using a radioactive tracer technique. The results obtained under initial conditions (negligible surface coverages) were compared to those predicted using a previously published theoretical model. It was found that for the deposition of negatively charged silica particles onto a positively charged plastic substrate, especially at intermediate counterion concentrations, good quantitative agreement between theory and experiment was obtained by assuming that the process was mass-transfer controlled. However, for negative particles and negative channel walls, although the theory provided an accurate qualitative description of the experimental results, the measured deposition rates were always much greater than those predicted theoretically. The evidence suggests that the primary cause of this discrepancy is the failure of the model to account for surface heterogeneity, which could result in preferential deposition onto areas of locally favorable potential or geometry. It was also found that, under the conditions of the present experiments, the release of deposited particles from the channel surface was negligible. Thus, the declining rate of accumulation with time observed in most runs could only be attributed to a diminishing rate of particle deposition.

Thinking about Heat Transfer Fouling: A 5 × 5 Matrix

Abstract Fouling of heat transfer surfaces, which leads to high economic penalties and is still dealt with by heat exchanger designers by the crude TEMA approach, is classified into five principal categories. The measurement of thermal fouling is considered critically, and this is followed by a discussion of the successive events, up to five in number, that characterize most fouling situations. The resulting 5×5 matrix of fouling categories and sequential events illustrates the fact that the fundamental fouling problem has now been mainly resolved, at least for liquid-solid interfaces, although it still remains largely unsolved.

Fine particle deposition in laminar flow through parallel-plate and cylindrical channels

Abstract The deposition of colloidal particles from a suspension in steady fully developed laminar flow onto the walls of a channel is rationalized as equivalent to mass transfer in the bulk with a first-order reaction at the walls. The resulting extended Graetz problem is solved for both parallel-plate and cylindrical channels. Through the use of confluent hypergeometric functions combined with asymptotic techniques, an evaluation of the resulting series solutions is made possible which is more accurate than all previous solutions, especially for the deposition of colloids and for cylindrical channels. Simple Leveque-type asymptotic solutions are also obtained for the case of large Peclet numbers, and when the reaction rate constant is infinite, these reduce to the corresponding well-established results for convective diffusion.

Spouted and spout-fluid beds : fundamentals and applications

Preface Common nomenclature 1. Introduction N. Epstein and J. Grace 2. Initiation of spouting X. Bi 3. Empirical and analytical hydrodynamics N. Epstein 4. Computational fluid dynamic modeling of spouted beds X. Bao, W. Du and J. Xu 5. Conical spouted beds M. Olazar, J. Bilbao and M. J. San Jose 6. Hydrodynamics of spout-fluid beds W. Zhong, B. Jin, M. Zhang and R. Xiao 7. Spouted and spout-fluid beds with draft tubes M. H. Morgan, III, H. Littman, Z. B. Grbavcic and J. D. Paccione 8. Particle mixing and segregation G. Rovero and N. Piccinini 9. Heat and mass transfer A. Kmiec and S. Englart 10. Powder-particle spouted beds T. Ishikura and H. Nagashima 11. Drying of particulate solids M. L. Passos, E. F. Costa, Jr and A. S. Mujumdar 12. Drying of solutions, slurries and pastes J. T. Freire, M. C. Ferreira and F. B. Freire 13. Granulation and particle coating S. C. S. Rocha and O. P. Taranto 14. The Wurster coater J. Seville, S. Palmer and A. Ingram 15. Gasification, pyrolysis and combustion A. P. Watkinson and A. Lisboa 16. Spouted bed electrochemical reactors J. W. Evans and V. Jiricny 17. Scale-up, slot-rectangular and multiple spouting J. Grace and C. J. Lim 18. Mechanical spouting T. Szentmarjay, E. Pillai and Judit Toth 19. Catalytic reactors and their modeling G. Rovero and N. Piccinini 20. Liquid and liquid-gas spouting Z. B. Grbavcic, H. Littman and M. H. Morgan, III Index.

The prediction of electrokinetic phenomena within multiparticle systems: II. Sedimentation potential

Abstract A geometric cell model for a concentrated suspension in aqueous electrolyte of identical charged dielectric colloidal spheres was employed in an earlier paper in a theory of electrophoresis and electroosmosis. The same model is used here to study the related phenomenon of the sedimentation of such a suspension. The theory is restricted to small surface potentials (in the linear Debye-Huckel range) and to values of κa ≳ 10, where a is the particle radius and 1/κ is the double layer thickness. The distortion from spherical symmetry in the diffuse layer charge density within a cell (the relaxation effect) due to the sedimentation is described by a simple approximation. A steady state “streaming potential” condition of zero net current flow through a cell and also Henrys condition of zero normal component of current flow at a particle surface are used to calculate the induced dipole moment, the induced sedimentation electric field and the sedimentation velocity. For very dilute suspensions and thin double layers, these calculated quantities tend towards the classic results of Smoluchowski, as required. In the limiting case of a single particle the value obtained for the sedimentation velocity lies between those calculated by Smoluchowski and by Booth. The predictions for the sedimentation velocity in concentrated suspensions are consistent with the rather limited experimental data available in the literature.

Numerical study of steady flow past spheroids

Numerical methods have been used to investigate the steady incompressible flow past oblate and prolate spheroids for Reynolds numbers up to 100. The ratio of minor to major axis of the spheroids investigated were 0·9, 0·5 and 0·2, together with 1·0, which represents the limiting case of a sphere. The pressure distribution and the skin and form drag coefficients were numerically evaluated for the various Reynolds numbers. Streamlines, equi-vorticity lines and equivelocity lines are presented and show in detail the flow characteristics.

Flow regime identification in gas-liquid flow and three-phase fluidized beds

Abstract Experiments were carried out in an 82.6 mm diameter by 2 m high vertical column with air and water as the gas and liquid phases. Three different types of solid particles (1.5 mm glass beads, 4.5 mm glass beads and 1.2 mm steel shot) were employed to investigate the effects of particle size and density on the flow regime transitions. Superficial gas velocities ranged from 0.0018 to 7.7 m/s, while the superficial liquid velocity was varied from 0 to 0.4 m/s. Criteria for determining flow regime transitions, developed in air-water two-phase flow based on bubble frequency, Sauter mean bubble chord length and the time taken by a bubble to pass a given point, were successfully applied to gas-liquid-solid three-phase fluidized beds. These quantities were determined by a two-element conductivity probe located at the centre-line of the column 0.65 m above the distributor. It is shown that churn flow, bridging flow and annular flow occur at high gas velocities in three-phase fluidized beds, as in gas-liquid two-phase flow. Flow regime maps are presented for the air-water two-phase flow and for the three different three-phase systems. In addition, empirical correlations are provided for the flow regime boundaries in the three-phase systems investigated.

HYDRODYNAMICS OF SPOUTED BEDS AT ELEVATED TEMPERATURES

A review of the literature reveals little information on the hydrodynamics of spouted beds at high temperature. Most existing correlations are based upon experiments done at ambient conditions; the...

Hydrodynamics of spout fluid beds

Abstract Experiments were carried out in a half-column incorporating auxiliary flow, introduced through up to five slots along a 60° conical base, in addition to a central flow of air. The column had a diameter of 0.15 m and inlet diameters of either 19 or 25 mm. Three different types of particle were investigated, all with mean particle sizes in the 2 – 4 mm range. Four different flow regimes — fixed bed, spouting with aeration, spout-fluidization and jet in a fluidized bed — were identified and mapped. The minimum total gas flow required for spouting with aeration and for spout-fluidization was always greater than that corresponding to minimum spouting. Gas percolation through the annulus increased by as much as 50% as the proportion of auxiliary flow was increased for a given total gas flow rate. Solids circulation was increased somewhat by addition of auxiliary flow for deep beds, but a decrease occurred for shallow beds. The overall bed pressure drop under minimum spouting with aeration conditions increased linearly with auxiliary flow. On the other hand, the fountain height decreased as the fraction of auxiliary flow was increased for a fixed total gas flow, and increased with auxiliary flow for a fixed central gas flow. The empirical correlation of McNab predicted the average spout diameter well if the sum of the central and auxiliary flows was used in the correlation.