A GENERALIZED BUBBLE RISE VELOCITY CORRELATION

A generalized bubble rise velocity correlation is developed to cover the range of conditions:

liquid-phase density = 45.1 to 74.7 lb/ft³,

liquid-phase viscosity = 0.233 to 59 cP., and

interfacial tension = 15 to 72 dynes/cm

The gas-phase is air and the bubble size ranged from 1.2 to 15 mm. The developed correlation is based upon new dimensionless groups which contain the parameters affecting bubble rise velocity as well as their interaction, The correlation is independent of flow regimes and applicable for Reynolds numbers from 0.1 to 10⁴. It is in good agreement with work appearing in the literature.     

AN ANALYSIS OF CELLULAR FLOW OBSERVED ON THE INTERFACE OF A PARTIALLY FORMED DROPLET†

In [16], during an experiment designed to model the internal circulation of a forming droplet, secondary surface flows were observed on the droplet interface.

After summarizing the experimental results of [16], we present one possible mechanism, based on the surface surfactant mass transport equation of Levich and the surface stress-strain boundary conditions at a free surface, that provides a good qualitative explanation of the origins and the nature of the secondary motion observed in [16]. The critical hypotheses in this mechanism are that the normal component of ihe vorticity at the free surface is determined primarily by the components of the velocity field tangential to the level lines of the surface surfactant density, near the maxima and minima of that density function and that the normal component of the fluid stress does not vanish at such points.

The consequent analysis of the mass transport equation in the interface shows that the resulting surface motion may be viewed as arising from a resonance phenomenon analogous to the forced vibrations of a spring at resonance.

The effects of adsorbtion-desorbtion and surface dilational viscosity may be incorporated in this mechanism. A method for the experimental measurement of surface dilational viscosities is proposed.     

DRAG AND MASS TRANSFER IN SLOW NON-NEWTONIAN FLOWS OVER AN ENSEMBLE OF NEWTONIAN SPHERICAL DROPS OR BUBBLES

An approximate solution for the slow motion of an ensemble of spherical drops through a power law fluid is obtained using Happel's free-surface cell model. It is shown that the drag coefficient decreases with decrease of the flow index and that this reduction is more significant at low voidage and large viscosity ratio parameter. The effect of the pseudoplastic anomaly on the mass transfer rate is more pronounced at low voidage for large values of viscosity ratio parameter, unlike the case of a single spherical drop

The present analysis covers the whole range of values of viscosity ratio parameter from infinity (an assemblage of solid spheres) to zero (a swarm of bubbles) and reduces to the solutions for those cases already known

The results for the motion of an ensemble of spherical drops also provide the basis for proposing a tentative expression for the expansion of liquid-liquid fluidized bed at low Reynolds number.     

THE ROLE OF GAS DISTRIBUTION IN FLUIDIZED BED CHEMICAL REACTOR DESIGN†

The design of fluid bed gas distributors may have a marked influence on the performance of a fluid bed reactor. The primary physical reason for this influence is that the distributor design influences the hydrodynamics and thus the gas/solid contacting pattern in the fluidized bed.

In the paper presented here the influence of distributor design on mass transfer and chemical reaction has been investigated systematically in fluid bed reactors with diameters of 0.2 and 1.0 meter. Coefficients of mass transfer between the bubble phase and the suspension phase were determined from chemical conversion and tracer gas residence time distribution measurements. In the experimental program the height of the fluidized bed was varied between 0.3 m and 0.9 m with superficial gas velocities in the range of 0.06 m/s to 0.30 m/s.

The comparison of the experimental results with a suitably modified and extended two-phase model yields quantitative relationships which allow to account for the influence of the gas distributor in the design of fluid bed chemical reactors.     

NEWTONIAN FLUID SPHERE WITH RIGID OR MOBILE INTERFACE IN A SHEAR-THINNING LIQUID: DRAG AND MASS TRANSFER

The drag force and the mass transfer rate of a Newtonian fluid sphere, having mobile or rigid interface, moving in a power law fluid, are obtained by an approximate solution of equations of motion in the creeping flow regime. It is shown that both the drag and mass transfer increase as the flow index of the external fluid decreases.

The increase of drag due to the pseudoplastic anomaly is more significant at large viscosity ratio parameter. The results obtained are in good agreement with available experimental data and with those analyses based on variational principle when the non-Newtonian flow behavior is not very pronounced.

Also, the predicted mass transfer rates are in good agreement with the trends presented in the literature. Unlike in the case of drag force, the effect of the pseudoplastic anomaly on mass transfer rate is more pronounced for low values of the viscosity ratio parameter. The analysis was extended to include the case when the surface of the sphere was immobilized by surface-active contaminants.     

DROP DISPERSION IN SUSPENSION POLYMERIZATION

Four models, two based on laminar shear and two based on turbulent flow, are proposed to describe drop dispersion in non-coalescing systems. The models predict the largest surviving drop size _dmax as a function of geometry, speed and physical property variables.

Laboratory data including suspension polymerization runs support the boundary layer laminar shear model for drops larger than approximately 200 microns. Smaller drops support a turbulence model.

The boundary layer shear model was confirmed in scale-up suspension polymerization runs aimed at producing 1000 micron maximum bead sizes. Five approximately geometrically similar polymerizers were used, varying in size from 7.5 to 15000 liters.     

COMPARISON OF SUPERHEATED STEAM AND AIR OPERATED SPRAY DRYERS USING COMPUTATIONAL FLUID DYNAMICS.

In this paper a numerical simulation of a spray dryer using the computational fluid dynamics (CFD) code Fluent is described. This simulation is based on a discrete droplet model and solve the partial differential equations of momentum, heat and mass conservation for both gas and dispersed phase.

The model is used to simulate the behaviour of a pilot scale spray dryer operated with two drying media : superheated steam and air Considering that there is no risk of powder ignition in superheated steam, we choosed a rather high inlet temperature (973 K). For the simulation, drop size spectrum is represented by 6 discrete droplets diameters, fitting to an experimental droplets size distribution and all droplets are injected at the same velocity, equal to the calculated velocity of the liquid sheet at the nozzle orifice.

It is showed that the model can evaluate the most important features of a spray dryer : temperature distribution inside the chamber, velocity of gas, droplets trajectories as well as deposits on the walls. The model predicts a fast down flowing core jet surrounded by a large recirculation zone. Using superheated steam or air as a drying medium shows only slight differences in flow patterns. Except for the recirculation which is tighter in steam.

The general behaviour of droplets in air or steam are quite the same : smallest droplets are entrained by the central core and largest ones are taken into the recirculation zone. In superheated steam, the droplets penetrate to a greater extent in the recirculation zone. Also, they evaporate faster. The contours of gas temperature reflect these differences as these two aspects are strongly coupled. In both air and steam there is a “cool” zone which is narrower in steam than in air. Finally, the panicle deposit problem seems to be more pronounced in air than in steam.

Adding to the inherent interest in using superheated steam as a drying medium, the model predicts attractive behaviour for spray drying with superheated steam. In particular. under the conditions tested with the model, a higher volumetric drying rate is obtained in superheated steam.     

A MONTE-CARLO APPROACH TO THE INTERPRETATION OF BUBBLE PROBE SIGNALS IN FREELY BUBBLING FLUID BEDS†

The interpretation of the signals generated by a double probe may be done by the three characteristic times method:

t₁ the time duration of the pulses;

t₂ the time shift between the signals of the two probes;

t₃ the time interval between two pulses on one channel.

Each of these times is largely dispersed and the corresponding histograms may be constructed.

The present work is a trial to go over from the time histograms to physical properties of the bubbles combining a Monte-Carlo simulation and a flexible simplex optimisation procedure.

As a result, the percentage of oblique bubbles cutting just one level, the bubble size distribution, the average velocity-size relation, and the individual dispersion around it may be defined.

The procedure is finally applied to experimental results obtained with a light probe in a fluid bed of glass beads.     

CONTRIBUTION TO THE ANALYSIS OF THE SELECTIVITY OF GAS-LIQUID REACTIONS PART II: COMPARISON OF EXPERIMENTAL RESULTS WITH MODEL PREDICTIONS

The chlorination of paracresol is used in an experimental study of selectivity in gas-liquid contactors.

Experiments in a batch reactor show the influence on selectivity of the dimensionless numbers presented in Part I and involving competition between mass transfer and chemical reaction together with the hydrodynamics.

The extension of open reactor model presented in Part 1 to the batch reactor permits a comparison between theory and experiments and shows a good agreement     

EFFECTS OF GEOMETRY ON HYDRODYNAMICS IN EXTERNAL-LOOP AIRLIFT REACTORS

Experimental investigations were carried out in model external-loop airlift reactors. Two reactors of laboratory scale (riser liquid height ranged between 1.16-1.56 m, riser diameter 0.03 m, A_D/A_R ratio between 0.111-1,000, total liquid volume V_T = (1.189-2.446).10^-3m³) and pilot-plant scale (riser liquid height of 4.4 and 4.7 m, respectively, riser diameter 0.200 m, A_D/A_R ratio of 0.1225 and 0.040 m, total liquid volume, V_T = (0.144-0.170) m³) were used.

The influences of reactor geometry characterized by some parameter as: A_D/A_R ratio, liquid height in riser and downcomer and liquid height in gas separator, together with the amount of introduced air, on the basic hydrodynamic design parameters: gas holdup and liquid circulation velocity were analysed.

The influence of gas sparger design on gas holdup and liquid velocity was found to be negligible.

The experimental liquid circulation velocity was correlated using a simplified form of the energy balance in airlift reactors, valid for external-loop airlift reactors with almost complete phase separation at the top.

An original dimensionless correlation for gas holdup prediction involving superficial velocities of gas and liquid, cross sectional areas, dispersion height, riser diameter, as well as Froude number, was obtained.     

EXPERIMENTAL DETERMINATION OF THE PERMEABILITY AND RELATIVE VISCOSITY FOR FINE LATEXES AND YEAST SUSPENSIONS

The specific cake resistances of thin layers of fine latexes and of yeast cells have been determined from flux data for pressure drops of up to 100 kPa in a static filtration device. A single correlation has been developed that relates the cake resistance to particle diameter for monodisperse rigid latex spheres with diameters between 1.0 and 6.7 μm. The specific resistance of the yeast cell layers was found to be almost 50 times larger than that of the rigid latex spheres of the same median diameter

The relative viscosities of a 7.3 μm latex and yeast cell suspensions have been measured in a cone-and-plate viscometer. Empirical correlations relating the relative viscosity to the solids volume fraction were developed from linear regression of the data for each suspension. A correlation was also developed that relates the relative viscosity of the yeast cell suspension to the cell count. The effective shear-viscosities were not observed to exhibit a significant shear-rate dependence. However, an apparent viscosity increase with time was observed. This is attributed to radial migration of the particles as a result of interactions with the surface of the cone.     

APPLICATION OF TURBULENCE FUNDAMENTALS TO REACTOR MODELLING AND SCALEUP

Applications of the fundamentals of turbulent mixing become clear once those fundamentals are understood. The first article in this series presented those fundamentals, in order to show how to apply turbulent mixing fundamentals modelling and scaleup, this article covers the following topics:

1. reaction types and their interaction with mixing;

2. closure of the Reynolds equations for mixing and reactions;

3. application to complex geometries;

4. random coalescence-dispersion modelling;

5. application to complex chemistry.

The most difficult problem in applying our knowledge of turbulence to mixer modelling and scaleup is the choice of model complexity. The levels of model complexity available and how to apply them to various problems are presented following the introduction.     

A NEW TOOL FOR NUCLEATE BOILING RESEARCH

A new tool for the study of nucleate boiling heat transfer has been developed. Photographic etching was shown to be effective in the manufacture of copper lest surfaces containing precise arrays of artificial pits, with densities as high as 2742 pits/cm².

The pits were shallow segments of spheres, with depth: diameter ratios on the order of 0.1. Pit diameters were on the order of 0.003 cm. Data showed that the pits significantly affected the characteristic boiling curves and critical fluxes for the surfaces studied while boiling Freon 113 at one atmosphere pressure.

Photoetching can be used in the future to produce a wide variety of test surface textures or site arrays. Careful control of such surface conditions may well lead to a better understanding of the nucleate boiling phenomena.     

Nanofluid impingement jet heat transfer

Experimental investigation to study the heat transfer between a vertical round alumina-water nanofluid jet and a horizontal circular round surface is carried out. Different jet flow rates, jet nozzle diameters, various circular disk diameters and three nanoparticles concentrations (0, 6.6 and 10%, respectively) are used. The experimental results indicate that using nanofluid as a heat transfer carrier can enhance the heat transfer process. For the same Reynolds number, the experimental data show an increase in the Nusselt numbers as the nanoparticle concentration increases. Size of heating disk diameters shows reverse effect on heat transfer. It is also found that presenting the data in terms of Reynolds number at impingement jet diameter can take into account on both effects of jet heights and nozzle diameter. Presenting the data in terms of Peclet numbers, at fixed impingement nozzle diameter, makes the data less sensitive to the percentage change of the nanoparticle concentrations. Finally, general heat transfer correlation is obtained verses Peclet numbers using nanoparticle concentrations and the nozzle diameter ratio as parameters.     

Highly selective fluorescent chemosensor for Zn2+ derived from inorganic-organic hybrid magnetic core/shell Fe3O4@SiO2 nanoparticles

Experimental investigation to study the heat transfer between a vertical round alumina-water nanofluid jet and a horizontal circular round surface is carried out. Different jet flow rates, jet nozzle diameters, various circular disk diameters and three nanoparticles concentrations (0, 6.6 and 10%, respectively) are used. The experimental results indicate that using nanofluid as a heat transfer carrier can enhance the heat transfer process. For the same Reynolds number, the experimental data show an increase in the Nusselt numbers as the nanoparticle concentration increases. Size of heating disk diameters shows reverse effect on heat transfer. It is also found that presenting the data in terms of Reynolds number at impingement jet diameter can take into account on both effects of jet heights and nozzle diameter. Presenting the data in terms of Peclet numbers, at fixed impingement nozzle diameter, makes the data less sensitive to the percentage change of the nanoparticle concentrations. Finally, general heat transfer correlation is obtained verses Peclet numbers using nanoparticle concentrations and the nozzle diameter ratio as parameters.     

HYDRODYNAMICS, MIXING AND MASS TRANSFER IN A LARGE DIAMETER JET BUBBLE COLUMN

Experimental measurements for the axial and radial variations in gas holdup, axial and radial dispersion coefficients, volumetric gas-liquid mass transfer coefficient and liquid phase circulation velocity in a cone of a large diameter (122 cm) jet bubble column are presented. Two diameters of the inlet nozzle, namely 10.16 cm and 15.24 cm, three superficial gas velocities (based on cylinder diameter), 3 cm/sec, 6 cm/sec and 8 cm/sec and two superficial liquid velocities, 0.3 cm/sec and 0.6 cm/sec, are examined. The experimental data are obtained for two different bed heights.

The experimental data showed significant axial and radial variations in the gas holdup. The volumetric average gas holdup was higher at higher gas velocity and larger nozzle diameter and somewhat higher at lower liquid velocity. The axial dispersion was high while the radial dispersion was low. The volumetric gas-liquid mass transfer coefficient was larger at higher gas velocity and larger nozzle diameter. The liquid recirculation begins only at the upper end of the cone. In general, experimental data indicate that a jet bubble column provides a high degree of mixing and transport rates.     

Elementary Mechanisms in the Interaction of Organic Molecules with Mineral Surfaces

Model systems are used to reproduce the actual situations encountered during the interaction of organic molecules with mineral solids under controlled experimental conditions.

The role of local electrical fields produced by surface heterogeneities and the influence of the electronic properties of the functional groups of the organic molecule and of the surface are demonstrated and discussed.

This study enables modelling of the basic mechanisms in the organic molecule-mineral solid bond and of the polymerization process of the organic film.

The results given here may be used to produce theoretical models of predictive nature in the field of adhesion and structural bonding.     

EVALUATION OF PENG ROBINSON EQUATION OF STATE IN CALCULATING THERMOPHYSICAL PROPERTIES OF COMBUSTION GASES

A set of simple equations of the thermodynamic and transport properties of the combustion gases of a gas turbine have been derived based upon the critically evaluated data and two equations of state: The virial equation of state and Peng-Robinson (PR) equation of state.

The properties which have been considered were, density, specific heat at constant pressure, enthalpy, entropy, viscosity and thermal conductivity.

The temperature range was (200-2600 K) theoretically while the pressure range was (0.3-1.2 MPa).

A computer program, to evaluate the departure of thermophysical properties using virial and PR equations of state, was used.

The Peng Robinson (PR) equation of state gave better estimated accuracy than the virial equation of state especially in evaluating the departure of thermodynamic properties.     

VISCOSITY OF GLYCEROL AND ITS AQUEOUS SOLUTIONS MEASURED BY A TANK-TUBE VISCOMETER

In this paper we demonstrate several series of experiments for the measurement of viscosity of neat glycerol and its aqueous solutions using a tank-tube viscometer. Measuring viscosity of highly viscous liquids with the tank-tube viscometer is easier than other types of viscometers. This inexpensive viscometer continuously generates numerous reproducible viscosity data of highly viscous neat glycerol and its aqueous solutions under given experimental conditions such as a desired temperature and a desired concentration of water in aqueous glycerol solutions.

Fabricating the tank-tube viscometer is inexpensive, since this viscometer does not need sophisticated accessories such as a high-pressure liquid pump, a sensitive pressure sensor, and an accurate flow meter. The tank-tube viscometer consists of a large-diameter reservoir and a long, small-diameter, vertical tube.

The viscosity equation was developed under the following assumptions. Both the quasi steady state approach and the negligible friction loss due to a sudden contraction between the reservoir tank and the tube are valid. The kinetic energy of the emerging stream from the bottom end of the vertical tube of the tank-tube viscometer also is assumed to be negligible. Very viscous glycerol and its aqueous solutions were used to test the viscometer by comparing viscosity values from the viscometer with those from literatures.

The main objective of this study is to demonstrate effects of water as well as temperature on viscosity of aqueous glycerol solutions, applying experimental data of accumulated amounts of aqueous glycerol solutions at various drain durations to the newly-developed viscosity equation for the fabricated tank-tube viscometer.