Drag Correlation of Drop Motion on Fibers

The objective of this article is to correlate a drag coefficient to the Reynolds number for axial motion of barrel drops on fibers. This work includes effects of vibration-induced motion of droplets and coalescence. The study of motion of drops is important to understand the drainage behavior of droplets. Drainage of liquid helps to eliminate moisture from media samples before applying thermal energy and hence reducing the drying cost. A significant amount of literature describes the mechanisms of droplet capture, coalescence, and drainage from filter media and models are developed at a scale that accounts for the liquid held in the filter through averaged parameters such as saturation. Few papers discuss the motion of individual drops attached to fibers.

The study of drop motion on fibers is of scientific and economic interest for many possible applications like printing, coatings, drug delivery and release, and filters to remove or neutralize harmful chemicals or particulates from air streams. Gas convection–induced drop motion in fibrous materials occurs in coalescing filters, clothes dryers, textile manufacturing, convection ovens, and dewatering of filter cakes. Droplet removal can significantly reduce drying costs by reducing the free moisture contained in fibrous materials prior to applying thermal drying techniques.

In this article, the experimental drag coefficient versus Reynolds number data are compared for 1-D and 3-D cylindrical drop models. The results show that 1-D models are inadequate to predict the drag coefficient but do show the same general trends.     

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.     

MAXIMIZING SELECTIVITY OF LIQUID-LIQUID REACTION SYSTEMS. CONTROL OF THE DISPERSION PROCESS

Currently available information on droplet coalescence and break-up rates in turbulent flows in mixing vessels can be used to control drop sizes in dispersed phase equipment. The effect of drop size distributions on the selectivity and productivity in multi-reaction systems is examined in this paper.

The reaction system features the primary desired product (C) as resulting from reaction (in the bulk phase) between a reactant (A) in the drop phase and a second reactant (B) in the bulk phase. An adverse reaction is also envisaged which consumes (C) by further reaction with (B) to form a waste product. While small drops promote conversion because of large interfacial area, larger drops promote selectivity because of the facility of the product to re-enter the drop phase avoiding further reaction (to form waste) in the bulk phase. The effect of the bivariate distribution of drop size and reactant (A) concentration in the feed to a continuous stirred tank reactor on the selectivity and productivity of (C) is investigated within the framework of film theory while neglecting drop dynamics such as coalescence and break-up.

The results show the selectivity can be substantially improved by controlling drop size and distribution of the reactants among the differently sized droplets. Contrary to conventional wisdom which emphasizes creation of interfacial area by promoting very small droplets, it emerges that optimal distributions of drop size and reactant concentration which maximize productivity of the desired product exist. The practical implications are discussed.     

THE EFFECT OF EQUILIBRATION TIME AND TEMPERATURE ON DROP-DROP COALESCENCE OF WILMINGTON CRUDE OIL IN A WEAKLY ALKALINE BRINE

The interfacial behavior of a Wilmington crude oil was studied as part of our investigations of enhanced oil recovery by weakly alkaline solutions. For some systems, the spinning drop apparatus can be used to measure transient interfacial tension (IFT) effects, coalescence times of oil drops, and film rigidity simultaneously, for rapid screening of chemical slug composition for the potential of improving oil recovery by the mechanisms of oil mobilization and oil bank formation. The experimental results presented include the effects of temperature, surface age, salinity, added surfactant, and polymer on coalescence time, film rigidity, and IFT behavior. Oil displacement tests were performed using surfactant-enhanced bicarbonate solutions formulated for improved mobility control and for improved oil mobilization and oil drop coalescence.

The most significant result of this work was that we were able to measure the dynamics in IFT between 2 coalescing oil drops as perturbations in the equilibrium concentration of surfactant at the interface occurred during film drainage. The accuracy of the technique for measuring IFT and film rigidity improved as the contact radii between the oil drops increased.     

THE EFFECT OF HETEROGENEOUS DRAG REDUCING SURFACTANT IN DRAG AND HEAT TRANSFER REDUCTION IN CRUDE OIL SYSTEMS

Pilot scale experiments have been performed to study the effect of a heterogeneous surfactant into the drag and heat transfer coefficient in crude oil pipelines. The effects of surfactant concentration, pipe diameter, Reynolds number and temperature were studied in this research program.

An extensive set of data was obtained for heat transfer and friction coefficients for a heterogeneous surfactant known as MDR-2000. A wide range of Reynolds numbers were covered and experiments were conducted for many different Prandtl numbers. All drag and heat transfer reduction experiments were performed in the same installation using the same measurement techniques which facilitates the assessment of the trends caused by the various parameters studied.

Typical results showed that the friction coefficient was reduced by half at the optimum concentration. While, the heat transfer coefficient was reduced even more dramatically.     

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.     

MULTI-STAGE SPRAY DRYING METHOD IN MANUFACTURING HEAVY DUTY DETERGENTS

Collision of droplets; counter-current spray dryer; drying rate; heat transfer; nonphosphated detergent; spray drying

The spray drying method of non-phosphated granular detergents is studied to decrease the amount of agglomerate particles. The formation of agglomerates is mainly influenced by the concentration of droplets in spray cloud and the water content of droplets at the time of collision. The overlaps of different spray clouds should be de- creased.

The drying rate near the nozzle zone is considerably faster than that calculated by Ranz-Marshal's equation. According to these phenomena, “Multi-stage spray drying” is developed, which is characterized by in stalling plural spraying stages in a spray dryer.

Consequently, non-phosphated detergents are manufactured with the same powder properties and productivity as phosphated detergents.     

A case study of simulating submicron aerosol filtration via lightweight spun-bonded filter media

The most common method of filtration is via fibrous nonwoven media. Fibrous filters are generally characterized by their collection efficiency and pressure drop. Traditional computational studies in this area are typically based on unrealistic 2-D geometries with the fibers simply placed in a lattice (regular array) perpendicular to the flow. The traditional approaches however, do not permit studying the relation between the 3-D structure of a filter media and its performance. In this study, for the first time, a virtual 3-D web is generated based on the fiber orientation information obtained from analyzing microscopic images of lightweight spun-bonded filter media. Pressure drop and collection efficiency of our virtual filter are simulated and compared with the previous 2-D analytical and numerical models as well as experiment. Our pressure drop calculation, unlike the previous models, showed a perfect agreement with the predictions of the Davies’ empirical equation. The collection efficiencies obtained from simulating a thin spun-bonded filter media challenged with submicron particles having diameters ranging from 50 to 500 nm showed a similar trend as that of the previous 2-D models. For the solid volume fraction (SVF), filter thickness, and the fiber and particle diameters considered in this study, we found collection efficiencies higher than that of the above mentioned 2-D models with a relatively good agreement with experimental data obtained from a TSI 8130 filter tester.     

ESTIMATION OF FUNCTIONS IN DRYING EQUATIONS

In drying problem, particularly for drying foodstuff, modelling is very difficult. Many physical effects have to be taken into account for mass transfer ; then mass transfer coefficient varies

In different models unknown functions must be estimated. It is particularly the case in simple models of drying using average values of water content, where the mass transfer varies versus mean water content in falling rate period. On the other hand in the “diffusion model” we have the same problem concerning the diffusion coefficient which must be also estimated

The method we propose in this paper for these two models : simple and “diffusion model” of drying consists from measurements of temperature and water content of the product to search a numerical approach of the unknown function. This method uses optimization techniques on computer and least squares criterion between model values and experimental data

Results are given for the “diffusion model” applied to shelled corn drying to find the diffusion coefficient and for a simple 11107 del applied to plum drying to find the mass transfer coefficient.     

HEASUREHENT OF INSTANTANEOUS RATES OF LOSS OF VOIATILE COMPOUNDS DURING DRYING OF DROPS

A novel technique serves to monitor instantaneous rates of loss of a volatile solute from a suspended drop during drying. A highly sensitive electron capture detector is used to monitor concentrations of SF6 released into a flowing gas stream from a suspended, drying drop. Simultaneously, the appearance and morphological development of the drop are monitored with a video camera. This provides the wherewithal of relating instantaneous rates of loss of the volatile solute to particular events during the development of particle morphology.

Initial experiments have been carried out with drops of aqueous solutions of glucose, sucrose, maltodextrin and coffee extract. The results clearly display the onset of the volatiles-retentive selective diffusion phenomenon. There is also substantial loss of the volatile component later in the drying process, when the drops undergo repeated ex ansion, bursting and cratering due to the formation of internaf bubbles. These experiments appear to be the first quantitative demonstration of major losses accompanying changes in drop morphology.     

FACTORS GOVERNING SURFACE MORPHOLOGY OF SPRAY-DRIED AMORPHOUS SUBSTANCES

Changes in particle morphology (size, shape, and appearance) have been monitored during drying of drops of foods and food-related materials. The apparatus produces a single stream of drops of uniform size, using a vibrating-orifice device for drop production. The drop size and the time-temperature history of the drops as they fall can be varied and controlled.

Qualitative observations are reported for drying of aqueous solutions of lactose, maltodextrin, skim milk, and coffee extract, with different feed concentrations. Particular emphasis is placed upon the tendency for development of folds upon the particle surface. A mechanistic model is developed, relating the tendency for folding to the extent of viscous flow of surface material in response to a surface-energy driving force. This model gives semi-quantitative agreement with observations for solutes of different molecular weight (and hence different viscosity) and for different feed concentrations.     

Experimental verification of the additivity between the barrel droplet's drag force and the fiber number

Research on the single fiber scale has an essential application value in the coalescence field. The study of the droplets' behavior on the fiber junctions can provide support data for optimizing the coalescer's drainage performance on the macroscopic scale. However, relevant research focusing on the force change of droplets during the transition from a single fiber to multifiber is relatively scarce. The droplet migration platform was built using the Lavision particle image velocimetry system, which can observe the behavior of droplets on fibers. The force and fiber number relationship were analyzed when the droplets were separated from the fiber junctions. Two detachment modes were observed during separation. Furthermore, the drag force satisfied the additivity theorem by increasing the number of fibers under the same detachment mode. In addition, the minimum Reynolds number prediction model was established under two separation forms, which had good prediction compared to the experimental data.     

Continuum Model Evaluation of the Effect of Saturation on Coalescence Filtration

Abstract

Coalescing filters are widely used throughout industry for removal of liquid aerosols from gases or the separation of liquid droplets from emulsions. Typical filters are constructed of non-woven fibers. Fibrous filters are capable of efficient removal of micron and submicron sized droplets and particles. The filtration process is highly complex due to variability in fiber sizes, particle sizes, mixtures of particles and droplets, mixture of types of droplets (oil, water, etc.), and effects of viscosity, surface tension, and chemical reactions between components or with the filter fibers. Prediction of filter performance under such complex conditions is difficult.

Performance of a filter depends on many factors like particle and fiber sizes, flow rate, surface properties of the fibers etc. One of those parameters is the saturation of the filter medium. Saturation is a measure of the amount of liquid present in the void space. Prior models assume that the saturation is uniform along the depth of the medium. In real media, the liquid holdup at steady state need not be uniform with position. Local velocity increases when the saturation is high.

In this paper, a steady state model for a coalescing filter is used to evaluate the effects of saturation on void fraction and its subsequent effect on filter performance. Single fiber mechanisms of direct interception and diffusion deposition are used to model droplet capture efficiencies and drag forces. These mechanisms are applied to volume averaged continuum equations in which the saturation is varied linearly with position in the filter. The results show the minimum pressure drop and largest quality factor occurs with a uniform saturation profile and that variation in average saturation has a greater effect on filter performance than does the slope of the linear saturation profile. The model predicts that uniform saturation profile performs better than the other profiles.     

AN EXPLORATORY STUDY OF A COMBINED SONIC AGGLOMERATION AND CROSSFLOW FILTRATION SYSTEM FOR HOT GAS CLEANUP

The Institute or Gas Technology has investigated a combined sonic agglomeration/crossflow filtration system to remove particles smaller than 10 microns from high-temperature, high-pressure gas streams. Sonic energy induces agglomeration so that particles can be removed in a continuously operating cross-flow filler element. Cold-model and preliminary high-temperature, high-pressure results are promising.

The objective of this investigation was to explore the potential effectiveness of sonic agglomeration, crossflow filtration, and a combination of these techniques to remove particles from high-temperature, high-pressure (HTHP) gas streams. The technique of sonic agglomeration has been known since the 1930's, and crossflow filtration has been used successfully in liquid filtration. This investigation is unique in that these two techniques were combined. Sonic energy was used to agglomerate particles to sizes large enough to be separated from the gas stream in a crossflow filter. The crossflow filter has advantages over conventional filters as a paniculate agglomerate removal system because it (1) operates continuously, (2) does not subject the fragile agglomerates to the high stress typical of inertial capture devices, and (3) can control the buildup of a filter cake when properly combined with a sonic agglomerator.

This investigation was supported by the Gas Research Institute and the Institute of Gas Technology Internal Research and Development Fund.

In this preliminary study, we found that—

• A 2-micron porosity filter must be used to achieve 98% paniculate removal from 95% of a dust-laden stream. (In the crossflow operating mode, 5% of the stream bypasses the filter.)

• When sonic agglomeration is combined with crossflow filtration, the same removal efficiency can be achieved with a 10-micron porosity filter.

• Combined sonic agglomeration/crossflow filtration removed particulates smaller than 10 microns in experiments at 265° C and 7000 kPa.

• The pressure drop across a 10-micron filter is about one-half that of a 2-micron filter, which could reduce the energy requirements for filtration.

This method of particulate removal should be applicable to many different coal reactor effluent streams, especially because it can operate at elevated temperatures and avoid gas cooling, liquid condensation, and subsequent liquid-solids separation. Preliminary estimates show that the power requirements of a combined sonic agglomerator/crossflow filter are lower than those of a crossflow filter alone, and that they are lower than or comparable with other particulate removal techniques. Additional tests are needed to establish the degree to which these benefits can be realized.     

IMPINGING JET DRYER

In coating and gravure printing, an impinging jet nozzle with high thermal efficiency for drying of coated film was developed.

Trial production 0f 40 kinds of nozzle enables to develop a high-performance impinging jet nozzle with heat transfer coefficient 1.5 times larger than that of current slit nozzle, through measurement of heat transfer coefficient, visualizations of air flow and heat transfer, and measuremenu of jet velocity and turbulence distribution. The purpose of the trial production was to expand a range of high heat transfer and promote turbulence compared with the current nozzle.

Paying attention to mass transfer within gravure ink coated film, drying characteristic of the film was analyzed by numerical solution of a set of equations governing the drying process in which concentration dependencies 0f the diffusion coefficient and the equilibrium vapor pressure were considered.

Applying these analyses. an industrial scale dryer with excellent drying efficiency has finally been developed.     

Food Drying and Dewatering

Food drying and dewatering raises a growing interest because of increasing requirements in quality, specially in the production of ingredients and additives for food formulation. Heat and mass transfers, as well as mechanical phenomena and reactions kinetics induced by these transfers must be more and more carefully controlled during drying and storage.

This chapter relates recent advances in

- drying of solids

- spray-drying

- drum-dryine

- superheateded steam drying

- osmotice dehydration

- hot oil immersion drying     

PROCESSES RELATED TO DRYING: PART II USE OF THE SAME MODEL TO SOLVE TRANSFERS BOTH IN SATURATED AND UNSATURATED POROUS MEDIA

From the mathematical formulation presented in part I, a numerical code is developed to simulate heat and: mass transfers in porous media. The aim of this· tool is to understand and to improve each process related to drying. The association of a comprehensive set of equations with a efficient 2-D computer code allows us to predict the comportment of several porous media even if submitted to severe drying conditions. A few runs have been selected with special attention paid to the effect of internal gaseous pressure:

Convective drying of softwood at high temperature illustrate the typical two-dimensional transfers that occur in an anisotropic medium.

Microwave drying of light concrete pinpoints liquid expulsion of water which is driven by the pressure due to internal heating.

Finally, appropriate physical behaviours of a bed of glass spheres allows one to deal with simple processes for which full saturation occurs.     

INVESTIGATION OF EMULSIFICATION AND COALESCENCE PHENOMENA IN CRUDE OIL/ALKALINE WATER SYSTEMS

Emulsihcation and coalescence processes in crude oil/alkaline water systems were examined and their influence on alkaline Hood enhanced oil recovery was assessed. Emulsification mechanisms were investigated under static and dynamic conditions using microvisual techniques. Coalescence rates were measured using the inclined spinning drop tensiometer. The relative impact of interfacial viscosity on coalescence processes was determined through measurements of interfacial shear viscosities. In addition, the influences of chemical composition on ease of emulsification, coalescence rate, and interfacial shear viscosity were examined.

Ease of emulsification was influenced by the composition of the crude oil, the electrolyte concentration, and the partitioning coefficient of surfactants. Coalescence was primarily affected by processes which disrupted the crude oil/water interface. Alkaline flood oil recovery efficiency was promoted by emulsification followed by rapid coalescence to form a stable oil bank.     

Influence of fiber orientation distribution on performance of aerosol filtration media

This work is conducted to better our understanding of the influence of fibers’ in-plane and through-plane orientations on pressure drop and collection efficiency of fibrous media. The Stokes flow equations are numerically solved in virtual, 3-D, fibrous geometries with varying in-plane and/or through-plane orientations. Pressure drop and aerosol collection efficiency characteristics of such media are calculated and compared with available studies from the literature. Our results indicate that pressure drop and submicron particle capture efficiency of common fibrous filters with a fiber diameter of about 10 μm are independent of the in-plane orientation of the fibers, but decrease with increasing the fibers’ through-plane orientation. More interestingly, it was found that filters with higher through-plane fiber orientations have a higher figure of merit if challenged with nanoparticles. The figure of merit of these media, however, decreases as the particle size increases, reversing the effect of fibers’ through-plane orientation. It was also shown that when the diameter of the particles is comparable to that of the fibers, collection efficiency increases with decreasing the fibers’ in-plane orientation, while the pressure drop remains almost unchanged. This indicates that decreasing the fibers’ in-plane orientation increased the figure of merit of media made of nanofibers.