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.     

EVALUATION OF CONDUCTIVE HEAT TRANSFER MECHANISMS BETWEEN AN IMMERSED SURFACE AND THE ADJACENT LAYER OF PARTICLES IN BUBBLING FLUIDIZED BEDS

The evaluation of the heat transfer coefficient h_wp between a heat exchanging surface immersed in a gas fluidized bed and the adjacent layer of dense phase particles is analyzed in this contribution. Gas convective and radiant effects are not included in the present analysis.

The inclusion of h_wp, or an equivalent formation, in mechanistic models describing heat transfer has been necessary because the sudden voidage variation close to the immersed wall restrains significantly the heat transfer rate. However, there is not at present a widely accepted expression to evaluate h_wp.

A precise formulation for h_wp accounting for transient conduction inside spherical particles, the Smoluchowski effect, the concentration of particles in the adjacent layer (N_p) and an effective separation gap (l₀) is developed here.

Although N_p can be estimated, in principle, from experimental evidence in packed beds, and it is reasonably expected that l₀ = 0, the analysis of experimental heat transfer rates in moving beds, packed beds, and bubbling fluidized beds indicate that values of h_wp are, in general, smaller than expected from these assumptions. Appropriate values of l₀ and N_p are then stimated by fitting the experimental data.

The probable effect of surface asperities is also discussed by analyzing a simplified geometrical model. It is concluded that the parameter l₀ can be also effective to account for particle roughness, independently of thermal properties.     

VISCOSITY OF BIOMATERIALS

Viscosity data for honey, corn oil, mayonnaise, yogourt, blood and banana puree have been analyzed using two Theological models: the Herschel-Bulkley model and a proposed model. The proposed model contains three parameters: a yield stress, a parameter having the units of time and a parameter having the units of viscosity.

The model parameters were obtained by non-linear regression and the proposed model was shown to compare favorably with the Herschel-Bulkley equation.

An Arrhenius-type of correlation could be verified between the viscosity of banana puree and the inverse of the temperature. Also, the time parameter (t₁) of the proposed model could be correlated with the temperature and the parameter η₁.

It is asserted that the proposed model should replace advantageously the commonly used Casson expression.     

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.     

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.     

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.     

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.     

Vibration and Damping Characteristics of a Beam with a Partially Sandwiched Viscoelastic Layer

The purpose of this study is to verify the vibration and damping characteristics of a partially-layered elastic-viscoelastic-elastic structure both theoretically and experimentally.

The fourth-order differential equations of motion are derived for the transverse vibration of a three-layered sandwich beam with a viscoelastic (or adhesive) core layer. The transverse displacements of the constraining layer and the base beam are assumed to have different parameters. Both the transverse normal strain and the longitudinal shear strain of the viscoelastic core layer are included in the equations of motion. The solution to the resulting equations is obtained by solving a boundary value problem.

Numerical analysis of the equations and experimental measurements is illustrated by a cantilever beam in transverse vibration.

The vibration and damping effects of completely and partially covered beams are investigated and the effect of the position changes of partial coverage is intensively analyzed.     

HYDRODYNAMICS OF LAMINAR LIQUID JETS. EXPERIMENTAL STUDY AND COMPARISON WITH TWO MODELS

Laminar jets of Newtonian liquids issuing from long vertical cylindrical nozzles and falling freely through stagnant air were studied experimentally for Reynolds numbers between 300 and 1000. Jet diameters were measured from still photographs, and radial distributions of axial velocity were obtained by laser Doppler anemometry. The effect of nozzle diameter, fluid viscosity and surface tension was investigated.

The experimental results were compared with numerical solutions of the Protean coordinate model developed by Duda and Vrentas. The boundary layer simplifications were confirmed to be valid only for the downstream region of the jet and for Reynolds numbers greater than 1000.

The experimental diameters were also compared with predictions from a form of the Bernoulli equation with a surface tension term. The asymptotic validity of the model was confirmed, provided that the dissipation term arising from fluid viscosity could be neglected.

Neither model correlated the jet formation region satisfactorily. For this region, an empirical correlation was developed which improves the diameter prediction and is complementary of either model.     

HYDRODYNAMIC CHROMATOGRAPHY: THREE DIMENSIONAL LAMINAR DISPERSION IN RECTANGULAR CONDUITS WITH TRANSVERSE FLOW

Experimental observations^1,9 indicate much poorer separations than are predicted by two dimensional theory. The purpose of this work is to explain these differences and suggest ways in which system performance can be improved.

The large effect of span-wise variation in axial velocity caused by side walls on hydrodynamic separations carried out in rectangular conduits with transverse flow is studied theoretically. As the aspect ratio increases, the steady stale retentivity (convection coefficient) approaches an asymptotic value obtained by neglecting side wall effects. However, the dispersion coefficient does not reduce to that for a flow with no side walls. Indeed, the asymptotic steady state dispersion coefficient is at least six times larger than that obtained by two dimensional theory which neglects side wall effects. As the transverse Peclet number increases, the effect of side walls on the dispersion coefficient becomes much larger.

The present three dimensional theoretical predictions, in contrast to two dimensional ones, are in good agreement with the experimental data of Caldwell, et al.⁹ and Kesner, et al.¹ on electrical field flow fractionation. The results indicate that side wall effects may be of major importance in hydrodynamic chromatography even when the aspect ratio is 70 or more.

The adverse effect of side walls may be avoided by having the membranes enclose thin annular regions rather than rectangular conduits. This should improve performance significantly.     

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.     

A DISTRIBUTED PARAMETER APPROACH TO THE DYNAMICS OF ROTARY DRYING PROCESSES

A nonequilibrium distributed parameter model for rotary drying and cooling processes described by a set of partial differitial equations with nonlinear algebraic constraints is developed in this work. These equations arise from the multi-phase heat and mass balances on a typical rotary dryer. A computational algorithm is devekped by employing a polynonial approximation ( orthogonal collocation) with a glotal splinc technique leading to a differential-algebraic equation ( DAE) system. The numerical solution is carried out by using a standard DAE solver.

The two- phase-flow heat transfer coelficient is computed by introducing a correction factor to the commonly accepted correlations. Since interaction between the falling particles are considered in the correction factor,the results are more reliable than those computed by assuming that heat transfer between a single falling particle and the drying air is unaffected by other particles. The heat transfer computations can be further justified via a study on the analogies between heat and mass transfer.

The general model devloped in this work is mathematically more ritorous yet more flexible that the lumped parameter models established by one of the authors (Douglas et al., (1993)). The three major assumptions of an equilibrium operation, perfect mixing and constant drying raic, are removed in the distributed parameter model.

The simulation results are compared with the operational data from an industrial sugar dryer and predictions from earlier models. The model and algorithm successfully predict the steady state behaviour of rotary dryers and collers. The generalized model can be applied to fertilizer drying processes in which the assumption of constant drying rate is no longer valid and the existing dynamic models are not applicable.     

RHEOLOGICAL AND MIST IGNITION PROPERTIES OF DILUTE POLYMER SOLUTIONS

A spinning disc atomizer has been used to characterize the mist flammability of Jet A and diesel fuels that contain high molecular weight polymers. The critical disc velocity required to produce significant flame propagation was shown to depend on polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The viscoelastic properties of these same polymer solutions have been characterized by a maximum Darcy viscosity measured from flow in packed tubes. For the polymers discussed in this paper, the maximum Darcy viscosity was independent of the bead size or tube length; however, it was strongly affected by the same variables that affected mist flammability; i.e., polymer concentration, molecular weight, solvent viscosity, and polymer degradation.

The critical ignition velocity of dilute polymer solutions is shown to depend on the Darcy viscosity in a similar manner as observed for viscous oils. At low viscosities, the ignition velocity is only slightly affected, but the dependence grows stronger as the viscosity (both shear and Darcy) increases. A close correspondence was also shown to exist between the ignition velocity of a polymer solution with a high Darcy viscosity and the ignition velocity of a Newtonian oil with approximately the same high shear viscosity.

Numerous similarities are described between flow-induced birefringence of dilute polymer solutions with opposed capillary jets and viscoelastic resistance of dilute polymer solutions in packed tubes. These similarities suggest that the maximum Darcy viscosity is associated with a condition of almost complete extension and alignment of the polymer molecules.     

MASS TRANSFER THROUGH PERMEABLE WALLS: A NEW INTEGRAL EQUATION APPROACH FOR CYLINDRICAL TUBES WITH LAMINAR FLOW

Mass transfer through cylindrical semipermeable walls is analyzed. The solution is obtained in terms of integral equations. Despite the existence of a non-homogeneous boundary condition on the semipermeable wall, the solution thus obtained is particularly advantageous since the associated eigenvalue problem is independent of the Sherwood number. This parameter takes into account the main conductances at the tube wall.

The approach is applied to the case of mass transfer from the interior of a capillary tube with semipermeable walls to an external fluid. The flow in the tube is laminar, and the external flow is assumed turbulent.

The mathematical methodology employed provides a framework to develop numerical schemes of fast and sure convergence.     

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.     

HIGH TEMPERATURE INCIPIENT FLUIDIZATION IN MONO AND POLYDISPERSE SYSTEMS

Tests have been made on the behaviour of fluidized beds at high temperature (15-950^°C). Bed materials used were silica sand of different sizes.

Bed voidage at minimum fluidization conditions was found to be dependent on temperature rise and on increase in Reynolds number. Plots of bed voidage function, bed voidage and Ar versus Re_mf show a change in the behaviour at Reynolds numbers between approximately 0.75-2. This is explained in terms of a variation in the fluid flow pattern inside the bed: at very low Re_mf creeping flow exists, but at higher values of Reynolds number, separation of boundary layer takes place and a wake appears at the rear of the particle, creating a low pressure zone. This contributes to attractive forces between particles at the minimum fluidization conditions, decreasing the value of ε_mf. If Re_mf increases, the separation point moves towards the rear of the particle and the wake shrinks; attractive forces decrease, and ε_mf increases.

Data on u_mf, both for monodisperse systems and binary mixtures, are compared with predictions from different equations.     

Peel Adhesion of Solid Films-The Surface and Bulk Effects

The peel strength of rubber and paint films has been measured over a range of peeling velocities using a dead weight method. At low peel rates the peel force is fairly constant but rises rapidly at higher peeling speeds.

Experiments show that the peel strength is a function both of the energy of interfacial bonds which must be broken as peeling proceeds and of bulk energy losses in a viscoelastic peeling material.

The interfacial effect has two components: an equilibrium surface force which accounts for the peel strength at low velocities, and a viscous peeling force which depends on the peeling rate. This viscous interfacial force explains the increase in peel strength of purely elastic films at higher peeling velocities.

The energy loss in the bulk of the peeling film introduces two additional effects: a magnification of the peel strength in steady peeling over a certain velocity range, and a slowing down or stopping of peeling as transient relaxation occurs shortly after the application of the peel force.     

A Numerical Investigation of the Effect of Induced Porosity on the Electromechanical Switching of Ferroelectric Ceramics

Ferroelectric ceramics have many applications ranging from microelectromechanical systems (MEMS) to explosively driven power supplies. In addition to chemical compositions and processing methods, porosity is an important material parameter that can affect both the electrical and mechanical responses of a ferroelectric. The main objective of the current study is to gain preliminary insight on the possible effect of porosity on the switching behavior of ferroelectrics.

Numerical simulation was used to address the research objective. The numerical code used is an arbitrary Lagrangian-Eulerian, multi-material, multi-physics finite element code developed by Sandia National Laboratories. To accomplish the research objective, a phenomenological electromechanical model developed by Landis was first implemented in the code. The effects of void density, which ranges from 0 to 11%, and shape, which includes sphere and cylinder, were then investigated through a parametric study.

The study indicates that the remanent polarization decreases with increased porosity density. For a given density, the porous solid that contains the cylindrical voids whose longitudinal axis is perpendicular to the applied electric field possesses the largest amount of the remanent polarization. The solid that contains the cylindrical voids whose longitudinal axis is parallel to the applied electric field has the least while the one containing spherical voids is intermediate. It is conjectured that the void shape effect is mainly due to the fact that the void perturbs the distribution of electric field and polarization with respect to from the applied electric field direction and different shapes of void result in different degrees of perturbation.

The limitation of the current numerical simulation and possible future work are also discussed.