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.     

TAYLOR DISPERSION OF MULTICOMPONENT SOLUTES

Coupled transport of multicomponent solutes in globally continuous systems is considered in the framework of the Generalized Taylor dispersion theory. Coupling between transports of n different species at the local (or micro-) scale, is considered to result from first-order irreversible surface reactions occurring on the local space boundaries, or from the off-diagonal terms of the solute diffusivity matrices.

General expressions are obtained for the global effective (long-time) solute dispersion matrix cofficients: mean global scalar reactivity, velocity vector and dispersivity dyadic.

The effect of surface chemical reactions is to partition the matter between different solute constituents. This is manifested in a coupling of the global transport coefficients, which may be mathematically removed by a linear (canonic) transformation applied to the effective global transport equation. This type of coupling does not exist for inert solutes.

The second type of the global coupling is represented by the off-diagonal terms of the global velocity and dispersivity matrices. It exists for both reactive and inert solutes. This coupling stems from the convective dispersion process (dependence or the global velocity vector on the local space coordinate). Is shown to be irremovable from the global transport equation by any linear transformation via the solute partition matrix. In the canonic form of the global equation the irremovable coupling is manifested by the traceless parts of the global solute velocity matrix and the global solute dispersivity.

The solution scheme is illustrated by calculating the mean global diffusivity of a solute consisting of two components, transport of which is coupled at the microscale via the molecular diffusivity matrix. At the macroscale the coupling is shown to be represented by negative off-diagonal terms of the global diffusivity matrix,     

EFFECTS OF SURFACE VISCOELASTICITY IN THE ENTRAPMENT AND DISPLACEMENT OF RESIDUAL OIL

Qualitative analyses are developed to explain the role that surface viscoelastieity could be playing during the entrapment and displacement of residual oil. The characteristic time of a simple surface fluid, which is a measure of the memory of the interface for past stress-deformation behavior, is taken to be a measure of the degree of surface viscoelastieity. The approach taken is similar to that used by Slattery (1974, 1979), in two prior qualitative analyses of displacement.

The entrapment of residual oil in the smaller pores of an oil-wet rock would be enhanced by reducing the degree of surface viscoelastieity. We predict a similar effect during a free or forced displacement of oil by water in a water-wet structure. No conclusions can be drawn for a restricted displacement of oil by water in a water-wet rock.

For values of the interfacial tension less than the critical value, the rate of displacement of residual oil will increase as the degree of surface viscoelastieity is decreased.     

Interfacial Dynamic Properties and Dilational Rheology of Sulfonate Gemini Surfactant and its Mixtures with Quaternary Ammonium Bromides at the Air–Water Interface

The dynamic interfacial properties and dilational rheology of gemini sulfonate surfactant (SGS) and its mixtures with quaternary ammonium bromides (DTAB, CTAB) at the air–water interface were investigated using drop shape analysis. Results suggest that the adsorption process of these surfactants is diffusion-controlled at dilute concentrations, whereas the adsorption mechanism gradually shifts to a mixed kinetic-diffusion control with increasing surfactant concentration. The mixed surfactant system possesses the best surface activity when the molar ratios of SGS/DTAB and SGS/CTAB mixtures are 9:10. The formation of catanionic complexes shields the electrostatic repulsion between surfactant molecules and lowers the electrostatic adsorption barrier. Therefore, SGS/DTAB and SGS/CTAB mixtures exhibit higher adsorption rates than either component alone. The effects of oscillating frequency and surfactant concentration on the surface dilational properties of SGS, DTAB, CTAB, SGS/DTAB, and SGS/CTAB mixtures were also determined. As the oscillating frequency increases, the dilational elasticity of these surfactants gradually increases. The dilational elasticity peaks at a certain concentration, which is less than the critical micelle concentration (CMC). Results show that the dilational elasticity of SGS/DTAB and SGS/CTAB mixtures is higher than that of either component, resulting from the formation of a denser monomolecular adsorption layer at the air–water interface. Our study provides a basis for understanding the interaction mechanism of catanionic surfactant mixtures containing Gemini surfactant at the air–water interface.     

The Role of the Interface in Carbon Fibre-Epoxy Composites

The final performance of a composite material depends strongly on the quality of the fibre-matrix interface. The interactions developed at the interface were studied using the acid-base or acceptor-donor concept.

The surface characteristics of the carbon fibres and the epoxy matrix were studied using a tensiometric method and the inverse gas chromatography technique. Acid-base surface characters could be determined allowing the interactions at the interface to be described by a specific interaction parameter.

It was shown that the shear strength of the interface, as measured by a fragmentation test, is strongly correlated to this specific interaction parameter, demonstrating the importance of acid-base interactions in the fibre-matrix adhesion.     

THE FLOODING CAPACITY OF PERFORATED PLATES IN ROTATING LIQUID-LIQUID-SYSTEMS†

Centrifugal extractors found wide applications in the industry, but up to now very little is known about what happens inside and how to calculate fluid-dynamic and mass transfer. For the basic research of dispersed liquid-liquid-systems in centrifugal fields a model centrifuge was built which is resistant to the high loads produced by rotation and which enabled us to observe the flow mechanism at the flooding points.

The processes inside have been measured and photographed by a high-speed-camera.

The calculation of centrifugal extractors is based mainly on the contact surfaces of the phases and the contact times. The maximum flow or flooding capacity is determined by three limits. Two of them are determined by the interface locations inside, controlled from the back pressure. The third limit is given by the maximum combined flow. This limit is dependent on the set of internals, the rotor speed and the physical properties of the liquid system. The experimental results will be shown and compared with new theories for the flooding capacities of perforated cylindrical plates in rotating liquid-liquid-systems.

The results predicted using the mathematical model for calculating the capacities are in fair agreement with the measurements.     

Freeze-Drying of Pharmaceutical Crystalline and Amorphous Solutes in Vials: Dynamic Multi-Dimensional Models of the Primary and Secondary Drying Stages and Qualitative Features of the Moving Interface

Dynamic and spatially multi-dimensional mathematical models of the primary and secondary drying stages of the freeze-drying of pharmaceutical crystalline and amorphous solutes in vials, are constructed and presented in this work. The models account for the removal of free and bound water and could also provide the geometric shape of the moving interface and its position. It is proved that the temperature of the moving interface can not be constant if the flux of heat flow to the sides of the vial is not zero. It is also proved that the slope of the free surface (moving interface) at the edge of the vial is always curved downward.

The numerical solution of the nonlinear partial differential equations of the models would allow model simulations that could indicate design conditions, operating conditions, and control strategies that could provide high drying rates and could lead to a series of novel experiments in freeze-drying.     

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.     

ATMOSPHERIC CONTACT DRYING OF GRANULAR BEDS WETTED WITH A BINARY MIXTURE

When regarding the atmospheric contact drying of granular beds wetted with a liquid mixture, both the drying rate and the selectivity of the process, i.e. the change of moisture composition, are of interest. The batch drying of a free flowing ceramic substance, wetted with a 2-propanol-water mixture, is investigated in a rotary dryer with heated wall and air flow.

The theoretical analysis is based on physical models for heat and mass transfer, moisture migration and particle transport, which are presented in examples.

The experimental and theoretical results show that higher selectivities can be achieved by reducing the particle size because of the lower liquid-phase mass-transfer resistance. An increase of the rotational speed leads to a higher drying rate with slightly decreased selectivity if the particles are sufficiently small, since contact heat transfer is enhanced.     

SCALE-UP OF CONTACT DRYERS

The scale-up of contact dryers is still based on experimental drying curves. In order to keep the effort to a minimum the drying curve is determined using a small laboratory or pilot dryer of similar geometry to the production dryer.

This paper introduces a new scale -up method for contact dryers. The new scale-up method is based on the assumption that heat transfer is the controlling mechanism. The scale-up method is derived from the material balance, the energy balance, the kinetic equation of heat transfer and thermodynamic equilibrium. The scale up method can be used to convert the drying time required to achieve a certain residual moisture content from the laboratory or pilot dryer to the production dryer and/or different drying conditions.

The scale-up method was verified by drying test with four different products in conical mixer dryers of 1, 60, 250, 1000 I volume. Two products were free flowing and two products were non free flowing in the wet state. The products can be considered non-hygroscopic in the moisture range investigated.     

Corona-discharge Treatment of Polypropylene films-Effects of Process Parameters

Corona treatment of films, mainly polypropylene (PP)-copolymers, was studied at commercial levels in a 2.7 kVA treater. The films were produced on a flat-film extruder with chill rolls. Degree of treatment was characterized by power of the generator divided by web speed and width of film (m Ws/cm²).

The effectiveness of the treatment was measured in terms of the polar and dispersion components of surface-energy, the peel adhesion of pressure sensitive tape (similar to ASTM Adhesion Ratio) and the peel adhesion of polyurethane adhesives.

The polar component of surface energy is a measure of the effectiveness of corona pretreatment. For a given degree of treatment, the polar surface energy component becomes greater as the film cooling rate increases (and the degree of crystallization falls).

A comparison of homopolymers and copolymers does, however, reveal that even where these have the same density or the same degree of crystallization one cannot count on them having equally-sized polar components.

Peel strengths of pressure-sensitive tapes and polyurethane-bonded patches confirm the influence of cooling conditions on wetting properties.

Contrary to the case for tape adhesion, the polyurethane adhesive strengths reach their maximum value at much lower treatment intensities, i.e. with much lower polar surface energy components, and thus question the validity of the ASTM tests for adhesion properties.     

Adhesion of Plasticized Polyvinyl Butyral) to Glass

A study of safety glass provides a good example of the interplay among the many physical properties involved in “adhesion”, and the relationship between adhesion and performance. This work demonstrates the value of applying known fundamentals to practical problems.

An idealized model of a windshield fracture event is described in terms of interactions among mechanical responses of the interlayer, the fracture characteristics of the glass and the high speed, low angle peel behavior.

Data on the surface energies of glass, polyvinyl butyral) and water show that at thermodynamic equilibrium a stable system comprising glass, water and polyvinyl butyral) phases, an aqueous phase must lie between the glass and PVB.

The potassium salts are shown to be effective because they are deliquescent and give solutions at equilibrium with the water in the PVB at water contents of ∼0.40% or higher. The greater the amount of salt at the interface and the higher the water content of the sheeting during lamination, the thicker the interfacial layer and delamination occurs more readily. This relationship is quantified using a modified form of the Stefan equation.

Data on diffusion of water and salt are shown to be consistent with the amount of salt at the interface required for the observed performance (∼ 3 mg KAc/m²).

Data on electrical resistivity of the interface correlate with peel force and provide convincing support for the hypothesis.     

RECIRCULATING REACTOR FOR THE STUDY OF MULTIPHASE KINETICS

A new laboratory reactor was set up to measure kinetic coefficients in a solid (catalyst)-liquid-gas reacting system.

The reactor consists of two parts: an absorber, where the liquid is partially saturated by the gas reactant and a reacting zone, where the liquid alone, containing the dissolved gas, flows through a fixed bed of catalyst.

The ricircle of the liquid in the absorber maintains a high concentration of the gas reactant in the liquid also in the zone of reaction, allowing the use of a high mass of catalyst (significative from a statistical point of view) and the achievement of sufficiently high conversion.

The tested reaction is the catalysed hydrogenation of ∝-metylstyrene: in order to consider a drastic situation and to verify the results with the literature data, the experimental conditions examined corresponded to very high chemical reaction rate (instantaneous reaction) at the surface of the pellets.

The tests were carried out with the reactor working both in batchwise and in continuous operative mode (steady state); the results show the reliability of the new reactor above all when the steady state operation is considered. For the use of the reactor in batchwise condition, the accumulation of the product inside the catalyst particles must be considered for an accurate measurement of the kinetic parameters,     

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.     

MIXED COBALT-BASED CATALYSTS IN AUTOXIDATION OF AQUEOUS SO2

The kinetics of aqueous sulphur dioxide autoxidation catalyzed simultaneously by ions of two different transition metals was studied. Basing on the mechanism of a chain reaction the rate equation for oxygen consumption has been derived. Interaction of the ions in redox steps was assumed. The equation was tested against experimental data collected during oxygen absorption performed in a gas-liquid reactor with a plane interface. Two catalytic systems were used in the experiments: CoSO₄-Fe₂(SO₄)₃ and CoSO₄-MnSO₄

The predicted occurrence of a minimum value of oxygen absorption rate at a certain concentration ratio of metal ions constituting a mixed catalyst was confirmed for both systems. Other phenomena related to the possible removal of a catalyst or sulphite from the place of reaction were also discussed.     

Welding Mechanisms of Plastics: A Review

Strength of welded joints is a function of technological parameters of the production process. The type of function is dependent on the welding mechanism. Different mechanisms were found under various welding conditions. The processes included in the plastic welding mechanism are divided into two groups:

1) Processes which realize the joining of the parts.

2) Processes which create conditions for the first group to proceed. The first series of processes includes:

a) diffusion of macroradicals, molecular segments or molecules of the polymer which can be either in a solid, melted or dissolved state.

b) convective mass transfer.

c) recombination of macroradicals across the contact surface.

d) physical (surface) interaction.

e) any combination of processes described above.

The second group contains:

a) formation of the real contact surface.

b) formation of the macroradicals.

c) destruction and removal of inert layers which prevent real contact of active material.

Each process and the conditions of its proceeding are discussed individually.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.     

HEAT EFFECTS FOR PHYSICAL AND CHEMICAL ABSORPTION IN TURBULENT LIQUID FILMS

An eddy diffusivity model was used to describe simultaneous heat and mass transfer for chemical absorption in turbulent liquid films. For absorption accompanied by a first-order reaction an approximate expression for the mass transfer coefficient is derived and shown to be in excellent agreement with exact numerical calculations. An equation is developed for the temperature rise at the free surface due to both the heat of reaction and the heat of solution. Relationships are also developed for the concentration of the liquid phase product at the free surface and the depletion of the liquid phase reactant at the free surface.

The temperature rise at the free surface for gas absorption accompanied by an instantaneous reaction due to both the heat of solution and the heat of reaction was determined. An equation is also derived for the concentration of liquid phase product at the free surface for the case of an instantaneous reaction.