Surface Energy Analysis of Carbon Fibers and Films

Amorphous and graphitic carbon fibers and film surfaces are characterized by wettability measurements and surface energy analysis which isolate the (London-d) dispersion γ^d_svand (Keesom-p) polar γ^p_sv contribution to solid-vapor surface tension γ_sv =γ^d_sv + γ^p_sv Graphitized carbon fibers which are surface treated to provide strong bonding to polar matrix resins show consistent strong polar contributions to total surface tension with γ^d_sv|γ_sv ≃ γ^p_sv|γ_sv ≃ 0.50. Amorphous carbon films prepared for biological implant applications display dominant dispersion character in surface energy with γ^d_sv|γ_sv ≃ 0-74 to 0.95 and γ^p_sv|γ_sv ≃ 0.05 to 0.24.     

Surface Energy Analysis of Treated Graphite Fibers

Wettability measurements and surface energy analysis are applied to isolate the (London-d) and (Keesom-p) polar contributions to solid-vapor surface tension γ_sv=γ^d_sv + γ^p_sv of surface treated graphite fibers. Surface treatments include metal coatings with Al, Cu, and Ni, chemically reducing heat treatments in H₂ and vacuum, and films of highly chlorinated polymers such as polyhexachlorobutadiene and polychloral. This study shows that the highly polar surface properties γ^p_sv|γ_sv ≃ γ^d_sv|γ_sv ≃ 0.50 of commercial graphite fibers can be modified by surface treatment to display dominant dispersion character with γ^d_sv|γ_sv ≃ 0.79 to 0.92 without substantial reduction in total surface energy γ_sv. For adsorption bonded fiber/matrix interfaces a new method of mapping the surface energy effects of an immersion phase upon the Griffith fracture energy γ_G is applied to define criteria for strong interfacial bonding under both air and water immersion.     

PHYSICAL ABSORPTION OF CARBON DIOXIDE IN WATER FLOWING IN AN INCLINED CELL

Studies of the mass transfer mechanisms which occur when CO₂ is absorbed into flowing water films in an inclined cell are described. The amount of gas absorbed is small and therefore a highly sensitive optical apparatus was used to obtain direct concentration readings. Gas bulk concentrations in the liquid were obtained by titration. The experimental work was mainly confined to angles of inclination less than 5^°.

Hydrodynamic studies showing increased flow rates at the sides of the inclined cell, due to meniscus effects, are presented. Hydrodynamic “end effects” at the liquid exit from the cell, which cause increases in the absorption, have been successfully minimised by the design of the apparatus and the experimental technique employed.

It is demonstrated, for angles of inclination less than 3^°, that convective disturbances (in the form of micioflows, eddies or perturbations) are present in the liquid. These perturbations are not visible or directly determinable. They produce an increased solute transport from the liquid surface over that which can occur by molecular diffusion alone. Beyond 3^° inclination the disturbances or perturbations persist and are reinforced by hydrodynamic instabilities eventually leading to observable wave formation.     

ESTIMATION OF EFFECTIVE SHEAR RATE FOR AERATED NON-NEWTONIAN LIQUIDS IN AIRLIFT BIOREACTOR”“

Effective shear rate is one of the indispensable parameters for the design of aerobic fermentors using a viscous non-Newtonian system. The estimation of effective shear rate in airlift loop bioreactors has been investigated with liquid circulation velocity. An empirical correlation of effective shear rate in airlift loop reactors is proposed.

γ_eπ= 3.26-3.51 ; 10²U_G + 1.48 10⁴U²_G

It is found that the effective shear rate is lower in airlift reactors than in bubble columns. This equation can be used for the cultivation of cells sensitive to shear stress.     

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.     

OPTIMAL TUNING OF A PRACTICAL DIGITAL PID CONTROLLER

Optimal Tuning of a practical digital PID controller is studied by using the performance indices such as ITAE. IAE. ITSE, and ISE. A simplex searching method that uses the flexible polyhedron is used to find the optimal parameters in the controller. Tuning relations for each of the controller parameters are correlated into the forms that have been used by C.L. Smith and his co-workers. That is:

P = A(θ/γ)^B

or

P = A(θ/γ) + B.

It is noted that the present tuning relations are more practical in determinations of PID parameters when digital computers or micro-processors are used to implement the practical PID control. For control practice, the use of the existing tuning relations without precautions may result in poor performance in some cases.     

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.     

Physico-Chemical Criteria for Maximum Adhesion. Part II: A New Comprehensive Thermodynamic Analysis

In this paper, two parameters defined as the relative work of adhesion [W_A/γ_L] and the relative interfacial energy [γ_SL/γ_L] have been examined for their assumed usefulness in correlating the thermodynamic properties of the components of the system substrate/ adhesive with its practical performance (strength). It is shown that the minimum value of [γ_SL/γ_L] relevant to conditions for the maximum adhesion becomes zero only for those systems (relatively rare) for which interaction factor Φ₀ is equal to 1.0.

Several transition points were identified for boundary conditions acquired at θ = 0° and θ = 90° which can be used to predict the properties and performance of an adhesive joint. These transition points are: a_MIN—energy modulus of the system (E. M. S.), relevant to the minimum interfacial energy; a_S—E. M. S. where self-spreading of adhesive occurs; a_CRIT—E. M. S. relevant to conditions under which the thermodynamic work of adhesion becomes negative and the system exhibits a tendency for self-delaminating or has “zero-strength”; a_CF—E. M. S. beyond which the geometry of the interface at any interfacial void or boundary of the joint may be regarded as a crack tip.

It is shown that only in those systems for which Φ₀ = 1.0 can a minimum contact angle of 0° indicate a condition for the maximum strength. If Φ₀ is known, the optimum contact angle can be estimated and hence the optimum surface energy of the substrate (adjusted by surface treatment, etc.) for the maximum adhesion.     

TRANSITION OF FLOW REGIME IN FLUIDIZED BEDS WITH SLANTING BLADE BAFFLES

A flow model is proposed to investigate the transition of flow regime from bubbling to turbulent fluidization postulating that the flow in the emulsion phase follows the Richardson-Zaki equation.

Void fraction of the whole bed ε_f and the mean velocity of bubbles U_b were measured in fluidized beds of 0.3 and 0.5 m ID, in which slanting blade baffles were positioned. Mo-catalyst, silica gel, sand and glass beads with size between 135-443 μm were fluidized by air.

Void fraction of the emulsion phase ε _e was calculated on the basis of the above model. Correlating ε _e with superficial gas velocity U_ƒ, we found that ε _e was very close to ε _mƒ in the bubbling regime and that e, increased with increasing U_ƒ in the turbulent regime.

Calculated values of the volume fraction of bubble phase δ were correlated with U_ƒ, from which apparent transition point from bubbling to turbulent regime was estimated. Combining information obtained, transition of flow regime in the above type of fluidized beds is discussed     

A SEMI-EMPIRICAL MOLECULAR ACTIVITY COEFFICIENT MODEL WITH IRREGULAR PARAMETER DISTRIBUTION

A new semi-empirical molecular model was proposed to predict activity coefficients, using two adjustable binary parameters. For γ_i's of 20 mostly polar, associated and dimerizable binary and 7 ternary systems, average relative root mean square deviation of 0.0373 and 0.0369 respectively were achieved.

It was shown that in most cases the new model is more suitable for correlating VLE data than the Wilson (0.0783, 0.0859), NRTL (0.0461, 0.0483), UNIQUAC (0.2598, 0.0546) and modified UNIOUAC (0.0580, 0,0558) equations*     

The Anisotropy of the Surface Tension of Polar Liquids: The Case of Liquid Crystals

The contact angle of the liquid crystal (LC) 4-phentyl, 4'-cyano biphenyl (5CB) on glass or polyethylene does not correspond to the value expected from its surface tension measured by the “du Nouy” method (29 × 10^-3 JM^-2). The value deduced from the Young-Dupre law is 40 × 10^-3 JM^-2.

Both these values have already been reported in the literature. Their apparent discrepancy is explained by the LC surface tension anisotropy. We show that 5CB as many other LCs orient perpendicular to the free surface but parallel to glass or polyethylene Thus both values of the surface tension correspond to two different molecular orientations.

The LC oriented perpendicularly has a surface tension of 29 × 10^-3 JM^-2 and 40 × 10^-3 JM when it lies parallel to the surface. We suggest that the anisotropy between the perpendicular and parallel state of LCs also exists between two perpendicular orientations. Furthermore, such anisotropy associated with any polar molecules explains the difference of the interfacial energy of similar polar or non polar (i.e., octanol-octane) compounds and water.     

A CONTINUUM ANALYSIS OF SURFACE TENSION IN NONEQUILIBRIUM SYSTEMS

The intermolecular forces that cause surface tension in multiphase systems at equilibrium give rise to pressure gradients in nonequilibrium systems. The present paper treats such systems within a framework of thermodynamics and continuum mechanics and uses a generalization of the conceptual experiment of Rowlinson and Widom which applies to systems with curved interfaces and to nonequilibrium situations where the phase interfaces are not fully developed. The pressure tensor has a component p_n acting in the direction normal to the concentration gradient and a component p_t acting in the plane tangent to the surface of constant concentration where

P_n —P_t = k(∇c)² The concentration gradient causes an additional volumetric force not present in homogeneous fluids

Here, k.- is the gradient energy parameter appearing in the Landau-Ginzburg functional, c is the concentration of the key component, ₁, and R₂ are the principal radii of curvature for the surface of constant constration, n is a unit vector normal to that surface, and ∇, is the gradient along the surface. The volumetric force generates pressure gradients in systems with curved interfaces at equilibrium or can drive flow in nonequilibrium situations.     

THE ROLE OF THE VOLUME-AVERAGED TEMPERATURE IN THE ANALYSIS OF NONISOTHERMAL, MULTIPHASE TRANSPORT PHENOMENA

The analysis of nonisothermal transport phenomena in multiphase systems is almost always accompanied by the use of some type of volume-averaged or spatially-smoothed temperature. In such systems one always encounters parameters, such as a reaction rate coefficient or a viscosity, that are temperature dependent. Given the point relation for some generic parameter in the β-phase, i.e., ψ_β = ψ_β(T_β), one can wonder how the volume-averaged form of this parameter depends on the volume-averaged temperature. In this paper we show that the local volume-averaged form of ψ_β is given by

$

in which A represents a second order tensor that depends on the system parameters. A somewhat more complex form is encountered for area-averaged functions of the temperature. These functions are especially prevalent in reactor design calculations, which are considered both in terms of early intuitive developments and from the perspective of the method of volume averaging.     

ELECTROHYDRODYNAMIC ENHANCEMENT OF NUCLEATE BOILING HEAT TRANSFER IN HEAT EXCHANGERS

The effect of a radial d.c. electric field on nucleate boiling heat transfer was investigated experimentally using a single-tube shell/tube heat exchanger. A dielectric liquid (Freon R. 114) was used in the shell and the tube was heated by circulating water through it.

It was found that the application of a sufficiently intense electric field to the boiling heat transfer surface resulted both in the elimination of boiling hysteresis and the enhancement of heat transfer for the range of superheat studied. An application of approximately 20 kV was more than sufficient to eliminate the hysteresis.

It was also observed that there appeared to be a transition between two situations. At lower superheat there is an appreciable improvement in the heat transfer coefficient due to both initial (0 to 10 kV) and incremental (10 to 20 kV) voltage increases. At higher superheat, however, the greater improvement (about four times) is obtained with the initial voltage application     

Low-rate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions

Low-rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/n-butyl methacrylate) P(MMA/nBMA) copolymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 6 liquids yield non-constant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid- vapour surface tension times the cosine of the contact angle changes smoothly with the liquid-vapour surface tension, i.e., γ_iv cos θ depends only on γ_iv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and noninert (polar and non-polar) surfaces [34-42, 51 -53]. The solid-vapour surface tension calculated from the equation-of-state approach for solid -liquid interfacial tensions [14] is found to be 34.4 mJ/m², with a 95% confidence limit of \pm 0.8mJ/m², from the experimental contact angles of the 6 liquids.     

A Reinterpretation of Organic Liquid-Polytetrafluoroethylene Surface Interactions

The wettability of polytetrafluoroethylene (PTFE) by organic liquids is reanalyzed in terms of dispersion-polar interactions across the liquid-solid interface. The analysis provides values of γ_s^d = 19.6 dyne/cm, and γ_S^D = 2.0 dyne/cm for the respective dispersion and polar parts of the surface tension γ_s = 21.6 for PTFE. The definition of a polar contribution to the surface tension of PTFE clarifies detailed aspects of the wettability of this polymer by different homologous liquid series. A modified analytical definition for work of adhesion is developed and applied to this discussion.     

CONTINUOUS GAS SEPARATION WITH LIQUID IMPREGNATED PARTICLES IN GAS-SOLID REACTORS

The absorption of a gas in liquid filled porous particles in gas-solid reactors was studied both theoretically and experimentally. In the theoretical study a micro mode!, describing mass transport accompanied with reaction inside the particles, was implemented in the macro balance for several asymptotic operation modes. The theoretical study showed that the gas separation can be carried out very efficiently with the liquid filled porous particles, especially for the countercurrent mode of operation. The results of the simulations for the removal of H₂S from a gas stream also containing CO₂ showed that a very selective absorption process can be obtained. For these kind of selective absorption processes the simulations showed that the residence time of the particles is a crucial parameter

In the experimental part of this contribution the absorption of CO₂ in porous y-alumina particles filled with water or 2M aqueous solutions of tertiary - or primary alkanolamines was investigated. Experiments were carried out in a gas-solid reactor where the particles were falling down in an empty tube while gas was flowing co- or countercurrently. The conversion for the particles filled with water or the aqueous primary alkanolamine was predicted satisfactorily. For the particles filled with the tertiary alkanolamines, however, the experimental conversions were much higher than theoretically predicted. This difference probably must be attributed to an underestimation of the surface adsorption of CO₂ on the γ-alumina carrier which was very important for the slowly reacting tertiary alkanolamines     

Physico-Chemical Criteria for Maximum Adhesion. Part I: Theoretical Concepts and Experimental Evidence

This paper presents an analysis of the literature with the aim of defining basic criteria and developing a general model to describe joint strength. Two particular cases of the relationship: cosθ = f(γ_L) have been identified as prerequisites for further analysis of interfacial phenomena and conditions governing their existence were discussed.

The fact has been pointed out, based on available experimental results, that for the most important case in practice where 0.6 ≤ cosθ ≤ 1.0, the relation cos θ = f(γ_L) can be treated as rectilinear. This finding will be utilized in the comprehensive development of criteria defining joint performance in Part II.

Variability of the interaction factor Φ for various systems has been investigated in relation to cos θ, for the identified particular cases of the relationship cos θ = f(γ_L) A special value of the interaction factor, ₀, was found. The importance of the rectilinear particular case of cos θ = f(γ_L) was shown, which involves constant factor Φ₀ instead of variable Φ.     

The Strength of Liquid Bridges Between Dissimilar Materials

The strength of the liquid bridge between a sphere and a plate of dissimilar materials was studied. An equation was derived using the surface energy approach. For small amounts of liquid, the force of adhesion f was f=2πRy(cosθ₁ + cosθ₂ where R is the sphere radius, y is the surface tension, and θ₂, θ₂ the contact angles. In the derivationn, major simplications about the meniscus shape were possible.

The equation was experimentally tested with water, ethyl alcohol, aniline and iodobenzene using factorial combinations with different solids. Force of adhesion measurements were carried out using a tensile testing machine at controlled loading rates. Excellent agreement was obtained in the experimental and predicted adhesion values. The McFarlane-Tabor equation was identified as correct only for small amounts of liquids and similarly wet solids.     

IMPORTANCE OF DISPERSED SOLIDS IN BUBBLES FOR EXOTHERMIC REACTIONS IN FLUIDIZED BEDS

Ignition of activated carbon particles were measured in a vertical tube reactor of 4 cm ID, where single particles fell consecutively through a gas mixture containing oxygen.

A two dimensional fluidized bed reactor 24 cm wide, 51 cm high and 2.5 cm in thickness was used for visual observation through a wide front window 24 cm × 35 cm covered with a silica glass plate 1 cm thick. Activated carbon particles were fluidized incipientiy by air, and a gas mixture containing oxygen was injected upwards into the bed through a nozzle positioned 5 cm above the distributor, forming single bubbles intermittently.

It was observed that carbon particles dispersed in rising bubbles were ignited abruptly at emulsion phase temperatures above 550°C. Experimental findings from the fluidized bed were compared with those from the tube reactor, suggesting that the igniting conditions for particles dispersed in bubbles are nearly the same as for single particles falling in the tube reactor.