Prediction of Axial Mixing for a Structured Packed Column Using a Two‐equation Model

A theoretical model based on the recently developed two‐equation method is proposed to predict the axial mixing behavior in a structured packed column. By solving the proposed model, the process of tracer injection experiments for determining the axial back‐mixing coefficient of structured packing can be simulated. Consequently, the axial Bodenstein number and dispersion coefficient under liquid single‐phase or gas‐liquid two‐phase flow conditions can be calculated. The validation of the proposed method is tested by simulating the two‐phase fluid flow behavior in Flexipac 2 structured packing. The simulated results are compared with the experimental data and satisfactory agreement is found between the simulation and the experiments.     

The behaviour of the dispersed phase in liquid-liquid cocurrent flow through a packed bed

The drop size distributions produced by the cocurrent flow of kerosene dispersed in water through a vertical column packed with spheres have been measured at different levels of flow rate, volume fraction dispersed phase, packing diameter and height of packed bed. The drop size measurements were made by isolating and photographing a portion of the dispersion as it emerged from the packing. The Sauter mean diameter is predicted by: where C is a constant, f(?) is the phase fraction effect, ∈ is the power input per unit volume, τ is the residence time and d_p is the packing diameter.     

A general correlation for purely viscous non-newtonian fluids flowing in ducts of arbitrary cross-section

An alternative correlation for the flow of purely viscous non-Newtonian fluids in ducts of arbitrary cross-section is proposed. It involves two dimensionless groups which are Unique relationships exist between ? and Re^*_G for both laminar and turbulent flows which enable direct predictions of pressure drop from flow rate results or vice-versa. Excellent agreement between the new correlations and available experimental data for purely viscous non-Newtonian fluids flowing in circular tubes and square ducts is demonstrated.     

Local heat transfer coefficients in a model “falling film” scraped surface exchanger

Utilization of an accurate technique to measure the local heat transfer coefficient in thin falling film scraped surface exchangers yields results which indicate that the local heat transfer coefficient is dependent on N^0.5 and, above a certain rotational speed, independent of axial flow rate. Both of these observations are in agreement with the theoretical penetration model. The results, however, are generally lower than would be expected from the theory, and as a result, heat transfer may be described by the penetration model in combination with an empirical factor, f. This term is based on the liquid physical properties and gives a measure of the intensity of cross sectional mixing within the liquid, i.e. where f, is defined as      

Thermodynamics of polymer solutions and blends

To describe the thermodynamic behavior of binary and larger polymer blends, the Hoch-Arpshofen model is used to describe highly asymmetric phase diagrams, and asymmetric enthalpies of mixing, where the miscibility gap and the extremum of the enthalpy of mixing leans toward one of the components. The Gibbs energy of mixing of polymer blends is described as where z can be mole fraction, volume fraction, or weight fraction. The Hoch-Arpshofen model contains an interaction parameter W = A + B*T independent of composition and an integer number n (2, 3, 4, …), which defines the asymmetricity of the binary phase diagram and of the Gibbs energy of mixing curve. In a binary system n defines the composition where the Gibbs energy of mixing is maximum or minimum or the composition is where the temperature of a miscibility gap is maximum or minimum. In a binary system A-B the maximum effect occurs at A_n–1B. The disorder reaction in polymers is treated as a transformation temperature, and defines T₀, the temperature where the ordered and disordered material is equal.     

Catalytic oxidation of benzene to maleic anhydride in a continuous stirred tank reactor

The kinetics of the vapor phase oxidation of benzene has been studied over an industrial catalyst in a continuous stirred tank reactor in the temperature range from 280 to 430°C and at atmospheric pressure. The products obtained are maleic anhydride, carbon oxides and water. The rate of the overall reaction (disappearance of benzene) is represented by the following expression based upon a steady state adsorption model The rate of formation of maleic anhydride is correlated by the equation which allows for a homogeneous depletion of maleic anhydride. The rate constants k_B, k_O, k_2(g) were found to follow Arrhenius behavior.      

Hydrodynamicst axial mixing and mass transfer in rotating disk contactors

Correlations for predicting characteristic velocity both above and below the critical rotor speed have been obtained under conditions with and without solute transfer. It has been found that (1) above the critical rotor speed, the characteristic velocity U₀ is proportional to g/D_rN², whereas below this value a transition region exists where U_o is proportional to (g/D_rN²)^0.26; (2) multiple regression analysis of the experimental data of continuous phase axial mixing shows that the axial dispersion coefficient varies not only with the rotor speed and modified velocity of continuous phase but also with the velocity of dispersed phase. With varying RDC operations, the true value of K_od corrected for axial mixing changes continually between the limiting values predicted from stagnant and fully turbulent drop models. However, the highest experimental values were only 30 to 40% of those predicted by the Handlos-Baron model at the same drop Peclet number.     

Polymeric composite systems with two continuous phases

A general mixture rule, which has the correct type of phase symmetry, is proposed for estimating the properties of composites having two continuous phases. The form of this equation is different from the equations used to predict the properties of composites with one continuous phase and one dispersed phase. The proposed equation for property P is where the volume fractions of components A and B are ø_A and ø_B, respectively, and n is a constant. A simple model is used to correlate the morphology of systems having two continuous phase with the parameter n of the mixture rule. The connectivity of the phase varies with concentration. The properties, such as elastic modulus, depend primarily upon the modulus of the material with the higher modulus. In general, the properties depend very little on the morphology of the system.     

The apparent rate constant model for kinetics of radical chain copolymerization: Chemical-controlled process

In this article the kinetics of chemical-controlled radical-chain copolymerization have been reduced to pseudohomopolymerization kinetics by introducing the apparent rate constants, The methods for the determinations of the values of the apparent rate constants, mode of termination, and the methods for the calculation of molecular weights and distributions are proposed. The data required for these determinations and calculations are simply obtained by the usual steady-state method. According to the traditional kinetics along with the definitions of the apparent rate constants, these apparent rate constants as functions of traditional rate constants, monomer compositions, and copolymer compositions are derived. Further utilizing the theoretical expressions obtained, we show that the apparent rate constants are the general rate constants for both radical chain homo- and copolymerizations. The bulk radical copolymerizations of methyl methacrylate and styrene at various monomer feed compositions at 60°C are used to test the proposed model. The empirical apparent rate constants obtained are described well, by the following expressions, and and the mode of termination on the combination termination is where K and K denote the apparent rate constants of propagation and termination, respectively. The term f₁(= 1 ? f₂) stands for the mole fraction of styrene in the monomer solution fed. F₁ is the copolymer composition produced at f₁. β is the mode of termination.     

Flow transition for natural convective heat transfer in a porous medium saturated with water near 4°C

In this paper, the problem of buoyancy-induced convection flow in water-saturated porous media near 4°C is examined using a numerical model. Darcy's law is used to model flow behavior and a single equation convective heat transfer model is used for the energy equation. As the Boussinesq approximation is not valid for this case, a parabolic dependence of density on the temperature is used. Natural convection is generated and sustained by a uniform heat source. Flow behavior is governed by three natural parameters appearing in the model. They are: (i) dynamical parameter, (ii) geometric parameter, γ = b/a; and (iii) wall temperature, in relation to the reference temperature at the density extremum. For certain ranges of θ_w (<0) and Gr, interesting density inversion effects are possible. Transient solutions are obtained for various aspect ratios and modified Grashof number values. For a wide range of Grashof number, steady state solutions could not be obtained. Flow mutations into periodic and chaotic solutions are investigated for a range of Grashof number (100 to 40,000) and aspect ratio values (1 to 10).     

The longitudinal mixing of liquids in bends

The longitudinal mixing of liquids flowing through straight pipes may be characterized by the coefficient of longitudinal dispersion K. In the case of pipings equipped with bends, the value of K must be extended by ΔK expressing the more intense longitudinal mixing in bend areas. Physically, the value of ΔK is determined by the secondary flow in pipe bends. The dependence of ΔK upon the Reynolds number N_R = 15 180-73 180/, the bend length /α = 30°.90°/ and the proportional bend curvature /R/D = 2-6/ has been measured on a 50,8 mm - diameter pipe. These dependences are expressed by empirical equations. Each of these partial results is further discussed from the view of relationships valid for secondary flows. The individual values of dependence are summarized in a final equation expressing the simultaneous effect of each observed variable upon the value of ΔK, i. e.      

Mass transfer in the entrance region for axial and swirling annular flow

Rates of mass transfer to the inner core of an annular flow system have been determined for the mass transfer entry region using the limiting current density method. Both in laminar and turbulent flow, the hydrodynamic and concentration boundary layers were not fully developed. The variation of the mass transfer coefficients with length of core section has been demonstrated, and the data for swirling flow correlated by the equation for 1500<Re < 14000, 1500 < Sc < 6200 and 1.75 < L/D^e < 10.14. The data for axial flow in the entry region have been correlated by the equation. for 1800 < Re < 12500 and Sc = 2604. Mass transfer enhancement in the entry region due to swirl when compared to axial flow-systems with a jetting transverse inlet is only noticeable for Re > 6000, but is very significant compared to systems with fully developed boundary layers in axial or swirling flow.     

Measurements of Pore Size Distribution,Porosity, Effective Oxygen Diffusivity,and Tortuosity of PEM Fuel Cell Electrodes

The characterization of proton exchange membrane fuel cell electrodes is essential for understanding the electrode performance. In this paper, mercury intrusion porosimetry and the nitrogen adsorption method were used to measure pore size distributions and porosities (ϵ) of various electrodes, which were made with either platinum supported on amorphous carbon (Pt/V_A) or platinum supported on graphitized carbon (Pt/V_G), and had ionomer‐to‐carbon weight ratios (I/C) of 0.5, 1.0, and 1.5. The oxygen effective diffusivity ( ) in electrodes was measured as a function of relative humidity (RH) in an apparatus that was previously described [Z. Yu, R. N. Carter, J. Power Sources 195 (2010) 1079–1084]. The tortuosity of electrodes at the dry condition (80 °C and 0% RH) was then determined from the measured porosities and . For a given catalyst, as the I/C ratio increased, it was found that the electrode's mean pore size, porosity, and all decreased, but the tortuosity increased. For a given I/C ratio, the Pt/V_A electrode exhibited larger mean pore size, larger porosity, larger , and smaller tortuosity compared with the Pt/V_G electrode. The contrast between Pt/V_A and Pt/V_G electrodes with the same I/C ratio indicates different ionomer distribution on the catalyst surface.     

Versatility of a succinimidyl‐ester functional alkoxyamine for controlling acrylonitrile copolymerizations

Styrene/acrylonitrile (S/AN) and tert‐butyl methacrylate/acrylonitrile (tBMA/AN) copolymers were synthesized in a controlled manner (low polydispersity $ {{\overline M _w } / {\overline M _n }} $ with linear growth of number average molecular weight $ \overline M _n $ vs. conversion X) by nitroxide mediated polymerization (NMP) with a succinimidyl ester (NHS) terminated form of BlocBuilder unimolecular initiator (NHS‐BlocBuilder) in dioxane solution. No additional free nitroxide (SG1) was required to control the tBMA‐rich copolymerizations with NHS‐BlocBuilder, a feature previously required for methacrylate polymerizations with BlocBuilder initiators. Copolymers from S/AN mixtures (AN molar initial fractions f_AN,0 = 0.13–0.86, T = 115°C) had $ {{\overline M _w } / {\overline M _n }} $ = 1.14–1.26 and linear $ \overline M _n $ versus conversion X up to X ≈ 0.6. tBMA/AN copolymers (f_AN,0 = 0.10–0.81, T = 90°C) possessed slightly broader molecular weight distributions ( $ {{\overline M _w } / {\overline M _n }} $ = 1.23–1.50), particularly as the initial composition became richer in tBMA, but still exhibited linear plots of $ \overline M _n $ versus conversion X up to X ≈ 0.6. A S/AN/tBMA terpolymerization (f_AN,0 = 0.50, f_S,0 = 0.40) was also conducted at 90°C and revealed excellent control with $ \overline M _n $ = 13.6 kg/mol, $ {{\overline M _w } / {\overline M _n }} $ = 1.19, and linear $ \overline M _n $ versus conversion X up to X = 0.54. Incorporation of AN and tBMA in the final copolymer (molar composition F_AN = 0.47, F_tBMA = 0.11) was similar to the initial composition and represents initial designs to make tailored, acid functional AN copolymers by NMP for barrier materials. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Elutriation characteristics of solids from liquid fluidized bed systems Part I: Onset of elutriation

Experimental data for the minimum elutriation velocity u_me of solids for 134 different systems have been correlated by The ranges of the different groups investigated were as follows: For all of the experiments, the fluidizing liquid was water and the tube had an inside diameter of 4.92 cm. The standard deviation for the above correlation is 21.6 per cent.     

Stress relaxation behaviour of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

The stress relaxation behaviour of liquid crystal-forming ethyl celllulose (EC) solutions in m-cresol was determined by means of a cone-plate type viscometer at 30°C. The effect of molecular weight (MW) on the behaviour was also determined. The relaxation behaviour could be fitted with the following equation: where σ_i and σ_f are steady-state shear stresses at shear rate $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, σ(t) is time- dependent stress, A₁ and A₂ are constants, τ₁ and τ₂ are relaxation times, t is time, and t_c is a characteristic time. When log σ* was plotted against time, one straight line was obtained for isotropic solutions, whereas anisotropic solutions yielded two straight lines. This suggests that the liquid crystalline solutions have two separate relaxation processes: Process 1 has a relatively short relaxation time, and process 2 has a long one. The parameters τ₁, τ₂, and A₂ were greatly dependent on polymer concentration, combination of $\dot \gamma _{\rm i}$ and $\dot \gamma _{\rm f}$, and MW, whereas A₁ was independent thereof and was close to unity. The process 1 was supposed to be valid for individual molecules, and process 2 for liquid crystalline domains or randomly aggregated or entangled molecules.     

Preparation,structure, and properties of two-phase co-continuous polymer blends

Phase continuity has been explored as a function of composition for three two-phase polymer blends produced by mixing in the melt: polystyrene/poly(methyl methacrylate), polystyrene/cis-polybutadiene, and poly(methyl methacrylate)/ethylene-propylene rubber. The condition for dual phase continuity Is the application of shear close to phase inversion and this can be predicted fairly accurately using the relation where 1 and 2 are the blend components, η is viscosity, \documentclass{article}\pagestyle{empty}\begin{document}$\mathop \gamma \limits^.$\end{document} is the shear rate in the mixing device used to produce the blend and ? is volume fraction. The co-continuous materials, which we call Interpenetrating polymer blends (IPBs) are non-equilibrium structures and are subject to disruption by changes in flow regime.     

Drainage of thin films beneath parabolic and spherical caps

The variation in film thickness h with time t for the approach of an infinite sphere to a plane horizontal surface (β = 1) or of two infinite spheres (β = 2) is given by: For finite spherical caps with edge radius r_f the variation is much more complicated and also involves the parameter S = βr²_f/2ah_o. Fortunately, the gradient is the same in both cases, providing t is large enough (the critical value of t increases with decreasing S). A similar result is obtained if the spherical cap is approximated by a parabolic cap with apex curvature 1/a equal to that of the sphere. In both cases the variation in dynamic pressure close to the centre of the draining film is identical and independent of the radial position where the dynamic pressure falls to zero when the film thickness is small. MacKay and Mason (1961) measured the film thickness beneath a sphere of finite size approaching a horizontal plane and experimentally verified Equation (b). This does not however, as they assumed, prove the correctness of Equation (a), which only applies to infinite spheres. The more complicated equations describing the approach of finite spheres and parabolic caps are presented in this paper.     

The glassy state,ideal glass transition,and second‐order phase transition

According to Ehrenfest classification, the glass transition is a second‐order phase transition. Controversy, however, remains due to the discrepancy between experiment and the Ehrenfest relations and thereby their prediction of unity of the Prigogine‐Defay ratio in particular. In this article, we consider the case of ideal (equilibrium) glass and show that the glass transition may be described thermodynamically. At the transition, we obtain the following relations: and with Λ = (α_gβ_l − α_lβ_g)²/β_lβ_gΔα²; and The Prigogine‐Defay ratio is with Γ = TV(α_lβ_g − α_gβ_l)²/β_lβ_gΔβ, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of ΔC_V and Γ, the ratio may take a number equal to, larger or smaller than unity. The incorrect assumption of perfect differentiability of entropy at the transition, leading to the second Ehrenfest relation, is rectified to resolve the long‐standing dilemma perplexing the nature of the glass transition. The relationships obtained in this work are in agreement with experimental findings. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 143–150, 1999