Drop size distribution in a graesser contactor

An investigation was conducted of drop size distribution in a Graesser contactor, employing five liquid – liquid systems, viz., kerosene/water, benzene/water, xylene/water, hexane/water and n–butyl acetate/water. A 100 mm (4 inch) diameter Graesser contactor was used for this purpose It was found that the drop size distribution in a Graesser contactor obeys the upper – limit distribution expressed as: where A correlation was developed relating the Sauter mean diameter (d₃₂) to other effective groups      

The kinetics and mechanism of the chloride-chlorate reaction

The kinetics of the reaction have been studied at 25°C. in strong acid solution; the effects of acidity, chloride, chlorate and chlorine are reported. A mechanism is postulated to interpret the peculiar features of this reaction as well as the stoichiometry and some of the kinetics of the parallel reaction The mechanism involves HClO₂ and HOCl as intermediates General rate expressions are derived for the formation of chlorine dioxide and chlorine, and the individual rate constants are calculated. An expression is obtained for the relationship between the ratio of chlorine dioxide to chlorine produced and the ratio of chlorate to chloride.     

The uniform film model for the gravitional approach of fluid drops to plane and deformable interfaces

Axisymmetric drainage within thin planar or spherical films of viscosity μ, area A and uniform thickness δ at time t is governed by the equation where F is the force pressing on the film and n the number of immobile interfaces. Assuming that the film ruptures at a critical thickness which is independent of the physical properties and applied force, expressions of the form may be obtained for drops approaching rigid and deformable interfaces and rigid spheres approaching deformable interfaces. The values of the exponents a, b and c suggest that an increase in drop volume, V, and density difference, δρ, and a decrease in interfacial tension, σ, should increase the coalescence time, τ, in liquid-liquid systems. However in gas-liquid systems an increase in δρ should decrease the coalescence time. The variation of δ with time was obtained experimentally from capacitance measurements. For drops approaching a deformable interface, the corresponding values of n are always close to 1 and in the region between 0 and 2. The values increase when the interfaces are made less mobile by adding surface active agents; they are also larger for drops approaching a rigid interface and for rigid spheres approaching a deformable interface. Consequently the uniform film model adequately describes the approach of drops to rigid and deformable interfaces.     

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     

Jet penetration measurements in a venturi scrubber

The maximum centreline penetrations, l^**, of cross-current liquid jets in a Venturi scrubber were measured for orifice diameters, d, of 1.397, 2.108, 2.565 and 3.860 mm. The data are correlated by for the range of conditions, 36 ≤ gas throat velocity V_g ≤ 125 m/s; 1.2 ≤ liquid injection velocity V_j ≤ 18 m/s; 0.06 ≤ liquid to gas ratio      

Struktur und eigenschaften von ABS-polymeren II.. Grenzviskositäts-molekulargewichtsbeziehungen für azeotrope styrol/acrylnitril-copolymerisate

Limiting viscosity numbers of azeotropic copolymers of styrene and acrylonitrile were measured in dimethylformamide (DMF) and in methyl ethyl ketone (MEK). Their weight average molecular weights (10⁴ g/mole ? M_w ? 10⁶ g/mole) were determined by light scattering. The viscosity – molecular weight relationships obtained, are for DMF and for MEK The number average molecular weights were determined by osmotic pressure measurements, and now molecular weight heterogenities were calculated. The homogenity in composition was investigated by light scattering measurements in different solvents. In addition the viscosity-molecular weight relationship for polystyrene in DMF was determined and compared with the relationship for the azeotropic poly (styrene-co-acrylonitriles) and for polyacrylonitrile: On account of the results a possibility is shown for calculating molecular weights of poly (styrene-co-acrylonitrile) of any composition from limiting viscosity numbers and the acrylonitrile contents.     

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.      

A modified correlation to predict the minimum velocity required to elutriate solids from a liquid-fluidized bed

The consideration of sphericity of solids for the prediction of u_me gives rise to some improvement of the correlation proposed earlier by the author. In the absence of wall-effect, the following correlation is obtained: which gives a standard deviation of ± 16.3% for 138 different experiments as against ± 21.6% for 134 runs by the correlation reported earlier. The ranges of the various groups are      

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.     

Thermal reactions between MII sulphates and acid orthophosphates in the solid state

Two general types of high temperature reactions between M^II sulphates and acid orthophosphates have been found and a survey of some representative examples has been made. The reactions are typified by two examples using Ca²⁺ salts: and . Similar reactions have been found for other alkaline earth sulphates and phosphates and for corresponding mixed alkaline earth systems. The products have been found to be largely determined by the phase relationships in the respective M^IIO–P₂O₅ systems.     

Prediction of steady-state dispersion height in the disengaging section of an extraction column from batch settling data

The decay of a dense dispersion formed under calm conditions is given by Experiments in a batch vessel with different liquid-liquid systems and initial drop diameters show that the dimensionless constant K is equal to 26,000. This agrees with the value previously determined from the variation in steady-state dispersion height with throughput in spray columns, the analogous equation being The results can thus be used to predict the height of the dispersion formed in the disengaging section of extraction columns.     

A one-point intrinsic viscosity method for polyethylene and polypropylene

A statistical analysis of dilute solution viscosity data for a wide range of polyethylene and polypropylene samples in Decalin at 135°C has shown that the Martin equation fits the experimental data better than the Huggins equation at higher values of [η]c. A grand average k of 0.139 is applicable to both polymers. Based upon this, tables have been calculated permitting the ready determination of [η] from a single relative viscosity measurement at a known concentration. The Martin equation has been put into a universal form, permitting [η] to be calculated from a measured η_sp if k and c are known. Graphs relating η_sp to [η] are included for use of the Martin equation over wide ranges of both k and c. It was found that the Solomon and Ciuta equation fits the experimental polyethylene and polypropylene data, and the reasons for this are discussed.     

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.     

Thermal conductivity of simple gases at normal pressures

Thermal conductivity measurements available in the literature for simple gases at normal pressures (approximately 1 atmosphere) were used to obtain the product k^*λ, where the parameter, λ =M^1/2T_c^1/6/P_c^2/3. Separate relationships between k^*λ and T_R resulted for monatomic, diatomic and triatomic gases. The relationships for monatomic gases can be expressed as follows For the diatomic and triatomic gases, linear relationships resulted, when at the same reduced temperatures, their k^*λ values were plotted against (k^*λ)_m on log-log coordinates. These relationships can be expressed in equation form as follows and Thermal conductivities calculated with these relationships have been compared with experimental values and produce an average deviation of 2.8% for the monatomic gases (219 points), 4.3% for the diatomic gases (282 points) and 4.6% for the triatomic gases (242 points). In this treatment, helium and hydrogen do not follow the general pattern and consequently these substances have been treated separately.     

Densities of hydrocarbons in their saturated vapor and liquid states

The Sum and differences of the saturated vapor and liquid densities of 23 hydrocarbons were used to develop the following reduced density relationships for these saturated states The hydrocarbons considered included n-parafins, olefins, diolefins, naphthenes, and aromatics. Constants β, γ, and δ, and exponent n were found to be dependent on,. Equation (a) can reproduce liquid densities with an overall average deviation of 1.1 % over the entire temperature range, while Equation (b) was found to apply only in the interval 0.900 ≤ T_R ≤ 1.00 with an average deviation of 2.2%. For temperatures of T_k < 0.90, the saturated vapor density was found to depend on temperature as follows where k and m were also found to be Z_c dependent. Values calculated using Equation (c), when compared with 81 available experimental densities for 12 hydrocarbons, produced an average deviation of 3.0%.     

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      

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.     

Spin coating behavior of polyimide precursor solutions

Experimental data confirm the utility of the following simple equation in predicting the spin coating behavior of polyimide precursor solutions: in which .     

Hydrolysis of 1,4-cyclohexanedimethanol-based copolyester

The solid state hydrolysis of a copolyester based on a mixture of 1,4-cyclohexanedimethanol and ethylene glycol condensed with terephthalic acid was studied at 100°C and 57 to 96 kPa water vapor partial pressure (55% to 95% relative humidity). The equilibrium water sorption in weight percent (C_∞) was found to be where P is the water vapor partial pressure in kPa. For specimens 0.32-cm thick, it took about 24 h to reach 0.9C_∞. The intrinsic viscosity (IV) was measured and used to calculate the relative change in molecular weight (M?_w) from the relationship IV ∝? (M?_w)^0.7. The decrease in molecular weight was linear with time, and the rate of decrease was found to be proportional to C_∞; the empirical correlation is where the rate constant, k, is in day^?1. A decrease of 50% in M?_w was observed after 22 days at 95% relative humidity.     

Some aspects of liquid-solid fluidized beds

Hydrodynamic characteristics of randomly packed fluidized beds were investigated using particles of different sizes and densities fluidized with water. The minimum fluidization velocity was found to be independent of the initial bed height. The minimum fluidization velocity was found to be Bed expansion followed the Richardson Zaki relationship and the exponent 'n' has been correlated as: