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.     

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      

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     

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.     

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      

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.     

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      

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.     

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.     

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.      

Relationship in polypropylene melt between its linear viscoelasticity and its steady capillary flow properties

It is the object of the present study to obtain clear knowledge of the relations in the polypropylene melt between its linear viscoelasticity and its nonlinear steady capillary flow, paying particular attention to the elastic properties in its capillary flow. By representing the linear viscoelasticity numerically with zero-shear viscosity, η₀, and steady-state compliance, J, evaluation has been made of the properties concerning the elasticity of polymer melt in the capillary flow, such as non-Newtonianity, the entrance pressure loss, the end correction, the Barus effect, and the melt fracture. The steady flow viscosity η, the entrance pressure loss P₀, the critical shear stress, τ_c, and the critical shear rate $\dot \gamma _c$ at which melt fracture begins to occur are subject to η₀ as follows: From the well-known relationship between η and the weight-average molecular weight M?_w, these quantities are governed by M?_w. Meanwhile, for such quantities as structural viscosity index N, end correction coefficient ν, and elastic pressure loss ratio P₀/P, following correlations hold: As η₀ and J are respectively determined mainly by M?_w and the molecular weight distribution MWD, these quantities are governed by both M?_w and MWD. Physical meanings of η₀·J and η₀² · J are, respectively, mean relaxation time and a measure of stored energy in steady flow. The Barus effect has a positive correlation to J, ν, and P₀/P. (The symbol ∝ employed here means positive correlation.)     

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%.     

Effectiveness factors for heat transfer in fluidized beds

Rates of heat transfer associated with the evaporation of water from the surface of porous particles into air were measured for both packed and fluidized beds. Direct measurements of the temperature on the surface of these particles permitted the calculation of the heat transfer coefficient, h_g, for both packed and fluidized bed systems. An effectiveness factor, χ, has been introduced to account for the non-plug flow characteristics of fluidized beds. This quantity has been used to define the rate of particle to gas heat transfer as follows where (δt)_m represents the log-mean temperature difference across the bed and h_{g b} is the heat transfer coefficient at the initiation of two phase fluidization defined as the “bubble point”. An analysis of the experimental measurements indicates that where g represents the ratio of the heat transfer factor of the fluidized bed to that corresponding at the bubble point of this bed. This effectiveness factor has also been related to the void fraction ratio as follows where ?_t, and ?_p, are the void fractions of the fluidized bed and its corresponding packed bed arrangement. This equation applies for ?_t/?_p > 1.22.     

Predicting elastic moduli of heterogeneous polymer compositions

A new method for predicting elastic moduli M of heterogeneous polymer compositions is proposed. It is based on a phenomenological adjustment between parallel and series models for upper and lower bound moduli M_U and M_L. Thus, where ?_H is the volume fraction of hard phase, ?_S is the volume fraction of soft phase, and n is the only adjustable parameter since the upper and lower bound moduli are given by and where M_H and M_S are the moduli of the pure hard and soft phases, respectively. Predicted values of M are in agreement with measured values in a number of systems which include polyblends and composite materials of fixed morphology. The significance of n is discussed relative to concentrations in the area of a phase transition for the polyblends or relative to phase morphology in the case of fixed morphology compositions. Interestingly, the relationship, by analogy, is in agreement with measured values of polyblend melt viscosities.     

Kinetics and mechanism of the thermal decomposition of potassium persulphate ions in aqueous solutions at 50°C in the presence of nitrogen gas and methacrylonitrile monomer

The initial rate of persulphate (I) decomposition at 50°C in the presence of nitrogen and methacrylonitrile (MAN) in an unbuffered aqueous solution (pH 4–7) may be written as: in the concentration ranges of persulphate (I) (0.25–2.50) × 10^?2 (m/dm³) and of (MAN) 0.18–0.36 (m/dm³). During the reaction, a white substance (polymethacrylonitrile) separates out in the colloidal state or in the precipitate form from the medium depending on the ionic strength of the medium. The pH of the medium was found to decrease rapidly and continuously with time in the absence of methacrylonitrile, but it decreased slowly and continuously with time in the presence of the monomer, MAN. If an additional quantity of MAN is injected late in a run, the rate of persulphate decomposition is further accelerated in a given run. However, the rate of persulphate decomposition is found to decrease continuously in the presence of MAN with time, i.e., as the monomer is converted to polymer. It is suggested that MAN accelerates the decomposition of persulphate ions, due to the following reactions in the aqueous phase: and where (M_j^˙)w is a-water soluble oligomeric or polymeric (j = 1–10) free radical. The estimated values of k₅ and k₁₀ are 1.05 × 10^?5 and 1.14 × 10³ (in dm³/m/s), respectively.     

The shape of a fluid drop approaching an interface

The shape of a fluid drop approaching an interface does not change appreciably with time and is very close to the equilibrium dimensions, in spite of the large pressure gradient which is present in the draining film. This is because the net vertical force due to the excess pressure in the draining film above that in the drop is identical with that for an equilibrium film being zero for a plane interface and —2Rσ sin² ? for a deformable interface. Employing this result in a force balance around the drop which is independent of the bulk interface shows that the area A of the draining film between a fluid drop of volume V and a deformable fluid-liquid interface is given by where σ is the interfacial tension and Δρ the density difference between the drop and surrounding fluid, 1/b is the curvature at the top of the drop and h is the distance between this point and the edge of the draining film which is inclined to the horizontal at an angle ?. When the interface is a rigid plane the overall curvature 1/R of the draining film and the volume v enclosed by it, together with the angle ? are all zero. The limiting cases of the expression for very small and very large drops agree with those previously established for both deformable and rigid interfaces. An approximate expression which applies when cV^2/3 (where c = Δρg/σ) is between 0.6 and 13.5 and which gives A to within ± e% is where for a rigid plane interface and for a deformable interface When the densities of the drop and bulk heavy fluids are equal, but their respective interfacial tensions σ₁₂ and σ₂₃ with the light fluids are different, the expression becomes which estimates A/V^2/3 to within about ± 25% for σ₁₂/σ₂₃ in the range 0.11 to 9.0 and cV^2/3 (where c = Δρg/σ₁₂) between 0.6 and 13.5.     

Transferts thermiques entre un serpentin et des fluides newtoniens ou non—newtoniens agités par une turbine à pales inclinées dans une cuve

The present work deals with the heat transfer from a hélicoïdal worm to newtonian or non-newtonian liquids, which and stirred by a 4 pitched blade-turbine in a cylindrical tank. The effective viscosity of the pseudoplastic liquids is determined by the Metzner-Otto model combined with the Ellis rheological equation. The heat transfer in the newtonian fluids in a turbulent system is most precisely represented by the following equations: (a) (b) In the case of non-newtonian fluids and of downward pumping, the following equation enables to obtain a very precise evaluation of the heat-transfer coefficient in a transitional flow.      

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.     

Some aspects of nonisothermal crystallization of polymers. III. Crystallization during melt spinning

Crystallization during melt spinning is studied as an example of the nonisothermal crystallization of polymers. The following equation is derived, taking the temperature distribution within a filament into consideration: where T = temperature, X = crystallinity, κ = thermal diffusivity, V = velocity, ΔH = heat of crystallization, and C_p = specific heat at constant pressure. The assumptions and the procedure for a numerical calculation of crystallinity and temperature within a running filament are described, and some results of calculation are illustrated. The results are compared with those obtained by a simpler calculation in which the radial temperature distribution is neglected. The simpler method proved useful in connection with x-ray measurements.     

A one-point intrinsic viscosity method for hydroxyethylcellulose,hydroxypropylcellulose, and sodium carboxymethylcellulose

Statistical analysis of viscosity measurements on dilute solutions of hydroxyethylcellulose (HEC), hydroxypropylcellulose (HPC), and sodium carboxymethylcellulose (CMC) in the solvents water, 50/50 (v/v) water/ethanol, and 0.1M NaCl, respectively, demonstrated that the Martin equation, fits experimental data better than the Huggins equation, An average Martin k of 0.191 is applicable to a variety of HEC and HPC samples, including fractionated and unfractionated experimental and commercial preparations covering a wide range of substitution. In the case of a similar variety of CMC samples, an average k of 0.161 is characteristic. Based on these k values and using the Martin equation in the form tables were developed which permit direct reading of [η] values corresponding to single η_rel measurements at concentrations of 0.05, 0.10, 0.20, or 0.50 g/dl. Intrinsic viscosities obtained in this fashion differ from those determined by the usual dilution multipoint technique on the same samples by an average of but 2%, at an estimated time saving of 50% or more. This degree of variation is no greater than that expected in routine measurements on duplicate solutions.