Solid state extrusion of semicrystalline polymers

The dynamics of solid state extrusion of polypropylene, high density polyethylene, and poly(tetrafluorethylene) have been investigated at various extrusion temperatures and piston velocities. A model of solid state extrusion of semicrystalline polymers is proposed. The formulae are obtained relating the value of the extrusion pressure with the parameters of the process and polymer properties. It has been found that for certain values of the parameters, defects of two main types emerge. A mechanism of defect formation is suggested.     

Determination of the transfer coefficient of natural turbulence occurring near the solid-propellant gasification zone. I. Two-phase model of the gasification zone

A model for solid propellant gasification is proposed which contains a two-phase medium in an intermediate stage. The formation of the gas phase proceeds in two ways: chemical reactions result in gaseous products, which, in turn, initiate the formation of bubbles in which vapor forms from the liquid phase of the propellant. Gaseous products play an important role only in the very early stage of bubble development; their critical pressure is used to determine the minimum size of gas-phase nuclei. The bubble volume grows primarily by evaporation of the liquid phase. A kinetic equation for the bubble concentration and the necessary boundary conditions are formulated. Arguments are given suggesting that a temperature maximum cannot occur in the gasification zone and that natural turbulence can be generated by collapsing bubbles. The sound produced by solid propellant combustion is explained by the collapse of a huge number of microscopic bubbles. If the processes in the two-phase zone are neglected, the formulated system of equations is transformed into the Belyaev–Zel’dovich model equations.     

脱硅中液固循环流化床清洁传热

考察了铝土矿熟料溶出粗液脱硅加热过程中的结垢行为,采用有机-无机复合材质的惰性固体颗粒研究了循环流化床对脱硅加热过程中硅渣结垢的清除及防止性能.结果表明：硅渣结垢曲线为具有诱导期的渐近式曲线,硅渣结垢机理为结晶结垢和微颗粒沉积结垢混合机理;循环流化床不仅能有效防止硅渣结垢的形成,而且能完全清除已有的硅渣垢层,硅渣结垢的清除速率随操作流速及固体颗粒浓度的增大而增大;惰性固体颗粒的引入不影响硅渣结垢的机理.根据液固流化床的防垢机理建立了结垢模型,其预报值与实验值吻合较好.     

Methane and ethane activation without adding oxygen: promotional effect of W in Mo-W/HZSM-5

The conversions of methane and ethane over Mo/HZSM-5 and W/HZSM-5 catalysts are compared. A reaction model for hydrocarbon formation over Mo/HZSM-5 catalysts is proposed, which involves heterolytic splitting of methane and a molybdenum-carbene intermediate. Ethene is shown to be the initial product of methane conversion, and it undergoes further reaction to form aromatics in a solid acid environment. The promotional effect of addition of tungsten in the Mo-W/HZSM-5 catalyst in methane conversion reaction suggests the formation of Mo-W mixed oxide. The product selectivity patterns of Mo/HZSM-5 and W/HZSM-5 catalysts in ethane conversion reaction are consistent with a dual-path model involving dehydrogenation and cracking (or hydrogenolysis) of ethane. The rates of both these reactions over Mo/HZSM-5 are higher than over W/HZSM-5.     

Reactions of solid particles with nonuinform distribution of solid reactant: The volume reaction model

The effect of non-uniform solid reactant distribution on conversion of solid particles in gas-solid reactions is analyzed based on the volume reaction model. Certain special features of such systems are pointed out. The possibility of ash layer formation in the kinetically controlled regime is discussed. Conditions leading to single or double ash layer formation, both at the center and surface of the particle, in the intermediate regime of diffusion with simultaneous reaction are described. Detailed mathematical equations which are useful for calculation of the conversion-time relationship for particles with non-uniform solid reactant distribution are presented. Comparison is made to reaction of uniform particles and differences in required reaction time for desired conversion are outlined.     

Synthesis of Solid, Spherical Zirconia Particles by Spray Pyrolysis

A model is used to predict solid particle formation during spray pyrolysis by correlating droplet shrinkage before salt precipitation with its relative solution saturation. For the rapid drying conditions and droplet size of ∼ 10 μm, which are characteristic of conventional spray pyrolysis, solid salt particles are formed when a droplet's initial relative solution saturation is ∼ 10⁻² and the precipitated salt is sufficiently permeable to permit evolution of the remaining solvent after precipitation. It is proposed that this concentration allows the drying droplet more time and a shorter diffusion distance in which to maintain chemical homogeneity before precipitation. Using these concepts it is demonstrated that zirconyl chloride (ZrOCI₂· 8H₂O) and zirconyl hydroxychloride (ZrO(OH)CI) are excellent zirconium salts for solid zirconia particle synthesis by spray pyrolysis.     

Modeling the rheology of gelatin gels for finite deformations. Part 2. Viscoelastic solid model

The viscoelastic solid model proposed in this work can predict the rheological responses of gelatin gels for finite deformations. This rheological model considers a degree of physical cross-links at a given maturation time, which is partially attained from those links totally available when a pure elastic network is achieved. Thus, both an elastic network formed by permanent links on the average and a viscoelastic network composed of the remaining adaptive links are described at each maturation time. This model for gelatin gels considers appropriately the interplay between the networks involving: (a) viscoelastic relaxation as a consequence of an imposed mechanical history, (b) average degree of physical cross-links in the partially generated permanent network acting in the short-term mechanical response. In this context of analysis the standard viscoelastic solid is obtained asymptotically for small deformations. Also the effect of shear rate on the shear test is studied and the braking phenomenon is analysed in relation to the formation of microstructure by considering viscoelastic parameters.     

Thermodynamics of wax formation in the fischer-tropsch synthesis products

A new method is suggested for calculating the thermodynamic equilibrium in a multicomponent multiphase system without chemical reactions. This method is based on ideas of statistical physics and non-equilibrium thermodynamics and includes numerical minimization of the Gibbs energy of the complex system. Component concentrations and the physically realizable roots of the equation of state are calculated as the steady state solutions of the set of ordinary differential equations that is implied by the procedure of seeking the probability maximum for the realization of the equilibrium distribution. The approach developed here is used to calculate the equilibrium distribution of the concentrations of vaporous, liquid, and solid substances in the Fischer-Tropsch synthesis products. A thermodynamic model of the formation of solid paraffins from the synthesis products is presented. The calculation of the properties of pure substances and liquid and gaseous products is based on the Lee-Kesler equation of state. The wax formation thermodynamics is considered in the regular solid solution approximation (Hildebrand-Scott model) and in the solid solution approximation taking into account the nonideality of the system (NRTL model). The calculated mass fractions of vaporous, liquid, and solid synthesis products are presented as a function of temperature for different values of the chain propagation constant.     

Equation of State of Explosion Products on the Basis of a Modified Van der Waals Model

A semi-empirical model is proposed for the equation of state of high explosives in a range of pressures and temperatures typical of detonation processes. A possibility of formation of solid phases (e.g., graphite or diamond) in the gas is implied. The model can be used to calculate all thermodynamic quantities for arbitrary molecular compositions and to calculate the thermodynamically equilibrium molecular (and phase) composition. An iterative scheme of calculations is proposed. The model contains several empirical functions whose form can be changed without violating the overall calculation scheme. A particular set of these functions is considered as an illustration. Some results calculated for a number of high explosives containing four elements (C, H, N, and O) are presented. The calculated results are compared with available experimental data. __________ Translated from Fizika Goreniya i Vzryva, Vol. 42, No. 1, pp. 87–99, January–February, 2006.     

Model of reactive diffusion upon ion exchange and phase formation in a glass

A phenomenological model for “reactive diffusion” of ions, atoms, or molecules in a solid stationary medium has been advanced by the example of the ion exchange in a glass-molten salt system. The kinetic curves are obtained for the diffusion process accompanied by the formation (in the diffusion layer) of a new structure differing in diffusion properties from the initial structure. Consideration is given to the case when the interaction between the mobile diffusant and the stationary matrix results in partial or complete fixation of diffusant by the new forming structure. It is shown that the equation for the second Fick law and a number of other known diffusion equations are the limiting particular cases of the reactive diffusion model proposed.     

Model of reactive diffusion upon ion exchange and phase formation in a glass

A phenomenological model for “reactive diffusion” of ions, atoms, or molecules in a solid stationary medium has been advanced by the example of the ion exchange in a glass-molten salt system. The kinetic curves are obtained for the diffusion process accompanied by the formation (in the diffusion layer) of a new structure differing in diffusion properties from the initial structure. Consideration is given to the case when the interaction between the mobile diffusant and the stationary matrix results in partial or complete fixation of diffusant by the new forming structure. It is shown that the equation for the second Fick law and a number of other known diffusion equations are the limiting particular cases of the reactive diffusion model proposed.     

液固搅拌槽中固、液相停留时间分布

本文以海沙和自来水为介质研究了在标准搅拌槽内影响固液两相停留时间分布的主要因素,以便比较两相之间的差异,并利用双区模型描述出口流体中固体和液体的停留时间分布。对所建立模型中的参数进行估值后,建立了模型参数与搅拌雷诺数、固体颗粒浓度及搅拌槽几何参数之间的关联式。     

Gas-solid reaction model for a shrinking spherical particle with unreacted shrinking core

A heterogeneous reaction model is developed to represent the gas-solid reaction consisting of two-step reactions: formation of a solid intermediate on the core of unreacted solid and consumption of the solid intermediate. The presented model takes into account the shrinkage of both the unreacted core and the solid particle itself. The model successfully represents the fluorination of uranium dioxide where uranium hexafluoride gas is produced through uranyl fluoride as a solid intermediate. The rates of the shrinkage are discussed in detail for general cases by solving an ordinary differential equation for two radii of the particle and the unreacted core. Two parameters, the ratio of the reaction rates between the two steps and the non-dimensional diffusion rate of a reactant gas into the intermediate, control the rates of the shrinkage. Effective range of the model is specified in terms of the two parameters.     

Single bubble formation in high pressure liquid—solid suspensions

Bubble formation from a single nozzle is investigated analytically and experimentally in nonaqueous liquid and liquid—solid suspensions at pressures up to 17.3 MPa. A mechanistic model is proposed to predict the initial bubble size in liquid—solid suspensions, by taking into account the various forces affecting the bubble growth including those induced by the presence of the particles, such as the suspension inertial force and the particle-bubble collision force. It is found that the initial bubble size in the suspensions is generally larger than that in the liquid mainly due to the inertia effect of the suspension. The initial bubble size increases with the solids holdup. The pressure has an insignificant effect on the initial bubble size in both the liquid and liquid—solid suspensions under the conditions of this study. The model can reasonably predict the initial bubble sizes obtained in this study and those reported in the literature.     

Solid Solutions of Silicon Oxide in Mullite

An explanation is proposed to account for the possibility of formation of solid solutions of silicon oxide in mullite. The difference in the diffusion coefficients of cations in complex oxides leads to the formation of a solid solution of the oxide containing the cation with the lower diffusion coefficient in the complex oxide and a phase containing the cation with the higher diffusion coefficient or rich in this oxide. Using yttrium or scandium additives, which are chemisorbed on the surface of aerosil (SiO₂ source), it is possible to make the rate of diffusion mass transfer of aluminum cations higher than that of silicon cations and thus obtain a solid solution of silicon oxide in mullite.     

Modelling the morphological evolution of nanosuspension droplet in constant-rate drying stage

A novel mathematical model of constant-rate stage of nanosuspension droplet drying is proposed. In contrast to previously published literature studies, the developed model considers two morphologically different periods of the constant-rate drying: before the shell formation and after the shell formation; the latter was named “transition period”. The point of initial “locking” between nanoparticles on the droplet surface and beginning of the shell formation is associated with theoretical maximum of solid volume fraction. It is postulated that shrinking and thickening shell of nanoparticles occurs fast, and thus the shell virtually remains submerged in the liquid during the overall transition period. Because of the submerged shrinking shell, in the transition period, the evaporation process still takes place from the droplet surface and the drying rate remains unchanged as it was before the shell formation. Correspondingly, the droplet temperature retains at the level of equilibrium evaporation temperature. The developed theory was successfully validated by the published experiment of silica nanosuspension droplet drying. Finally, the developed model proposes a simple morphology criterion based on comparison between the calculated droplet volume at the end of transition period and the corresponding volume of solid final particle with the given porosity.     

Deposit Growth on Chemical Reactor Walls and the Associated Heat and Mass Transfer

A mathematical model is formulated for the crystallization of the product of a bimolecular reaction in a laminar flow of a viscous solution containing foreign solid particles that serve as crystallization centers. A model is reported for the layerwise formation of a deposit consisting of the reaction product crystals and the foreign solid particles on the walls of a continuous flow reactor. A classification of the deposits is suggested, and the formation rate of the deposits of some types is calculated in the framework of the formulated model. The role of the reactor design in deposit formation is disclosed. The hydrodynamic interaction between the crystals formed in a reactor and those deposited on its walls is studied.     

A model of an evolutionary route for the preparation of functional materials

A mesokinetic model of the formation of a solid substance and the change in its properties under the action of factors that transform a substance into a functional material is proposed. Equations are introduced that represent the conditions of preservation of the number of molecules and particles of the substance during their nucleation, growth, and aggregation in supersaturated environments as well as during the ordering of the particles after the imposition of a temperature field and the introduction of additives. The equations describe the rate of change in the state distribution function of particles and can be reduced to the Liouville equation and the Fokker-Planck equation. The model contains unknown frequency functions subject to experimental determination. After these functions are determined, the model makes it possible to construct a methodological scheme for seeking the optimum route for the preparation of a new nanomaterial with desired properties.     

Correlation and estimation of solubilities of fatty acids in supercritical carbon dioxide using solution model approach

In this study, solid solubility data of five fatty acids in supercritical carbon dioxide (CO₂) at different temperatures and pressures are correlated using a two-parameter solution model developed from the regular solution model coupled with the Flory⿿Huggins equation. The developed solution model with fewer parameters yields correlated results comparable to those from commonly used semi-empirical equations. In addition, both parameters in the solution model can be further generalized with the chain length of fatty acids and a new predictive solution model is proposed for solubility prediction. The predictive solution model proposed in this study provides better predicted results and yields average deviation in predicted solubilities of 22.1%. To further apply this solution model to other compounds, solid solubility data of three triglycerides in supercritical CO₂ at 313 K are also correlated. After model simplification and generalization, a new predictive solution model for triglycerides is also proposed, which yields average deviation in predicted solubilities of 29.8%. These results demonstrate that the solution model used in this study is applicable for correlation and prediction of solid solubilities of structure-related compounds in supercritical CO₂.