A new perspective on vegetable oil epoxidation modeling: reaction and mass transfer in a liquid-liquid-solid system

A rigorous mathematical model was developed for a complex liquid-liquid-solid system in a batch reactor. The approach is general but particularly well applicable for the indirect epoxidation of vegetable oils according to the concept of N. Prileschajew. The model considers intra- and interfacial mass transfer effects coupled to the reaction kinetics. The liquid phases were described with chemical approach (aqueous phase) and a reaction-diffusion approach (oil phase). The oil droplets were treated as rigid spheres, in which the overall reaction rate is influenced by chemical reactions and molecular diffusion phenomena. The model was tested with a generic example, where two reactions proceeded simultaneously in the aqueous and oil phases. The example (i.e. fatty acid epoxidation à la Prileschajew) illustrated the power of the real multiphase model in epoxidation processes. The proposed modelling concept can be used for optimization purposes for many applications, which comprise a complex water-oil-solid catalyst system.

MODEL REPRESENTATIONS OF THE MELTS STRUCTURE DESCRIPTION BY THE MODEL OF HARD SPHERES

In the article the optimization of the oil and gas enterprise, a complex process both from the technological and from the economic point of view is investigated. It is noted that today the development of methods of mathematical modeling of physical processes, for example, in oil fields on the basis of theoretical research and modern computer technology is absolutely relevant One of the ways is to create new or improve existing mathematical models of processes occurring in oil and gas reservoirs, and calculate on their basis the characteristics of the process that optimize production. From this perspective, the study appears particularly relevant liquids in a narrow, purely physical and chemical aspects – namely melt. Various fluid models have been proposed to describe the equilibrium and kinetic properties of liquids (melts), as well as to interpret experimental results. Model representations are also used in solving integrodifferential equations that relate distribution functions to interaction potentials. It is noted that integrodifferential equations are a powerful mathematical algorithm for describing inhomogeneous dynamic models, but they depend directly on the efficiency of software that implements the proposed models. The model of hard spheres as simple fluid model proposed use. The reasons that allow you to choose this model as optimal were defined. Namely: the presence of analytical expression for the structural factor; application to describe the electronic and atomic properties of melts. The optimal methods for obtaining optimal values for the theoretical calculation of the structural factor of the proposed model were determined. As a result of the analysis of existence of correspondence between the calculated and experimental structural factors it is established. This led to the conclusion that the possibility of applying the model of rigid to calculate the equilibrium and kinetic properties of melts exists. It is determined that the model of rigid spheres could be used as an approximation to describe the structure of both one-component and multicomponential melts (liquids).

Distributions of Two Atoms Collisions over the Surface of the Condensed Phase

The processes of heat and mass transfer are closely related to the evaporation of a substance from the surface of the condensed phase. The interaction of outgoing molecules from the surface of the condensed phase with condensed phase molecules plays a fundamental role. A simpler case of evaporation is the departure of atoms from the surface of the condensed phase, i.e. the atoms overcome the potential barrier on the surface of the condensed phase. Depending on the evaporation rate, a Knudsen layer appears above the surface of the condensed phase. In this paper, based on the model of rigid spheres, the density distributions of the collision distances and the average values of the collision distances of two atoms emitted simultaneously from the surface of the condensed phase above the surface are analyzed. Distributions of the collision distance depending on the surface temperature, the size of the potential barrier, and the size of the evaporation area are obtained. Computer experiments were performed using the Monte Carlo method. To obtain the results of numerical simulation, a parallel algorithm adapted to calculations on graphics processors with CUDA technology was developed.

Cohesion of bird nests

One striking difference between aggregates of flexible frictional fibres and other granular materials like rigid spheres is the effective cohesion of their assembly. While glue or capillary bridges are needed to shape aggregates of spherical particles and build sandcastles, for fibres, no need for glue to build a nest. Here we study an assembly of mono disperse flexible fibres. We first use X-ray microtomography to characterise the geometry of the initial assembly, the number of contact points and mean curvatures of the fibres. Using forcedisplacement measurements, we characterise the macroscopic cohesive strength of the aggregate by varying the geometry of the fibres, the fibres mechanicals properties and the packing of the preparation. Finally, we relate the macroscopic mechanical behaviour of the assembly with the filament reorganisation at the microscopic scale.

A simplified metaelastic model for coated sphere-filled random composites

A simplified metaelastic model is presented to study long-wavelength dynamics of random composites filled with coated rigid spheres under the condition that the characteristic wavelength of the displacement field is much larger than the average distance between adjacent coated rigid spheres. The model is characterized by a simple differential relation between the displacement field of the composite and the displacement field of the mass center of a representative unit cell. The validity and accuracy of the model are demonstrated by comparing its predicted bandgap frequencies with known numerical and experimental data. The efficiency and merits of the model are demonstrated by applying it to study vibration isolation of coated rigid sphere-filled composite rods and (periodic or non-periodic) free vibration caused by initial displacement or velocity disturbance of the embedded rigid spheres inside an otherwise static composite rod. The proposed model could offer a simple method to study various long-wavelength metaelastic dynamic problems of coated rigid sphere-filled random composites.