Frederico W. Tavares

Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations

Knowledge of the properties of granular materials is important for efficient and safe design of industrial equipment. In this work, the Monte Carlo method is used for simulating granular systems of spherocylindrical particles. After presenting an overview of such method and of overlap detection in systems of hard spherocylinders, the application of the method for granular systems is discussed. Then, porosities, calculated for simulated monodispersed beds, are presented as functions of the particle elongation. Next, results for vibration-induced segregation of binary mixtures of spherocylinders with identical volume and density, but with different elongations, are evaluated, showing the influence of the particle shape on this phenomenon. Finally, effects of size and shape on such segregation are contrasted using results with simultaneous variation of particle volume and elongation.

Phase behavior of olive and soybean oils in compressed propane and n-butane

Abstract - The aim of this work is to report the experimental data and thermodynamic modeling of phase equilibrium of binary systems containing soybean and olive oils with propane and n-butane. Phase equilibrium experiments were carried out using the static synthetic method in a high-pressure variable-volume view cell in the temperature range from 30 to 70 o C and varying the solvent overall composition from 5 to 98 wt%. Vapor-liquid, liquid-liquid and vapor-liquid-liquid phase transitions were observed at relatively low pressures. The Peng-Robinson and the SAFT equations of state without any binary interaction parameters were employed in an attempt at representing the phase behavior of the systems. Results show the satisfactory performance of SAFT-EoS in predicting qualitatively all phase transitions reported in this work. Keywords : Vapor-liquid equilibria; Liquid-liquid equilibria; Triglycerides; Propane; N-butane. INTRODUCTION Triglycerides and their fatty acid esters are important raw materials in many industrial processes. Their transformation provides products with high market values such as monoglycerides, widely used as emulsifiers in the food, cosmetics and pharmaceutical industries (Schmid, 1987; Ranalli and Mattia, 1997; Shiomori et al., 1995; Bhaskar et al., 1993). Furthermore, the transesterification of oil and fats produces a mixture of esters known as biodiesel. Such products have attracted considerable environmental interest in the past few years, mainly due to the low levels of pollutant emitted by user engines. Generally, the oil transformation in industrial scale is commonly accomplished by an acid or base-catalyzed reaction. However, yields reported as well as the quality of the products are usually low (Al Saadi and Jeffreys, 1981). An alternative process for obtaining products of high-grade quality is the use of enzyme-catalyzed reactions in supercritical or compressed solvents. Numerous studies have shown that many reactions can be conducted in compressed liquid or supercritical solvent and, in some cases, rates and selectivities achieved are greater than those obtained in normal liquid or gas phase reactions (Rendon et al., 2001; Oliveira and Oliveira, 2000; Jackson and King, 1997; Savage et al., 1995; King et al., 1987). To conduct such reactions, knowledge of the phase behavior of all components in the compressed solvent is of primary importance for process design optimization and for preventing enzyme inactivation due to the effects of high pressure.

Liquid film flow and area generation in structured packed columns

Several correlations are available in the literature for the prediction of wetted area or the effective interfacial area in packed columns. A careful examination shows considerable discrepancies in the calculated areas and conflicting predictions concerning the influence of viscosity on the interfacial areas. In this work, the effect of physical properties of liquids and of surface treatment on wetted area of structured packings was experimentally studied. Several wetting tests were performed on metallic and ceramic plates with flat, smooth or textured surfaces, using a circulation system, specially designed for this purpose. The liquid film width and thickness were measured for solutions with different surface tension and viscosities in a wide range (1 to 200 cP). The experimental results show that the liquid film width, and hence the wetted area, decreased with liquid viscosity, contrary to earlier correlations in the literature. Also the influence of contact angle is not so strong as stated in the literature for random packings. In this study, a new statistical correlation for the estimation of the wetted area and for the liquid film thickness is proposed, reflecting the measured variations with viscosity and advancing contact angles.

Calculations of thermodynamic equilibrium in systems subject to gravitational fields

The objective of this work is to present a procedure for the calculation of chemical and phase equilibrium (CPE) in multicomponent mixtures subject to the effect of gravitational fields. The specifications are the total volume, initial number of moles of each species and temperature. The problem is formulated as the minimization of a modified form of the Helmholtz function that contains a term to account for the potential energy. To solve this problem, the system is divided into layers. It is assumed that each of these layers is a homogeneous part of the system, and that each phase occupies a specified number of layers. Layers in the same phase are assumed to have the same size whereas those in different phases typically have different sizes. In the minimization of the modified Helmholtz function, the independent variables are the volume fraction of each phase (thereby defining the location of the interfaces) and the number of moles of each species in each layer, taking into account the possibility of chemical reactions. The procedure is used to calculate density and pressure profiles with height for pure fluids close the critical point and composition profiles for reactive and non-reactive mixtures.

Group contribution equation of state based on the lattice fluid theory: Alkane–alkanol systems

Abstract A new group-contribution equation of state (EOS) is proposed and applied to phase equilibrium calculations. The EOS is based on the generalized van der Waals theory and combines the Staverman–Guggenheim combinatorial term of lattice statistics with an attractive lattice gas expression. The EOS is applied to vapor–liquid equilibrium (VLE) calculations in systems containing pure hydrocarbons, alcohols, and their binary mixtures. These systems cover a wide range of situations, including nonpolar and polar compounds of different sizes and mixtures ranging from nearly-ideal to azeotropic behavior. Using VLE data for pure substances and binary mixtures of linear hydrocarbons, the parameters of linear alkane groups (CH 3 and CH 2 ) were simultaneously fitted. For pure linear alkanes up to C 12 , calculated vapor pressures deviate less than 1.7% from the experimental values. Predicted vapor pressures of eight heavy hydrocarbons (from C 14 to C 28 ) are in satisfactory agreement with experimental data. The parameters for other groups (branched alkanes and alcohol groups) were fitted sequentially, using data for pure compounds and binary mixtures only containing the characteristic group being estimated and linear alkane groups. Satisfactory predictions of the vapor pressures of pure substances and bubble pressures of binary mixtures were obtained.

The influence of ion binding and ion specific potentials on the double layer pressure between charged bilayers at low salt concentrations

Measurements of surface forces between double-chained cationic bilayers adsorbed onto molecularly smooth mica surfaces across different millimolar salt solutions have revealed a large degree of ion specificity [Pashley et al., J. Phys. Chem. 90, 1637 (1986)]. This has been interpreted in terms of highly specific anion binding to the adsorbed bilayers. We show here that inclusion in the double layer theory of nonspecific ion binding and ion specific nonelectrostatic potentials acting between ions and the two surfaces can account for the phenomenon. It also gives the right Hofmeister series for the double layer pressure.

Finite volume solution of the modified Poisson–Boltzmann equation for two colloidal particles

The double layer forces between spherical colloidal particles, according to the Poisson-Boltzmann (PB) equation, have been accurately calculated in the literature. The classical PB equation takes into account only the electrostatic interactions, which play a significant role in colloid science. However, there are at, and above, biological salt concentrations other non-electrostatic ion specific forces acting that are ignored in such modelling. In this paper, the electrostatic potential profile and the concentration profile of co-ions and counterions near charged surfaces are calculated. These results are obtained by solving the classical PB equation and a modified PB equation in bispherical coordinates, taking into account the van der Waals dispersion interactions between the ions and both surfaces. Once the electrostatic potential is known we calculate the double layer force between two charged spheres. This is the first paper that solves the modified PB equation in bispherical coordinates. It is also the first time that the finite volume method is used to solve the PB equation in bispherical coordinates. This method divides the calculation domain into a certain number of sub-domains, where the physical law of conservation is valid, and can be readily implemented. The finite volume method is implemented for several geometries and when it is applied to solve PB equations presents low computational cost. The proposed method was validated by comparing the numerical results for the classical PB calculations with previous results reported in the literature. New numerical results using the modified PB equation successfully predicted the ion specificity commonly observed experimentally.

Phase behavior of isotactic polypropylene/C4-solvents at high pressure. Experimental data and SAFT modeling

Abstract The phase behavior of two types of polypropylene (PP) (commercial Ziegler–Natta PP and a metallocenic PP) in n-butane and in 1-butene is investigated in a high-pressure variable-volume view cell. For these systems, three types of phase equilibrium are observed: vapor–liquid, liquid–liquid and vapor–liquid–liquid. The statistical associating fluid theory equation of state (SAFT-EOS) is used to model the experimental data through bubble-point calculations. A simplified strategy to calculate the three-phase equilibrium in polymeric solutions via SAFT-EOS is presented. Results show a good agreement between the SAFT model and experimental data when a binary interaction parameter is employed to fit the experimental values.

Role of attractive forces in self-diffusion and mutual diffusion in dense simple fluids and real substances

Abstract Diffusion is an important practical consideration in the design of processes involving mass transfer. From a theoretical standpoint, it is a relevant information when developing an understanding of dense-phase fluid structure. Recently, due to increase in computational power, the molecular dynamics (MD) technique has been applied extensively to the study of thermodynamic and transport properties. Diffusion is the most studied transport coefficient since it is an individual property, not a collective one like viscosity or thermal conductivity. This work investigates the role of attractive forces in the diffusion coefficient of pure simple fluids and their mixtures at infinite dilution. The intermolecular potential is broken down according to the ideas of Weeks, Chandler, and Andersen (WCA). It is then applied to study diffusion in idealized fluids (such as Lennard–Jones), idealized fluid mixtures, pure real substances and real substance mixtures. Molecular dynamics simulations were performed in the canonical ensemble with the Hoover–Nose thermostat for pure simple fluids and binary mixtures of simple fluids with one component and infinite dilution. These simulation results, that provide new data for pure fluids in the region of high temperature and intermediate densities, are compared to experimental results for real substances such as ethylene, sulfur hexafluoride and pure supercritical carbon dioxide (CO2) and a CO2/phenol mixture, where phenol is at infinite dilution. In addition, the Taylor–Aris dispersion technique was employed to measure the mutual diffusion of phenol in both liquid and supercritical CO2. Agreement between simulation and experimental data corroborates the idea that diffusion in pure and binary simple fluid mixtures at moderate densities and high temperatures is primarily determined by repulsive forces.

Square-well chain mixture: analytic equation of state and Monte Carlo simulation data

An analytic perturbation theory equation of state developed for mixtures of freely-jointed square-well chain fluids of variable well width is tested against Monte Carlo simulation data. The equation of state is based on second-order Barker and Henderson perturbation theory to calculate the thermodynamic properties of the reference sphere fluid, and on first-order Wertheim thermodynamic perturbation theory to account for the connectivity of spheres to form chains. A real function expression for the radial distribution function of hard spheres and one-fluid type mixing rule are used to obtain an analytic, closed form expression, for the Helmholtz free energy of mixtures of square-well spheres. In order to test the theories, Monte Carlo simulations for binary mixtures of square-well chains were performed to obtain the radial distribution function at the contact point, the compressibility factor, and the configurational internal energy of these mixtures. The proposed equation of state leads to good predictions of compressibility factor of square-well chains and their mixtures when compared with the simulation data.