THE ISOTHERMAL COMPRESSIBILITY OF n-PARAFFIN LIQUIDS AT LOW PRESSURES

Volumetric measurements were made on members of the homologous series of n -paraffin liquids ranging from n-decane to n-heptadecane at 25.0, 45.0, and 65.0°C at pressures up to 100 bar. The data were numerically analyzed to yield the isothermal compressibility function. With the addition of the density function, the coefficient of thermal expansion at 1 atm abs can also be evaluated.     

Pressure-volume-temperature behavior of polypropylene

The pressure-volume-temperature behavior for both solid and molten polypropylene was determined for pressures up to 618 atmospheres. These data were measured with a newly developed compressibility device capable of obtaining precise and accurate data. Compressibilities calculated from the experimental data compared favorably to the limited existing literature data. Constants were determined for the Spencer-Gilmore polymer equation of state for both the solid and molten material.     

Natural convection on a vertical plate with variable heat flux in supercritical fluids

The present article investigates laminar free convection with uniform or non-uniform prescribed surface heat flux over a vertical flat plate in supercritical fluid, numerically. A new equation for thermal expansion coefficient in a supercritical fluid is derived based on Redlich–Kwong equation of state as a function of pressure, temperature and the compressibility factor. Calculated values of thermal expansion coefficient have been compared with the experimental results which show better accuracy in comparison with van der Waals ones. The governing systems of partial differential equations were solved numerically using the finite difference method. The local Nusselt number was calculated and plotted as a function of the local Rayleigh number. Using supercritical fluids in constant heat flux free convection, decrease wall temperature in comparison with under critical fluids. It was observed that positive and negative slopes of surface heat flux distribution increases and decreases the heat transfer coefficient, respectively.     

Pressure–volume–temperature behavior of high density polyethylene

Equilibrium pressure-volume-temperature behavior in both the solid and molten regtions was determined for a high density (ρ = 0.958 g./cm.³) polyethylene. Data were measured with a recently developed compressibility device capable of obtaining precise and accurate data. Residual curve treatment showed that the data were true equilibrium data. Compressibilities calculated from the data of this Work compared favorably to existing data which were limited to 205°C. The presented work extended the compressibility behavior to 250°C. It was also found that differences in compressibility of low and high density polyethylenes were not eliminated. in the molten region, indicating that the effect of differences in morphology was not eliminated. The Spencer-Gilmore equation was fitted to the data of the present work. The internal pressure (π) term of the equation showed a definite relation to polymer morphology.     

Isothermal Compressibility of Liquids at Low Pressures

A simple borosilicate glass compressibility cell was constructed which allowed the measurement of relative volumes of liquids to a precision of ± 0.00002. The relative volumes of water, acetone, n-hexane and neopentane were measured at 25°C at pressures to 70 atm. In addition the relative volumes of n-hexane were measured at 50°C. Isobaric thermal expansion coefficients were measured for acetone and n-hexane in a narrow temperature range near 25°C. The isothermal relative volume data were fitted to theTait equation from which the isothermal compressibilities of the four liquids were computed. The compressibilities were slightly different from the compressibilities calculated from high pressure literature data fits of the Tait equation     

Isothermal Compressibility of Liquids at Low Pressures

A simple borosilicate glass compressibility cell was constructed which allowed the measurement of relative volumes of liquids to a precision of ± 0.00002. The relative volumes of water, acetone, n-hexane and neopentane were measured at 25°C at pressures to 70 atm. In addition the relative volumes of n-hexane were measured at 50°C. Isobaric thermal expansion coefficients were measured for acetone and n-hexane in a narrow temperature range near 25°C. The isothermal relative volume data were fitted to theTait equation from which the isothermal compressibilities of the four liquids were computed. The compressibilities were slightly different from the compressibilities calculated from high pressure literature data fits of the Tait equation     

Temperature dependence of viscosity of polyurethane polyol solutions: Application of rheological models

Polyurethane polyols were synthesized by reacting the diols with polyisocyanates. Viscosity of their 50% (w/w) solutions in various solvents has been determined at different temperatures by using Haake Roto Visco RV12 Rotational Viscometer. The temperature dependence of viscosity data was solved by Levenberg Marquardt's algorithm by using nonlinear regression models based on WLF, Vogel, and Arrhenius equations. The T_g values obtained from WLF and Vogel equation are comparable to each other and these equations can be satisfactorily used for the analysis of temperature dependence of viscosity data of oligomer solutions. The residuals are random and the absolute average percentage error in analyzing the viscosity data by these equations is minimum. The values of constants in WLF equation are found to be system dependent and adjustable parameters. The predicted In η values obtained from WLF and Vogel equations fit well with the plots of experimental In η values as a function of temperature. © 1996 John Wiley & Sons, Inc.     

A study on the predictive capability of the SAFT-VR equation of state for solubility of solids in supercritical CO2

In this study, a version of the SAFT-VR equation of state based on the Yukawa potential is used for modeling the solubility of diverse organic compounds, mostly drugs, in supercritical carbon dioxide. Prior to any calculations, the SAFT parameters of pure CO₂ were obtained by correlating the vapor–liquid equilibrium data within the range of 220–300 K. The validity of these parameters was examined by applying them in prediction of the compressibility factor and density in wide temperature and pressure ranges. Due to dependence of the rest of the calculations on the sublimation pressure and lack of its experimental values for most of the solids, it was estimated through two main approaches: application of a group contribution method prior to correlating the solubility data, and calculating it in relation with temperature while correlating the solubility data. For each compound, the first isothermal set of the available experimental data was used for correlation and the rest were predicted. Adopting the same procedure for three empirical models and comparing the resulting deviation percents validated the superiority and high capability of this equation of state in correlating and particularly predicting the solubility in supercritical region. The predicted densities were also in very good agreement with the available experimental values.     

Mathematical Modeling of Supercritical Extraction of Valerenic Acid from Valeriana officinalis L.

The dynamic behavior of supercritical fluid extraction (SFE) of valerenic acid (VA) from valerian (Valeriana officinalis L.) roots was studied by mathematical modeling. The extraction yield of VA was considered as the most desirable compound among the other extracted constituents. A two‐phase desorption model was developed by considering a diffusion controlled regime in the particle and axial dispersion in the bed. The mass transfer parameters, i.e., pore diffusivity, film mass transfer coefficient and axial dispersion, along with the solubility parameters were chosen as the model parameters. The first three mass transfer parameters were predicted using nondimensional equations from the literature. The solubility equation and the parameters were studied using different equilibrium models, i.e., Henry, Langmuir, Freundlich, Langmuir‐Freundlich (L‐F) and Toth isotherms. The equilibrium parameters were correlated by comparing the outlet results of the dynamic SFE model with experiments. The experimental yield of the VA extraction was obtained at a pressure of 15.0–36.0 MPa, temperature of 310–334 K, solvent flow rate of 0.50–1.10 · 10^–6 m³/min and different particle sizes ranging from 0.18–2.00 · 10^–3 m in diameter, at a 20 min constant static period, in the presence of 46.9 μL/g ethanol as the co‐solvent, followed by dynamic time extraction for up to 50 min. From the results, the mathematical model using the L‐F equation exhibited the best agreement with the experimental yield of VA extraction in the range of studied conditions. The present model can be applied to design and scale up the SFE process of VA from Valeriana officinalis L. roots.     

Experimental optimization and mathematical modeling of supercritical carbon dioxide extraction of essential oil from Pogostemon cablin

The supercritical carbon dioxide extraction was applied to obtain essential oil from Pogostemon cablin in this work. Effect of extraction parameters including temperature, pressure, extraction time and particle size on extraction yield was investigated, and the response surface methodology with a Box-Behnken Design was used to achieve the optimized extraction conditions. The maximum yield of essential oil was 2.4356% under the conditions of extraction temperature 47℃, pressure 24.5 MPa and extraction time 119 min. Moreover, based on the Brunauer-Emmett-Teller theory of adsorption, a mathematical modeling was performed to correlate the measured data. The model shows a function relationship between extraction yield and time by a simple equation with three significantly adjustable parameters. These model parameters have been optimized through simulated annealing algorithm. The predicted data from the mathematical model show a good agreement with the experimental data of the different extraction parameters.     

Technical Improvements for SEC Studies

An on-line system to measure hoop-strain of strain evaluation cylinders (SECs) has been developed. The experimental results compared with the data measured by intermicrometer are acceptable. A modified mathematical equation to calculate thermal expansion coefficient of propellant is proposed and gives excellent agreement in comparing with the data measured by thermomechanical analysis (TMA).     

Determination of the kinetic parameters of the thermal oxidative degradation of styrene/butadiene copolymers

The intensity of the thermal oxidation has been followed through kinetic parameters. In styrene/butadiene copolymers, soft polybutadiene phase (PB) and hard polystyrene phase (PS) have different sensibilities to thermal degradation. The thermal oxidative stability of high-impact polystyrene (PS-HI), styrene/butadiene/styrene block copolymers (SBS), and PS-HI + SBS blends were investigated by isothermal DSC analysis. The kinetic parameters of the thermal oxidative degradative process: the reaction rate constants, the reaction orders and the activation energies have been determined. The total area under the exothermic curve was used to calculate the isothermal heats of degradation. The conversion (α) and the rate of the thermal oxidative degradation (dα/dt) have been derivated. The experimental data have been tested with a kinetic model for autocatalytic reactions: dα/dt = k α^m (1 ? α)ⁿ. Activation energies have been determined from the Arrhenius equation and the order of the thermal oxidative stability evaluated. The extent of agreement of the experimental data with the autocatalytic model is discussed.     

Influence of Air Compressibility on the Permeability Evaluation of Refractory Castables

Air compressibility is important in attaining an accurate quantification of the permeability parameters for refractory castables. Nevertheless, this effect is often neglected in the permeability equations that are found in ceramics literature. The consequences of omitting the compressibility effect in two of the main permeability equations are highlighted and discussed. The permeability to air flow of high-Al₂O₃ ultra-low-cement refractory castables has been quantified by Darcy's law according to U.S. ASTM C577–96 and European PRE-16th permeability methods, which propose distinct approaches for air compressibility. Forchheimer's equation, which establishes a more realistic dependence between fluid pressure and fluid velocity, also has been used to obtain the permeability constants k ₁ and k ₂. Results show that equations proposed by the ASTM and the PRE methods may yield very distinct values of Darcian permeability k ₁ for the same sample. Forchheimer's equation for compressible fluids provides the best fitting with experimental data.     

Pressure build-up during the packing stage of injection molding

A thorough study of an isothermal fluid motion within the mold cavity during the packing stage is presented. The fluid is considered Newtonian, and its compressible behavior is assumed to obey the Spencer-Gilmore equation of state. Mathematical results indicate that the pressure built up during the packing stage is strongly dependent on the melt viscosity and the boundary of the cavity. The effects of pressure gradient and distribution, during this stage, on the shrinkage of the final products are also discussed.     

Prediction of solvent‐diffusion coefficient in polymer by a modified free‐volume theory

Several versions of free‐volume theory have been proposed to correlate or predict the solvent diffusion coefficient of a polymer/solvent system. The quantity of free volume is usually determined by the Williams–Landel–Ferry (WLF) equation from viscosity data of the pure component in these theories. Free volume has been extensively discussed in different equation‐of‐state models for a polymer. Among these models, the Simha–Somcynsky (SS) hole model is the best one to describe the crystalline polymer, because it describes it very approximately close to the real structure of a crystalline polymer. In this article, we calculated the fractions of the hole free volume for several different polymers at the glass transition temperature and found that they are very close to a constant 0.025 by the SS equation of state. It is quite consistent with the value that is determined from the WLF equation. Therefore, the free volume of a crystalline polymer below the glass transition temperature (T_g) is available from the SS equation. When above the T_g, it is assumed that the volume added in thermal expansion is the only contribution of the hole free volume. Thus, a new predictive free‐volume theory was proposed. The free volume of a polymer in the new predictive equation can be estimated by the SS equation of state and the thermal expansion coefficient of a polymer instead of by the viscosity of a polymer. The new predictive theory is applied to calculate the solvent self‐diffusion coefficient and the solvent mutual‐diffusion coefficient at different temperatures and over most of the concentration range. The results show that the predicted values are in good agreement with the experimental data in most cases. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 428–436, 2000     

Thermal conductivity of plastic foams

A simple equation enabling the prediction of the thermal conductivity of plastic foams, without the aid of adjustable parameters, is proposed. The equation is based on a recurrent method, previously developed, that showed reasonable agreement with experimental results. Ways of decreasing the thermal radiation contribution are shown. In particular, the influence of cell size, radiation transmission through solid membranes, and low-emissivity boundary surfaces are analyzed. Errors involved in steady techniques of measuring the thermal conductivity associated with radiation are discussed.     

Prediction of thermodynamic properties of polymeric liquids using a new equation of state

In this paper, we have used a simple equation of state (EoS) to predict the density for polymeric liquid mixtures at different temperatures, pressures, and compositions. The excess molar volumes of these mixtures have been also calculated using this equation of state. Also, we have computed isothermal compressibility. A wide comparison with experimental data has been made for each thermodynamic property. The values of statistical parameters between experimental and calculated properties show the ability of this equation of state in reproducing and predicting different thermodynamic properties for studied polymeric mixtures.     

Equation of state for gaseous nitrogen determined from isotropic model potentials

A four‐term virial equation of state was combined with isotropic potential models to predict accurate volumetric and caloric thermodynamic properties of nitrogen in the gas phase. The parameters of the model potentials were determined from a fit to acoustic data alone; no other data was used. For nitrogen, it was only necessary to approximate the fourth virial coefficient at the level of interactions that contained no more than one triplet potential; higher order approximations offered no further advantage. It was shown that the four‐term virial equation was more accurate than the three‐term analogue. It was found that predicted virial coefficients became consistent with experimental values when temperature was >150 ± 30 K; conversely, below this range virial coefficients predicted by the model did not agree with experiment. It was believed that predicted fourth virial coefficient was reliable and accurate only above about 150 K. Predicted compressibility factors deviated by <0.05% at pressures of up to 10–12 MPa, or densities up to 4 mol/dm³ (≈0.4ρ_c), only when temperature was >220 K. Values of enthalpy predicted from the equation of state showed good agreement with experimental data.     

Volumetric properties at high pressure of waste oil methyl ester compared with diesel oil

In this paper, the isothermal compressibility coefficient, the cubic expansion coefficient and the propagation speed of pressure waves of waste oil methyl ester (WOME) and diesel oil (DO) are presented. These properties can be derived mathematically from the specific volume, the only property measured in this work (from 288.15 to 328.15 K and from atmospheric pressure to 350 MPa). The modified Tait–Tammann Equation has been adjusted to the experimental data with a high correlation coefficient and confidence level. Because of their different physical properties, the use of WOME instead of DO can affect the behaviour of some diesel equipments and, for instance, the economic efficiency and the behaviour of heat engines.