Influence of Fluid Concentration on the Elevation of Boiling Point of Blackberry Juice

The rise in boiling point of blackberry juice was experimentally measured at soluble solids concentrations in the range of 9.4 to 58.4Brix and pressures between 4.9 103 and 9.0 104 Pa (abs.). Different approaches to representing experimental data, including the Duhring`s rule, a model similar to Antoine equation and other empirical models proposed in the literature were tested. In the range of 9.4 to 33.6Brix, the rise in boiling point was nearly independent of pressure, varying only with juice concentration. Considerable deviations of this behavior began to occur at concentrations higher than 39.1Brix. Experimental data could be best predicted by adjusting an empirical model, which consists of a single equation that takes into account the dependence of rise in boiling point on pressure and concentration.

Influence of Fluid Concentration on the Elevation of Boiling Point of Blackberry Juice

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Elevation of boiling point of coffee extract

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal evaporation: Representation of rise in boiling point of grapefruit juice

The rise in boiling point of grapefruit juice was experimentally measured at soluble solids concentrations in the range of 9.3-60.6 °Brix and pressures between °6.0 × 103 and 9.0 × 104 Pa. Different approaches to represent experimental data, including the Dhring's rule, the Antoine equation and empirical models proposed in the literature were tested. In the range of 9.3-29.0 °Brix, the rise in boiling point was nearly independent of pressure, varying only with juice concentration. Considerable deviations of this behavior began to occur at concentrations higher than 29.0 °Brix. Experimental data could be best predicted by adjusting an empirical model, which consisted of a single equation that takes into account the dependence of rise in boiling point on pressure and concentration. © SAGE Publications 2007.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

A new strategy for selecting and evaluating physical solvents for gas absorption

This work describes how the physical properties of a solvent affect the design variables of a physical gas absorption process. The role of every property in determining the capital and the running cost of a process has been specified. Direct mathematical relationships have been formulated between every item of capital or running cost and the properties which are related to that item. The accuracy of the equations formulated has been checked by comparing their outcome with some actual design data. A good agreement has been found. The equations formulated may be used to evaluate on the basis of economics any suggested new solvents. A group of solvents were selected for evaluation. Their physical properties were estimated or collected as experimental data. The selected ones include three important solvents, the first is polyethylene glycol dimethyl ether (Selexol) which represents the currently most successful one, The other two solvents are acetonyl acetone (B2) and n-formyl morpholine which have been suggested previously as potential credible alternatives to the current ones. The important characteristics of: acetonyl acetone are its high solubility and its low viscosity, while the n-formyl morpholine is characterised by its low vapour pressure and its high selectivity. It was found that acetonyl acetone (B2) is the most attractive solvent for commercial applications particularly for process configurations that:include heat exchangers and strippers. The effect of the process configuration on the selected solvent was investigated in detail and it was found that there is no universal solvent which is the best for any process configuration, but that there is a best solvent for a given process configuration. In previous work, acetonyl acetone was suggested as a commercially promising physical solvent. That suggestion was not fully based on experimental measurement of all the physical properties. The viscosity of acetonyl acetone and its solubility at 1 atm were measured but the vapour pressure and the solubility of C02 and CH4 at high pressure were predicted. In this work, the solubilities of C02, CH4 and C3H8 in acetenyl acetone were measured for a partial pressure range of (2 ~ 22) bar at 25°C, The vapour pressure of this solvent was also measured, and the Antoine equation was formulated from tbe experimental data. The experimental data were found to be not In agreement with the predicted ones, so acetonyl acetone was re-evaluated according to the experimental data. It was found that this solvent can be recommended for further trials in a pilot plant study or for small scale commercial units.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Exploring first-year academic achievement through structural equation modelling

The purpose of this research was to develop and test a multicausal model of the individual characteristics associated with academic success in first-year Australian university students. This model comprised the constructs of: previous academic performance, achievement motivation, self-regulatory learning strategies, and personality traits, with end-of-semester grades the dependent variable of interest. The study involved the distribution of a questionnaire, which assessed motivation, self-regulatory learning strategies and personality traits, to 1193 students at the start of their first year at university. Students' academic records were accessed at the end of their first year of study to ascertain their first and second semester grades. This study established that previous high academic performance, use of self-regulatory learning strategies, and being introverted and agreeable, were indicators of academic success in the first semester of university study. Achievement motivation and the personality trait of conscientiousness were indirectly related to first semester grades, through the influence they had on the students' use of self-regulatory learning strategies. First semester grades were predictive of second semester grades. This research provides valuable information for both educators and students about the factors intrinsic to the individual that are associated with successful performance in the first year at university.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.