E. Rotstein

A general closure scheme for the method of volume averaging

Abstract The method of voluem averaging is used to derive the governing differential equations for multiphase transport, and a general closure scheme is developed for the spatial deviations. The closure scheme takes the form of a set of partial differential equations that are obtained without recourse to homogeneous or spatially periodic systems. However, solution of these equations in representative regions of a multiphase system naturally gives rise to spatially periodic boundary conditions. The method is illustrated with an analysis of the process of diffusion and reaction in a rigid porous medium.

Drying of cellular material—I. A mass transfer theory

Abstract The method of volume averaging is used to present a general theoretical analysis of the problem of mass transfer during the drying of shrinking multiphase systems. The results are used to derive a complete theory for the drying of cellular materials in the stage during which the cellular structure prevails. Constitutive equations for the diffusive flux of water in each phase of the system and the assumption of local equilibrium are used to obtain the one-equation model of water transport. The method of closure for the spatial deviations is discussed in detail, and a closure scheme is developed that allows for theoretical prediction of the effective mass conductivity tensor.

Drying of cellular material—II. Experimental and numerical results

Abstract The theory developed in Part I of this paper is used in this work to model the one-dimensional drying of food tissues. Equilibrium relations and shrinkage constitutive equations are discussed in detail. The closure scheme is solved for a simplified geometrical model of the cellular system. On this basis, theoretical predictions of the effective mass conductivity tensor are obtained and the relative contributions of the different mechanisms of water migration to the drying process are analyzed. A good agreement between predicted and experimental drying rates is obtained for the stage during which the theory applies.

Computer model of shrinkage and deformation of cellular tissue during dehydration

Abstract Deformation and shrinkage during drying of a porous medium made of cellular tissue are analysed by means of a computer model. Typical such media such media are natural foodstuffs like fruits and vegetables. The medium is considered to be an array cells and pores randomly distributed. It is represented by a tessellation of a 2-D domain into irregular polygons, some of which are given the properties of a cell, the remaining being representative of the pores. Drying induced changes are described and introduced in the tessellation by means of a geometrical approach. A set of equations representing the polygon vertices displacement due to dehydration is posed and solved by numerical techniques. The procedure is applied to an apple tissue model subject to drying.

Studies on the synthesis of chemical reaction paths—II. reaction schemes with two degrees of freedom

Abstract A reactive system, with a number of species larger than the number of elements involved, has meaningful invariant algebraic properties in the space of the Gibbs function of reaction and temperature These properties, developed for a reactive system with two degrees of freedom, show that an, in principle, an infinite number of reactions can be reduced to smaller clusters whose thermodynamic feasibility can be evaluated through simple measures. The invariant algebraic properties of reactive systems in the [Δ G , T ] space, together with the definition of a bounded feasibility region in the same space, allow the formulation of a search algorithm, which is used for the synthesis of feasible chemical production schemes. These ideas are demonstrated in an application to C 1 chemistry, indicating that the approach developed can generate reaction paths some of which coincide with existing commercial processes.

Fundamentals of Drying of Foodstuffs

The method of volume averaging is used to formulate a complete theory of mass transfer during the drying of cellular material in the stage in which the cellular structure prevails. The theory recognises the complex structure of the system and considers the different mechanisms of water transport. The volume-averaged transport equations for all the phases are added to obtain a total moisture transport equation in terms of water content and explicitly related with the shrinkage of the system. Then the assumption of local equilibrium is used to obtain the one-equation representation of water transport. A closure scheme is presented that allows for theoretical prediction of the effective mass transport coefficient. The general theory presented in this work would provide the basis to model water transport in different cellular materials.

Prediction of thermal conductivity of cellular tissues during dehydration by a computer model

Abstract A cellular tissue is an heterogeneous, porous, chaotic medium which can be represented by a subdivision of a 2-D domain into irregular, convex polygons, known as a Voronoi tessellation, on which some polygons are randomly defined as cells and the remainder as pores. The model is used to predict the effective thermal conductivity, k *, of fruit tissues at different moisture contents, taking into account the expected morphological changes undergone by the material during drying, and the properties of cells and pores which are assumed to have the polygons representing them. At any stage of the dehydration process, the fraction of total area occupied by polygons playing the role of pores equals the porosity of the actual sample at the corresponding water content. This is done either by simply substituting cells by pores or by shrinking the cells and enlarging the pores as drying proceeds. The variational principle associated with the conduction problem leads to the calculation of upper and lower bounds for k *. The procedure is applied to the case of apples and pears, giving good results when compared with experimental data. Predictions using the shrinking cells approach, however, yield better results than the substitution one.

Simulation modelling and optimal operation of an apple juice concentrate plant

Abstract It is possible to operate apple juice concentrate plants to maximize profits. To do this a mathematical model of the plant is made and solved by linear programming. To this end an actual plant was selected and all the relevant variables were measured. An optimal operation pattern was found. The analysis allowed identification of operating bottlenecks in the clarification and concentration sections. The response of the plant to prevention of milling waste and juice dilution, as well as to debottlenecking, was quantified. It was shown that the selection of apple varieties has a significant effect on profit. In situations of scarcity or surplus of raw material, the optimal operation and corresponding profit can be found in each case.

Thermodynamic availability analysis in the synthesis and analysis of complex processing systems

Abstract A steady state flow system which undergoes physical and chemical transformations can be analyzed thermodynamically in terms of its availability change, for the ideal case. In an actual case reversibility is not accomplished and the system energetic performance can be judged in terms of the irreversible creation of entropy. This analysis results in an upper and lower bound, respectively. The lower bound is evolutionary in nature. Large interactive processing systems can be described in terms of a linear programming model. By setting as objectives either the maximization of change in thermodynamic availability or the minimization of irreversible creation of entropy, it is possible to select the set of technologies which defines the bounding optimum structure of the system considered.

Exergy analysis and thermodynamic accounting of utilities

The exergy balance is a powerful tool for analysis of the energy status in a process installation. Proper incorporation of utilities is a significant issue. The approach of considering the contribution of utilities as heat exchanged reversibly via Carnot cycles is compared with that of handling utility streams in the same manner as process streams. The second approach is more realistic and flexible. Two applications illustrate this point.