Optimal Control of the Primary Drying Stage of Freeze Drying of Solutions in Vials Using Variational Calculus

The problem of operating freeze drying of pharmaceutical products in vials placed in trays of a freeze dryer to remove free water (in frozen state) at a minimum time was formulated as an optimal control problem. Two different types of freeze dryer designs were considered. In type I freeze dryer design, upper and lower plate temperatures were controlled together, while in type II freeze dryer design, upper and lower plate temperatures were controlled independently. The heat input to the material being dried and the drying chamber pressure were considered as control variables. Constraints were placed on the system state variables by the melting and scorch temperatures during primary drying stage. Necessary conditions of optimality for the primary drying stage of freeze drying process in vials are derived and presented. Furthermore, an approach for constructing the optimal control policies that would minimize the drying time for the primary drying stage was given. In order to analyze optimal control policy for the primary drying stage of the freeze-drying process in vials, a rigorous multi-dimensional unsteady state mathematical model was used. The theoretical approach presented in this work was applied in the freeze drying of skim milk. Significant reductions in the drying times of primary drying stage of freeze drying process in vials were obtained, as compared to the drying times obtained from conventional operational policies.     

Network topology and the theory of rubber elasticity

The earliest investigations on rubber elasticity, commencing in the 19th century, were necessarily limited to phenomenological interpretations. The realisation that polymers consist of very long molecular chains. commencing c. 1930, gave impetus to the molecular theory of rubber elasticity (1932-). according to which the high deformability of an elastomer, and the elastic force generated by deformation, stem from the configurations accessible to long molecular chains. Theories of rubber elasticity put forward from 1934-1946 relied on the assumption that the junctions of the rubber network undergo displacements that are affine in macroscopic strain. The theory of James and Guth (1947) dispensed with this premise, and demonstrated instead that the mean positions of the junctions of a ‘phantom’ network consisting of Gaussian chains devoid of material properties are affine in the strain. The vital significance of the distinction between the actual distribution of chain vectors in a network and their distribution if the junctions would be fixed at their mean positions went unnoticed for nearly 30 years. Experimental investigations, commencing with the incisive work of Gee in 1946. revealed large departures from the relationship of stress to strain predicted by the theories cited. This discrepancy prompted extensive studies, theoretical and experimental, during succeeding years. Inquiry into the fundamentals of polymer networks, formed for example by interlinking very long polymer molecules, exposed the need to take account of network imperfections, typically consisting of chains attached at only one end to a network junction. Various means were advocated to make corrections for these imperfections. The cycle rank ζ of the network has been shown (1976) to be the fundamental measure of its connectivity, regardless of the junction functionality and pattern of imperfections. Often overlooked is the copious interpenetration of the chains comprising typical elastomeric networks. Theories that attempt to represent such networks on a lattice are incompatible with this universal feature. Moreover, the dense interpenetration of chains may limit the ability of junctions in real networks to accommodate the fluctuations envisaged in the theory of phantom networks. It was suggested in 1975 that departures from the form predicted for the elastic equation of state are due to constraints on the fluctuations of junctions whose effect diminishes with deformation and with dilation. Formulation of a self-consistent theory based on this suggestion required recognition of the non-affine connection between the chain vector distribution function and the macroscopic strain in a real network, which may partake of characteristics of a phantom network in some degree. Implementation of the idea was achieved through postulation of domains of constraint affecting the equilibrium distribution of fluctuations of network junctions from their mean positions. This led in due course to a theory that accounts for the relationship of stress to strain virtually throughout the ranges of strain accessible to measurement. The theory establishes connections between structure and elastic properties. This is achieved with utmost frugality in arbitrary parameters.     

Facile modifications of polyimide via chloromethylation: II. Synthesis and characterization of thermocurable transparent polyimide having methylene acrylate side groups

From chloromethylated polyimide, a useful starting material for modification of aromatic polyimides, a thermocurable transparent polyimide having acrylate side groups was prepared. In the presence of 1,8‐diazabicyclo[5,4,0]undec‐7‐ene, chloromethylated polyimide was esterified with acrylic acid to synthesize poly(imide methylene acrylate). The polymer was soluble in organic solvent, which makes it possible to prepare a planar film by spin coating. The polymer film became insoluble after thermal treatment at 230 °C for 30 min. Optical transparency of the film at 400 nm (for 1 µm thickness) was higher than 98 % and not affected by further heating at 230 °C for 250 min. Adhesion properties measured by the ASTM D3359‐B method ranged from 4B to 5B. Preliminary results of planarization testing showed a high degree of planarization (DOP) value (>0.53). These properties demonstrate that poly(imide methylene acrylate) could be utilized as a thermocurable transparent material in fabricating display devices such as TFT‐LCD. Copyright © 2004 Society of Chemical Industry     

The impacts of a GTL plant on Brazil's oil products supply and refinery expansion

This paper assesses the impacts of a GTL plant on the expansion of Brazil's oil refining segment. The GTL plant (50,000 bpd) was sized to start up operations in 2015, producing diesel and naphtha through the indirect route (FT-synthesis). This plant will consume the non-associated natural gas production from the recent discoveries at the Santos Basin (around 419 Bm³), and the associated gas production from the Campos Basin. Both basins are located in the Southeast of Brazil, the most populated, rich and industrialized region of the country. Two different criteria for refinery expansion were simulated in order to meet oil product demand scenarios. Findings show that depending on the refinery expansion criteria considered GTL will play a fundamental hole to meet the oil product demand forecast to Brazil in the next 10 years.     

Study of liquid injection impact on the performance of new refrigerant mixtures

In this paper, the test results of liquid injection impact on the performance of new alternative refrigerant mixtures such as: R-410A, R-507, R-407C and R-404A are discussed, analysed and presented. The test results were obtained using an air-source heat pump set-up with enhanced surface tubing under various liquid injection ratios. Performance tests were conducted according to the ARI/ASHRAE standards. The performance data demonstrated that as liquid injection ratio increases, compressor head pressure and discharge temperature decrease. This has a positive effect in protecting the compressor. The effect of liquid injection on mixture behaviour varies from one mixture to another depending upon the mixture's composition. Furthermore, liquid injection appears to have a significant influence on R-410A behaviour compared to the other mixtures in question. Copyright © 2002 John Wiley & Sons, Ltd.     

The impact of roasting on the ochratoxin A content of coffee

Roasting coffee led to a drop in the ochratoxin A (OTA) concentration, as measured by the reference method, especially for dark type roasts. The way the beverage was prepared also affected the OTA content, which could paradoxically be higher than that of the initial roasted coffee. Assays on the thermal stability of pure OTA showed that it ought to be found in larger quantities in roasted coffee. This suggested that OTA was masked by reactions with the substrate during roasting. The absence of OTA in green coffee is therefore the best guarantee of safety.     

Exchange and oxidation of CO on O-predosed Rh---Al2O3 and Rh---CeO2 catalysts

Exchange and oxidation of C¹⁶O were investigated at 450°C on ¹⁸O-predosed Rh and Pt catalysts supported on A1₂O₃, CeO₂ and CeO₂-Al₂O₃. In all cases, a rapid exchange of C¹⁶O with the surface can be observed. CO oxidation leads to C¹⁶O₂, C¹⁶O¹⁸O and C¹⁸O₂. Significant formation of C¹⁶O₂ is due to the relatively high ¹⁶O coverage in reaction resulting from the C¹⁶O exchange and from an exchange between O surface species and ¹⁶O internal atoms. Hydrogen is also formed via a water-gas shift reaction (CO + surface OH) in higher proportion on CeO₂-containing catalysts than on A1₂O₃. Chlorine inhibits all the reactions (exchange, oxidation and WGS) and particularly the internal exchange.     

Electrochemical Aspects of Electroosmotic Dewatering of Clay Suspensions

An attempt is made to elucidate the electrochemical aspects of the electroosmotic dewatering (EOD) of clays as reported in some recent work, especially that on interrupted DC power electroosmotic dewatering published by Rabie, Mujumdar and Weber (2). These authors showed that the dewatering by EOD stops after the DC power has been on for several minutes or hours; on interruption of their power and on short-circuiting of the electrodes, conditions can be created again for some further dewatering by DC power EOD. This discovery, of Rabie et al. is interpreted as a fuel cell effect and it is shown that it affords clues to several other electrochemical strategies for the possible enhancement of the efficiency of the EOD by DC power.

Further, the open circuit potentials observed by Rabie et al. (2) on the interruption of DC power are given an electrochemical interpretation which leads to quantitative estimates in agreement with the experimental values.