Property, attainable region

Feinberg, M. and D. Hildebrandt. Optimal Reactor Design from a Geometric Viewpoint I. Universal Properties of the Attainable Region. Chem Eng Sci 52(10) 1637-1666 (1997). 

Feinberg M, Hildebrandt D. Optimal reactor design from a geometric viewpoint. I. Universal properties of the attainable region. Chem Eng Sci 1997 52 1637. 

More recently, Glasser et al. (1987) developed geometric properties of the attainable region along with a constructive approach for determining this region. They defined the necessary conditions for the attainable region as follows ... 

Chemical Engineering Science, Vol.54, No.7, pp. 2535-2543, ISSN 0009-2509 Feinberg, M, Hildebrand, D. (1997). Optimal reactor design from a geometric viewpoint -1. Universal properties of the attainable region. Chemical Engineering Science, Vol.52, No.lO, pp. 1637-1665, ISSN 0009-2509... 

The solution of the gas flow and temperature fields in the nearnozzle region (as described in the previous subsection), along with process parameters, thermophysical properties, and atomizer geometry parameters, were used as inputs for this liquid metal breakup model to calculate the liquid film and sheet characteristics, primary and secondary breakup, as well as droplet dynamics and cooling. The trajectories and temperatures of droplets were calculated until the onset of secondary breakup, the onset of solidification, or the attainment of the computational domain boundary. This procedure was repeated for all droplet size classes. Finally, the droplets were numerically sieved and the droplet size distribution was determined. 

Unlike IgG, IgA does not cross the placenta, but like IgG, both the 10 S and the 11 S dimers of IgA are known to fix complement and seem to have the ability to block IgE reaction. This property, as well as its phagocytic role, adds to its efficient antibody role in the mucosal surfaces of the body. Normal serum concentration in tropical populations are similar to, or slightly higher than, those of persons living in the temperate regions. However, it should be noted that normal Caucasians do not attain adult levels of IgA until the fifteenth year whereas in some tropical children the adult level of IgA may be reached by the tenth year of age (W7) (see Fig. 2). 

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