Attainable region definition

A definite methodology to find the Attainable Region for given fundamental processes is not available. A trial and error procedure is necessary. However, the AR technique is supported by a powerful test procedure. The candidate region must respect the following necessary conditions, as demonstrated by the works of Glasser, Hildebrand (1997) ... 

An interesting aspect arises in the transition region for the polyacrylamides B1 and M3, definite changeover points are recognizable, whereas for polyacrylamide 40/1 there is a steady transition, so that a difference between laminar and turbulent flow cannot be pinpointed. For the curve of PAAm M3, the Newtonian turbulence reference-line is not attained. This phenomenon will be discussed in more detail in the following section on concentration dependency. 

With fluids, we think of the pump as the source of pressure as well as the flow rate determining device. However, with supercritical fluids (in contrast to t3q)ical liquids), a pump needs a control point downstream to hmit the passage of molecules per unit time. This restriction then "holds-back" the previously unlimited flow of molecules to a definite, but not always pre-determined level. Ideally then, the restrictor serves to restrict the flow until the density of molecules distributed from the pump through the extraction region right up to the final restriction point in space is such that the operating density desired in the extraction zone is achieved. This is much easier to state in words than it is to achieve in actual experimental practice. This is especially true if you wish to achieve an experimental set of parameters and hold those values over a finite period of time (ranging from minutes to hours) and do it with the statistical precision and accuracy that are necessary to attain the final quantitative analytical results. 

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