“Mathematical constraints that imperatively need to be applied to α-function of cubic EoS to get accurate and physically sound results”
Abstract
Since Van der Waals, the attractive term a( T ) of any cubic equation of state is expressed as the product of its value at the critical temperature ( ac ) by the so-called alpha function. Our recent investigations made it however possible to conclude that to get accurate and physically meaningful behaviors in both the subcritical and supercritical domains, it was necessary to work with a consistent a-function, i.e., with an α-function which is positive, decreasing, convex and with a negative third derivative. This presentation will explain how such conclusions were derived.
In a second step, an extensive review of the mostly used α-functions described in the open literature will be performed and will show that all of them are not consistent. Some component-dependent α-functions may however become consistent but only if mathematical constraints are added to their parameters.