Phase equilibria for chain‐fluid mixtures near to and far from the critical region

Application of a renormalization-group treatment to the statistical associating fluid theory for potentials of variable range (SAFT-VR)

“…The second term on the right hand side of equation (36) is very similar to that in (33) used by Prausnitz and later contributions 48,49,[51][52][53][54][59][60][61] with the addition of the extra parameter Φ, while ω is given by:…”

“…However, in these other works 48,49,[51][52][53][54][59][60][61] , the cutoff length L has a slightly different meaning: it instead separates the classic (mean-field) part of the free energy and the non-classic (critical)…”

“…Defining the volume as V n = (λ n ) 3 leads to the expression of K n used by Prausnitz et al 48,49,51,52 and later contributions 53,54,[59][60][61] , where…”

“…Following work carried out by previous authors 44,48,49,[51][52][53][54]59,61,[63][64][65] the integral in equation (29) is evaluated by numerical integration using the trapezoid rule method and equal size steps. Our standard method was set to use a 1000-point grid in density for the integration.…”

Vapor–liquid critical properties of multi-component fluid mixture

“…The extension of RG for pure fluid-to-fluid mixtures is essentially based on an isomorphism assumption suggested by Fisher and others [26][27][28][29]. Other kind of extension involves multi-dimensional integration requiring tremendous computer time and thus is not practical for engineering purposes [30,31]. The isomorphism assumption claims that a universal property of a mixture near its critical point is isomorphic to that of a one-component system, provided that certain appropriately chosen thermodynamic variables are kept constant and the correct order parameter is known.…”