A new approach to non-randomness in mixtures of r-mer fluids is presented. This approach leads to new consistent analytical expressions for the local compositions or the non-randomness factors in solutions. These expressions are compared with the corresponding expressions of Guggenheim's quasi-chemical approximation. The new expressions are implemented in an equation-of-state framework valid for both the liquid and the gaseous state. The resulting new model is applied to systems of small molecules as well as to polymers. The model calculates a significant degree of non-randomness in the distribution of free volume even in non-polar systems such as the linear polyethylene. (c) 2005 Elsevier B.V. All rights reserved.