The objective is to propose a solvent able to mix with polymers that hardly mix to based vegetable oils solvent (such as terephthalate polyethylene having undergone a certain crystallization or addition of additives). The methodology consists of measuring the unmixed solvent fraction through a series of experiments of partial cooking of the same polymer quantity. The solvent is a mixture of vegetable oils adjusted by the addition of a well-defined tiny sulfuric acid quantity. This methodology is based on the Hildebrand's approach in the Flory-Huggins theory of polymer mixtures according to which the best solvent is the one whose solubility parameter is the closest to that of the polymer. Then, hardly miscible polymers were successfully mixed to based vegetable oils solvent. The behavior of the obtained polymeric mixtures as a function of the added sulfuric acid tiny amount is in good agreement with the Hill-Langmuir models on the equilibrium between the adsorption and the desorption of species in well determined quantity. The «Solvent» entities are «Ligands», while the «Polymer» sites are «Receptors». This behavior also shows that, for a solvent adjusted by adding a well-defined tiny sulfuric acid amount, the mixing phenomenon can be an enduring process in time. The results of this work suggest that it is possible to adjust the solubility parameter of the previous study solvent to that of the polymer by adding a tiny amount of an appropriate element to the solvent/polymer mixture.