Experiments of partial cooking of the same quantity of polyethylene were carried out at fixed temperature and pressure in different solvents consisting of a mixture of vegetable oils. The final product obtained from certain oil mixtures showed three phases: a relatively fluid polymer-poor gelatinous phase, a polymer-rich gelatinous phase, and a solid phase consisted of polymeric lumps. The final product obtained from other oil mixtures did not show a solid phase of polymeric lumps, but only the polymer-rich gelatinous phase and the relatively fluid polymer-poor gelatinous phase. The polymer fraction effectively mixed with the solvent during the experiments of partial cooking was measured by the amount of the relatively fluid polymer-poor gelatinous phase. The amount of the collected relatively fluid polymer-poor gelatinous phase was studied in accordance with the Flory-Higgins theory as a function of the volume fraction of the oil mixture components in the initial solvent. This study shows that the behavior of the Flory parameter and that of the solubility parameter of the solvent can be described by the amount of the relatively fluid polymer-poor gelatinous phase. This study also suggests a method for obtaining an optimal two-component solvent that can mix with a thermoplastic polymer as polyethylene. The optimal solvent is the one that minimizes the amount of the relatively fluid polymer-poor gelatinous phase.