NOVELTY - Method-1 of treating an initial lipid mixture, which comprises lipids of varying degrees of unsaturation in their aliphatic chains, comprises: (a) preparing a solution of silver(I) (Ag(I)) salt in an ionic liquid to form a Ag(I) salt solution; (b) combining the Ag(I) salt solution with a first organic solvent and the initial lipid mixture to form an extraction mixture comprising two primary phases; (c) inducing the lipids in the extraction mixture to partition between the two primary phases; (d) separating the first extracted phase from the second extracted phase; and (e) removing the lipids.    USE - The method is an enrichment process for separating and/or fractionating and/or enriching monounsaturated fatty acid/ester molecules from polyunsaturated fatty acid/ester molecules or monounsaturated molecules from saturated molecules. The method is useful for the production of biofuels and biolubricants.    ADVANTAGE - The method is more facile and/or more tailorable for fatty acid/ester separation by degree of unsaturation.    DETAILED DESCRIPTION - Method-1 of treating an initial lipid mixture, which comprises lipids of varying degrees of unsaturation in their aliphatic chains and has a corresponding average unsaturation number, comprises: (a) preparing a solution of silver(I) (Ag(I)) salt in an ionic liquid to form a Ag(I) salt solution; (b) combining the Ag(I) salt solution with a first organic solvent and the initial lipid mixture to form an extraction mixture comprising two primary phases, where the Ag(I) salt solution provides for a first primary phase and the first organic solvent provides for a second primary phase; (c) inducing the lipids in the extraction mixture to partition between the two primary phases, where a portion of the lipids contained within gravitate to the first primary phase in such a way as to give a first extracted phase comprising lipids having a net increase in their average unsaturation number relative to that of the initial mixture of lipids, and where another portion of lipids gravitate to the second primary phase in such a way as to give a second extracted phase comprising lipids having a net decrease in their average unsaturation number relative to that of the initial mixture of lipids; (d) separating the first extracted phase from the second extracted phase to give a first extracted mixture and a second extracted mixture; and (e) removing the lipids from the first extracted mixture to give a first lipid product enriched in unsaturated lipids. An INDEPENDENT CLAIM is included for a method-2 for manipulating lipids, where the manipulation is based largely on differences in unsaturation number, comprising treating a lipid-containing precursor material so as to yield an initial lipid precursor mixture comprised largely of free lipids, subjecting the initial lipid precursor mixture to fractional crystallization to yield an initial lipid mixture comprised largely of free lipids and having an average unsaturation number that is higher than that of the initial lipid precursor mixture, preparing a solution of a pi-complexing metal salt in an ionic liquid to form a metal salt solution, combining the metal salt solution with the first organic solvent and the initial lipid mixture to form an extraction mixture comprising two primary phases, where the metal salt solution provides for a first primary phase and the first organic solvent provides for a second primary phase, inducing the lipids in the extraction mixture to partition between the two primary phases, where some lipids gravitate to the first primary phase in such a way as to yield a first extracted phase comprising lipids having a net increase in their average unsaturation number relative to that of the initial mixture of lipids, and where lipids gravitate to the second primary phase in such a way as to yield a second extracted phase comprising lipids having a net decrease in their average unsaturation number relative to that of the initial mixture of lipids, separating the first extracted phase from the second extracted phase to yield a first extracted mixture and a second extracted mixture and removing the lipids from the first extracted mixture to yield a first lipid product enriched in unsaturated lipids.