Methods and compositions for separating materials are provided. In an embodiment, the present invention provides a method of separating a first material from a second material. For example, the method can comprise mixing the first material and the second material in a slurry with a beneficiation composition. The beneficiation composition can comprise one or more fatty acid by-products derived from a biodiesel manufacturing process or derived from transesterification reactions involving triglycerides. Air bubbles can be provided in the slurry to form bubble-particle aggregates with the first material and the bubble-particle aggregates can be separated from the second material.