A method for separating lean meat from lean meat-containing material includes combining a particulate material with fluid, subcritical carbon dioxide at a pH of about 7 or less and a pressure of about 600 psig. The material and fluid is introduced into the vessel and is separated into low density and high density fractions. The material from the low density fraction is removed via an outlet and has a higher percentage of fat than the material introduced into the vessel. The material from the high density fraction is removed via an outlet and has a higher percentage of lean meat than the material introduced into the vessel. The vessel can include a centrifuge or a vessel disposed toward the vertical having an upper and lower outlet, wherein the separation is achieved by the respective densities of the material, and the natural or an artificial gravity field.