Does the sudan red test differentiate between saturated and unsaturated fats

NO, Sudan red can not differentiate between saturated and unsaturated fats. Sudan red is a dye which is soluble in lipids. When the dye is added to a mixture of water and lipid, the dye will migrate into the lipid layer, imparting a red colouration on it. To differentiate between saturated and unsaturated lipids another test will be used.