TECHNOLOGY FOCUS - BIOLOGY - Preferred Components: The source of a fatty acid is selected from soybean, corn, sunflower, palm, jatropha, nut, safflower, olives, cotton, linseed, mustard seed, rapeseed, canola, peanuts, coconut, castor beans, tall oil, algae, raw or rendered animal fats, brown grease, white grease, yellow grease, lard or tallow from pork, chicken, mutton, beef, horse, and wastes, effluents and residues from the processing of at least one source of a fatty acid.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: In the method (P1) reaction mixture being maintained in at least one of hydrodynamic cavitation zones for less than 1 (preferably less than 0.1) second. The two controlled flow cavitation apparatuses are arranged in series such that the at least two apparatuses comprise a first controlled flow cavitation apparatus and a second controlled flow cavitation apparatus. The two controlled flow cavitation apparatuses being in direct fluid connection such that the reaction mixture passes through the first controlled flow cavitation apparatus and directly into the second controlled flow cavitation device. In the method (P1) processing pressure is greater than 120 psi and the pressure differential across the first and second controlled flow cavitation apparatus is at least 60 psi. In the method (P2) reaction mixture passes through the constriction and creates a pressure differential across the constriction is 30-500 (preferably greater than 60) psi. In the method (P2) reaction mixture being passed through the at least two controlled flow cavitation apparatuses at a processing pressure capable of generating the hydrodynamic cavitation zone in each the apparatus, where the conversion rate of the fatty acid in the reaction mixture to the fatty acid alkyl ester occurs in the hydrodynamic cavitation zone; and reaction mixture being maintained in at least one of the hydrodynamic cavitation zones for less than 1 (preferably less than 0.1) second. In the method (P2) two controlled flow cavitation apparatuses comprises a first controlled flow cavitation apparatus in series with a second controlled flow cavitation apparatus, where first apparatus and second apparatus are in direct fluid connection. The method (P2) of increasing the conversion rate of fatty acid to fatty acid alkyl ester involves combining the feedstock containing fatty acids with alcohol and catalyst to form a reaction mixture, where the temperature of the reaction mixture is 40-200 degrees C; passing the reaction mixture through a controlled flow cavitation apparatus at the processing pressure of at least 250 psi; maintaining a pressure differential across the controlled flow cavitation apparatus of at least 250 psi; converting at least 95% of the fatty acids in the reaction mixture to fatty acid alkyl esters, where the conversion occurs in a single pass through the controlled flow cavitation apparatus. Preferred Components: The two controlled flow cavitation apparatuses each comprises localized flow constriction, where the pressure differential occurs across the localized flow constriction. The localized flow constriction is an orifice, baffle or nozzle. EXAMPLE - A oil (1 part), methanol (6 parts), and sodium hydroxide (0.219 parts) combining in two holding tank to form reaction mixture. The reaction mixture was passed through one cavitation apparatus at 100 degrees C, a residence of time of 0.12 microseconds in the hydrodynamic cavitation zone and a pressure differential across the orifice of 250 psi to form fatty acid alkyl ester.