NOVELTY - Manufacturing (M1) a biodiesel fuel, involves: generating micro-droplets of a first reactant; mixing the micro-droplets of the first reactant with a second reactant that is immiscible with the first reactant; transferring the mixture of the first reactant and second reactant into a reaction vessel; and forming a biodiesel fuel in the reaction vessel by a transesterification reaction, where the first reactant is one of an alcohol or an oil, and the second reactant is the other of the oil or the alcohol.    USE - For manufacturing biodiesel fuel (claimed).    ADVANTAGE - The step of conducting the transesterification reaction at higher temperatures favorably shifts the equilibrium towards the desired biodiesel fuel reaction product, thus enhancing the yield of biodiesel fuel. The step of conducting the transesterification reaction at higher temperatures greatly increases the rate of the reaction, at least when the reaction is not transport limited. The use of high temperature reaction mixtures can improve the separation of the biodiesel product from other reaction products, or, remaining reactants. The use of a high temperature reaction mixture enables the removal of the alcohol in a step, prior to and different from, separating the biodiesel fuel from the other reaction products, e.g. the unreacted alcohol leaving the reaction vessel is removed to a flash tank. By removing the excess unreacted alcohol from the material leaving in the reaction vessel, the separation of the biodiesel product from glycerol in a subsequent separation step is improved. By condensing the alcohol vapor removed in the flash tank and re-using this alcohol in subsequent biodiesel fuel manufacturing processes, the alcohol and glycerol are separated without the need for spending additional time and energy.    DETAILED DESCRIPTION - Manufacturing (M1) a biodiesel fuel, involves either: generating micro-droplets of a first reactant; mixing the micro-droplets of the first reactant with a second reactant that is immiscible with the first reactant; transferring the mixture of the first reactant and second reactant into a reaction vessel; and forming a biodiesel fuel in the reaction vessel by a transesterification reaction, where the first reactant is one of an alcohol or an oil, and the second reactant is the other of the oil or the alcohol; or mixing a co-solvent, a first reactant and a second reactant together in a mixing chamber to form a homogeneous solution, where the first reactant and the second reactant are immiscible with each other in the absence of the co-solvent; and transferring the homogeneous solution into a transesterification reaction vessel. INDEPENDENT CLAIMS are included for the following:    (1) manufacturing (M2) a biodiesel fuel, involving: performing a transesterification reaction between a reactant mixture including alcohol and oil at a temperature that is greater than a normal boiling point of the alcohol; transferring biodiesel fuel and glycerol transesterification reaction products and a remainder of the reactant mixture into a flash tank; flashing vapors of the alcohol out of the flash tank; and transferring a remaining content of the flash tank into a separation vessel; and    (2) a biodiesel fuel manufacturing system, comprising either: an atomizer configured to generating micro-droplets from a first reactant passed through the atomizer; a mixing vessel configured to receive the micro-droplets of the first reactant and combine the micro-droplets with a second reactant to form a reactant mixture; and a reaction vessel configured to receive the reactant mixture and convert the reactant mixture into a reaction product that includes a biodiesel fuel in a transesterification reaction, where the first reactant is immiscible with the second reactant; or a mixing vessel configured to form a homogeneous reactant solution of a co-solvent, an alcohol and an oil; a delivery system configured to deliver the co-solvent, the alcohol and the oil to the mixing vessel; a reaction vessel configured to receive the homogeneous reactant solution and convert the homogeneous reactant solution into a reaction product that includes a biodiesel fuel in a transesterification reaction; or a reaction vessel configured to perform a transesterification reaction between a reactant mixture that includes an alcohol and an oil, where the reactant mixture is at a temperature that is greater than the normal boiling point of the alcohol; a flash tank fluidly coupled to the reaction vessel, the flash tank configured to receive biodiesel fuel and glycerol transesterification reaction products and remaining the reactant mixture, where the flash tank includes a flush valve configured to allow flushing of vapors of the alcohol out of the flash tank; and a separation vessel fluidly coupled to the flash tank, where the separation vessel configured to receive a remaining content of the flash tank into the separation vessel.