Mathematical analysis of the effects of operating conditions and rheological behaviour of reaction medium on biodiesel synthesis under ultrasound irradiation

Ultrasound assisted transesterification has recently been introduced as an effective technology for biodiesel synthesis. However, the behaviour of micro bubbles under ultrasound is affected by operating conditions or rheological properties of reaction mixtures. This paper aims at investigating the changes of micro bubbles characteristics when operating conditions or rheological behaviour of the reaction medium are altered. The mechanistic simulation of micro bubbles was combined with the CFD simulation of reaction mixture to achieve the aims of this work. Continuity and momentum equations of Keller-Miksis model were employed along with reaction, mass and energy balances to simulate different characteristics of micro bubbles such as temperature, pressure, oscillation velocity, maximum radius of micro bubble, equilibrium state of bubble content, diffusion rates of reaction compounds towards bubbles and reaction within bubbles. It was found that among different combinations of reaction temperature, reactants ratio and intensity of ultrasound irradiation, the last one played the most important role. Radius, internal temperature and pressure of bubbles significantly increased with power amplitude due to stronger expansion and greater energy accumulation. At the same time, increase in reaction temperature and alcohol concentration made the bubbles characteristics rather moderate. It was also found that the growth of bubbles radius was reduced by about 4 times as the reaction progressed and the reaction mixture became more viscous and dense. The maximum internal temperature and pressure decreased by about 178 K and 220 bar due to moderate expansion of bubbles. Oscillation velocity was also restricted in this situation.