Result and Discussion
Effect of sonication tip position on extent of mixing
Before determining thermal effects of sonication, a simple acoustic streaming model is used to study the effect of sonication tip position on extent of mixing. A tip placement that induces near to complete mixing is necessary to simplify the heat transfer model (assumption of uniform mixing, decoupling acoustic model from thermal). From our finite element model (see methods), we obtain stationary flow velocities at each point inside the sonication tube. As estimated from other literature sources (Trujillo & Knoerzer, 2011), it is observed that the liquid flows as a uniform jet downward from the sonicator tip, gets deflected by the bottom of the vessel and flows upward, turning near the vessel neck back towards the tip creating a circulation zone of rotating streamlines (yellow color in Fig 2a). Outside the circulation zone there are two regions with moderate to low, irregular velocity (‘dead zones’ at the top and bottom of the tube, indicated by the grey area in Fig 2a). Our goal is to maximize the circulation zone and reduce the dead zone in each tube based on tip position.
This simulation was run for different tip depths starting at 0.5 cm and increasing at intervals of 0.5 cm for each of the four standard tube sizes used in tip sonication of cell extract (1.5, 1.5, 5, 15 and 50 mL) with volumes of 1.5, 1, 5, 10, and 15 mL respectively. Simulation results are shown as streamline diagrams, indicating the boundary of the circulation zone in each of the four tubes (1.5 mL diagram is shown in Figure 2, remainder can be found in Supplementary Fig 1-5). The circulation zone fraction to total fluid volume is quantified with ImageJ and percent circulation zone is plotted as function of tip immersion depth from surface percentage to total liquid depth. It is observed that for each of the tubes simulated the greatest percentage of volume is mixed, if the tip depth is within 20-30% from the top of the total liquid height and is best mixed in a 50 mL tube (with 15 mL total volume).