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).