4) Optimizing temperature sensitive sonication using the heat transfer model
The finite element heat transfer model (COMSOL code in Supplement, also as a module) is readily adaptable and can be used to efficiently determine optimal sonication settings for new temperature sensitive processes. For cell-free extract, this could be using a different sonication vessel, cooling method, or cell extract density. This also has utility beyond cell-free, such as preparation of temperature sensitive emulsions, nanoparticles, or nano-sensors in which the same model can predict temperature rise (after adjusting fluid intrinsic properties). This can be done in a logical stepwise process (summarized in Fig 5).
First, the vessel materials and associated thermal parameters, vessel geometry, sample volume, cooling method (water bath, ice water bath, ice water bath with cooler, insulation or no cooling) are specified as scalar values and proper boundary conditions within COMSOL. The energy requirement per volume is determined according to process requirement (e.g. for cell extract, the energy needed to lyse the cells). In most cases, this is done by empirical measurement. For cell lysis of BL21 DE3 cells, the Kwon et al. data shows yield > 90% lies between 0.27 J/μL to 0.85 J/μL (solid blue slopes shown on Fig 5a). In our model the midpoint, optimal energy density of 0.55 J/μL is used.
Next, the minimum power density and threshold temperature for the specific sonication task should also be specified. In cases of larger volume sonication, if the power density is too low there will not be sufficient power to cause cavitation (and thereby lysis of cells, formation of nanoparticles, etc.) (Chemat et al., 2017). Again, one estimates the minimum power density from process knowledge or empirical data, but this is used as a starting point for the simulation and is adjusted to meet the target threshold temperature (which is again found empirically). For BL21 DE3 star cells, good yield was obtained using a power density between 0.003 and 0.01 W/\(\mu\)L.
The optimum power density and pulse time is obtained iteratively from the model. First the duration of sonication is calculated using the equations in the third process model block (Fig 5) using an initial guess of power density higher than minimum and set pulsing times. The FE model is then used to calculate temperature rise over time. If temperature surpasses the threshold, the power density and pulsing are changed (less power, shorter pulses to drop temperature) and the simulation is again repeated until pulse timing and set power density is obtained for which temperature is below threshold.