## 4 Discussion
### Models and Measurements for Setup Validation  
The acoustic field transmitted through the dish and the heat produced in the system were modeled under the specified experimental conditions. The measured radiation profile at the surface of the culture medium (or water in experiments) was congruent in amplitude with the modeled field (Figure 3a,b). For the no-dish condition, the modeled distribution adequately follows the measured profile, with minor variations. The relative amplitudes are also congruent with overall differences of 9% caused by attenuation and transmission losses, which confirms the emitted radiation of (1) is valid for this transducer. However, the acoustic pattern measured through the dish differs from the modeled field. Although the average amplitude is accordingly reduced by the effect of attenuation and transmission losses, the local pressure amplitude is increased at the central region (\(r<5\) cm) and reduced at more external zones for \(r>5\) cm. The modeled field does not show that deformation when the dish is included. The deformation at the center of the field in experiments could be produced by the water movement at the surface provoked by the acoustic force. The displacement of the water, more intense at the center of the well, modifies the shape of the water-air interface, which increases the concentration of the field at that zone. It was not easy to replicate this behavior in the models to demonstrate this hypothesis; however, since average amplitudes were correctly reproduced, we considered that this demonstration was not required. Moreover, using an acoustic absorbent cap in a full filled culture well could be an alternative to reduce standing waves and avoid water agitation at the surface [30,31]; this alternative can be studied in future work. When varying the distances between the transducer and the dish (_TD_) and the depth of the culture medium (_CM_), some resonant behaviors were found. Standing waves are produced at distances that are multiples of half-wavelength of ultrasound in the transmission medium [12]. Figure 3c shows the effect of standing waves in the averaged pressure amplitudes at the surface of the culture medium when the bottom of the dish and the surface of the transducer were perfectly parallel. As predicted, resonances were generated each half-wavelength of both culture medium (vertical trend) and water (horizontal trend), which creates circle-like regions of resonant amplitudes with no-resonant interior zones. At the very center of the dark zones, single points of anti-resonant conditions are produced by destructive interference which reduces the average pressure by half of the emitted pressure. The production of standing waves is regular and predictable when the surfaces are perfectly parallel. Considering the ultrasound wavelength in water is around 1.5 mm (temperature dependent), there is a resonant point each 0.75 mm that would create unpredictable and inconsistent results during cell treatments. In order to have reproducible results using this setup, it is expected to work in the dark circular regions outside the center. The standing waves were reduced when the model included the inclinations of the dish and the transducer. Figure 3d shows a representative result when the dish was inclined 1\({}^{\circ}\) relative to the transducer surface, and the culture medium was inclined another 1\({}^{\circ}\) relative to the bottom of the culture dish. The average amplitudes of the inclined setup were smoother with less resonant zones that help us finding adequate regions to work without standing waves. Although the simulations were carried out varying the angles \(\xi\) and \(\varphi\) from \(-2^{\circ}\) to \(2^{\circ}\), the combinations with less resonant behaviors were found when both relative rotations had the same direction (angles with opposite sign according to Figure 1c).