The best cavitation can be obtained only with an appropriate frequency ratio and phase difference. To optimize dual-frequency ultrasonic cavitation and to analyze the influence of the frequency ratio and phase difference, a dynamic model of dual-frequency ultrasonic cavitation that considers energy and material exchange inside and outside the bubble was established. The results show that the negative-pressure amplitude of dual-frequency ultrasound is higher than that of single-frequency ultrasound for the same energy input. For a harmonic, the phase difference that results in a maximum of the negative-pressure amplitude of dual-frequency ultrasound is periodic for different frequency ratios. The phase difference that results in expansion–contraction oscillations of the bubble changes periodically as 1.5π → π → 0.5π → 0 → 1.5π for different frequency ratios. The maximum bubble radius and the maxima of the pressure, energy, and number of water vapor molecules inside the bubble all reduce spirally and the intensity of cavitation decreases with an increase of the frequency ratio. Compared with a harmonic, the maxima of the cavitation parameters are less affected by the phase difference for an ultraharmonic. Therefore, similar cavitation can be easier to obtain by employing an ultraharmonic, which is helpful in achieving stable cavitation.

只有在具有适当的频率比和相位差的情况下，才能获得最佳的空化作用。为了优化双频超声空化并分析频率比和相位差的影响，建立了考虑气泡内外能量和物质交换的双频超声空化动力学模型。结果表明，在相同能量输入下，双频超声的负压幅值高于单频超声的负压幅值。对于谐波，导致双频超声负压幅度最大的相位差对于不同的频率比是周期性的。导致气泡膨胀-收缩振荡的相位差周期性地变化为1.5π→π→0.5π→0→1。不同的频率比为5π。最大气泡半径和气泡内压力，能量以及水蒸气分子数量的最大值都呈螺旋形减小，并且空化强度随频率比的增加而减小。与谐波相比，对于超谐波，空化参数的最大值受相位差的影响较小。因此，通过使用超谐波可以更容易地获得类似的空化，这有助于实现稳定的空化。对于超谐波，空化参数的最大值受相位差的影响较小。因此，通过使用超谐波可以更容易获得类似的气蚀，这有助于实现稳定的气蚀。对于超谐波，空化参数的最大值受相位差的影响较小。因此，通过使用超谐波可以更容易获得类似的气蚀，这有助于实现稳定的气蚀。