Improved formulas for thermal behavior of oscillating nanobubbles

The study of nanobubbles (with sizes of the order of tens to hundreds of nanometers) is currently a hot spot of cavitation and bubble dynamics. In the literature, classical formulas are widely employed for the predictions of the thermal behavior of oscilla- ting macro-bubbles. However, for modelling nanobubbles, the classical formulas may not be adequate due to the effects of the surface tension. In the present paper, a formula with the effects of surface tension fully considered is proposed for the predictions of thermal behavior. The predictions based on the classical formula are also presented for comparisons to show the advantages of the present formula.