The blake threshold of a cavitation nucleus having a radius-dependent surface tension

The Blake threshold is encompassed in most theoretical models of transient acoustic cavitation. Previously, this threshold has been calculated for a bubble having constant surface tension. However, such a bubble is unstable against dissolution and is not a realistic model for a cavitation nucleus. In this article, the Blake threshold is calculated for a more realistic nucleus a bubble having a radius-dependent surface tension. An expression is derived for the dependence of the surface tension on radius for a surfactant-stabilized cavitation nucleus. Two cases, appropriate for charged and polar surfactants, are examined. The Blake threshold for the former case exceeds that of the standard (constant surface tension) case by approximately 1% to 20% for radii ranging from 3.0 m down to 0.01 m. In the latter case, the Blake threshold exceeds that of the standard case by approximately 2% to 38% over the same range of radii. It is concluded that, for the sizes important for cavitation processes, both unstabilized and surfactant-stabilized bubbles become mechanically unstable under essentially the same acoustic conditions. Thus the use of the simpler, albeit unrealistic, nucleus in theoretical models results in no serious error.