Role of Capillary Fluctuations in Stabilizing Bulk Nanobubbles

The existence of bulk nanobubbles (BNBs) has long been questioned, primarily due to the limitations of experimental techniques and the widespread assumption that spherical bubbles cannot achieve a stable equilibrium. In this study, we develop a model that describes the stability of BNBs based on experimental observations, revealing that the intensity N of thermal capillary waves, which affect BNB through localized thermal fluctuations inducing deformations and altering pressure distribution, significantly influences the stability of these BNBs in different saturated environments. Our computational results corroborate three frequently reported but controversial characteristics of BNBs: their typical size distribution ranges from 100 to 200 nm around R_stable = 107 nm with N = 10,000; they maintain stability in undersaturated conditions; and their size distributions show minimal fluctuations across different saturation levels. Our results provide a possible mechanism for understanding BNB stability and align well with experimental observations, thereby significantly enhancing the potential for their application in the field of soft matter science.