As predicted by classical macroscopic theory, the lifetime for nanoscale gas bubbles is extremely short. However, stable gas nanobubbles have been experimentally observed in recent years. In this report, we theoretically show that, if the inner density of gas bubbles is sufficiently high, the lifetime of nanobubbles can increase by at least 4 orders of magnitude, and even approaches the timescale for experimental observations. nanobubble, stability, long lifetime, inner density Interfaces of solid surfaces against liquids are of broad interest. If nanoscale gas nucleates at the liquid/solid interface, interfacial properties and dynamics of the system might significantly change, for example, by the occurrence of long-ranged interactions between hydrophobic interfaces immersed in water [1][2][3] , stability of colloidal systems [4] , flotation of minerals [5][6][7] , rupture of wetting films [8] , and reduction of friction and drag in microfluidic transportation [9][10][11][12][13] .There are many experiments supporting the existence of surface nanobubbles at the solid-liquid interface by atomic force microscopy (AFM) measurements [14][15][16][17][18][19][20][21][22] , and also other techniques [23,24] . However, the Laplace equationpredicts that nanoscale bubbles have a very high inner gas pressure. In the equation,ΔP is the pressure difference of bubble between its inner and outer, γ is the surface tension at the interface between bubble and liquid, and R is the radius of bubble. For example, a nanobubble with a radius of 10 nm would have an inner pressure of 144 atm. Consequently, the gas in the nanobubble would rapidly dissolve in ambient liquid. It should be noted that the validity of the Laplace equation on the nanometer dimension is questionable, and the surface tension on the nanometer dimension may be
