The Influence of Line Tension on the Formation of Surface Nanobubbles
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THE INFLUENCE OF LINE TENSION ON THE FORMATION OF SURFACE NANOBUBBLES S. I. Koshoridze and Yu. K. Levin
UDC 621.311.25
The paper investigates the formation and stability of the surface nanobubbles with regard to the line tension at the triple phase boundary; the pinning effect, when the bubble stands on the surface and the triple phase boundary does not move; and the Kelvin equation. It is shown that the negative line tension can cause a spontaneous nanobubble formation at the small diameter of the phase boundary curve and the small contact angle. Keywords: surface nanobubble, Kelvin equation, line tension, line pinning.
In the last few years, there has been a growing interest in the surface nanobubbles (NBs) due to their wide application in many fields of technology [1], while neither the thermodynamic conditions of the nanobubble formation nor their unusually long lifetime are still unclear. There is a hypothesis that the stability of both bulk and surface NBs is conditioned by the charge adsorbed on their surface, which creates an electrostatic repulsive force [2]. According to our early research [3, 4], the surface NB stabilization with charge can be provided by approximately one elementary charge (this is considered to be hydroxide ions (OH–)) for each square nanometre of a nanobubble. At a typical 1014 m-3 concentration of the surface NBs in water [5], having the size of 100 nm, approximately 1018 hydroxide ions for one cubic metre of water are required to stabilize the surface NBs. On the other hand, the neutral pH = 7 at room temperature corresponds to OH– concentration of 6 1019 m 3 . Thus, the NB stabilization with adsorbed charges is possible only in a neutral or alkaline medium. However, according to numerous experiments, stable nanobubbles are also observed in an acid medium (e.g. [6]), and thus the hypothesis [2] faces certain difficulties. It is therefore advisable to seek alternative mechanisms for stabilizing the surface NBs. Several publications [7–10] demonstrated that the line tension slg at the triple phase boundary was essential for the NB formation. Moreover, in works [1, 11] the authors showed that the pinning effect, when the bubble sat on a substrate and the triple phase boundary did not move, stabilized the surface nanobubbles. Additionally, Kaptay [12] took into consideration the capillary effect due to the small nanobubble size. This work focuses on the thermodynamic analysis of the surface NB formation with regard to the above effects (line and surface tension, pinning, and the Kelvin equation) in order to determine the role of each factor in the NB nucleation and stability. It should be noted that the composite effect of those factors was not previously examined. The nanobubble formation force for isobaric and isothermal processes equals the Gibbs free energy of the system, i.e. Amin G . The surface component Gs of the Gibbs free energy can be calculated in accordance with formula [4]
Institute of Applied Mechanics of the Russian Academy of Sciences, Moscow, Russia, e-mail:
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