However, if this is indeed the case, there must be a mechanism and a third component in the system which causes the inhibition of the diffusion, and which, by extension, exerts a pressure that opposes the surface tension and the external pressure, along with the internal pressure. The third component is suspected to be the hydroxide ion, which is always present in aqueous solutions, and which is detected around collapsing microbubbles, and has already been applied to wastewater treatment. This ion tends to aggregate around the nanobubble surface, and is suspected to be present in the form of a cloud of ions around the bubble, attracted to the surface by an as yet unconfirmed force, but widely thought to be physical bonds of the nature of van der Waal’s force, and plays a part in the inhibition of gas diffusion out of the bubble. The exact mechanism, distribution of the ions, the extent to which they inhibit the diffusion, and other concerns regarding their roles in the mechanism of stabilization is not yet determined, but several theories have been proposed as to their role, and more also exist which do not take into account their role, or do not require them to play any role in the process at all. The role of the ions is suspected to be due to the repulsion of the ions toward each other, which in some way opposes the external pressure and the surface tension, but this is yet to be confirmed. Thus, while there are several approaches to the question, as of recent efforts it still remains unresolved. Several theoretical approaches have been proposed, many of which are highly specific to the circumstances for which the study was conducted, and none thus far have proposed an overarching theory as to the formation and evolution of bulk nanobubbles. As far back as 1997 Ljunggren and co-workers proposed theoretical explanations for colloid-sized gas bubbles based on diffusion of the gas into the liquid,fodder system for sale which could now be considered nanobubbles. Seddon et. al. also contributed to the emerging idea around the same time, but there have been few contributions to understanding their stable presence since then.
Explanations for specific cases of phenomena such as surface nanobubbles, nanobubbles generated electrochemically, and so forth have been offered so far. Early on, the Young Laplace equation was used to describe nanobubble stability, but the internal pressures required are far higher than would be possible at ambient temperature for the amount of gas that is contained within the bubble. Attard and co-workers analysed the thermodynamic stability of bulk nanobubbles, but it was found that the radius of nanobubbles could not be accurately predicted from thermodynamic considerations, nor was an expression offered for the rate of decrease in nanobubble size. Brenner and Lohse presented a model for predicting the radius of surface bubbles based on the dynamic equilibrium between diffusion into and out of nanobubbles situated at a surface. Further work in specific cases by Weijs and Lohse suggested the use of increased length scales to counter the problem of high internal pressures due to the relatively high surface tension of a bubble in that size range. Sverdrup and colleagues offered explanations as to the rates of decrease in size based on diffusion in all directions possible through the gas-water interface at the nanobubble surface. In their models they consider the possibility of diffusion both into and out of the nanobubble, with a sufficiently high mass transfer coefficient. Their models consist of a combination of Henry’s Law and Taylor series expansion. The equations are plotted, taking time as a function of radius and show coherence with previous models given by Ljunggren. However, no comparisons with experimental data are provided. The Young-Laplace equation seems inadequate to completely describe the phenomenon as it requires extremely high internal pressures of the gas to balance the surface tension that causes the nanobubble to shrink, as summarized by Attard and coworkers. However, the interface through which the diffusion occurs has thus far been considered to have constant properties of being composed only of water molecules and gas molecules.
Yasui and colleagues also detail several theories that attempt to explain bulk nanobubble stability, based on the armoured bubble model, a particle crevice theory, a skin theory, the dynamic equilibrium model and electrostatic repulsion. Among these theories, it appears that electrostatic repulsion has the most experimental support. Studies of interfaces between water and practically all surfaces such as glass are negatively charged, assumed to be due to the accumulation of hydroxide ions physisorbed to the monolayer as reported by Zangi and Engberts. Thus, it is reasonable to suppose that the water-gas interface is also negatively charged due to similar congregation of hydroxide ions at the bubble surface. Furthermore, studies conducted by Takahashi and others have shown that nanobubbles are indeed negatively charged, with oxygen nanobubbles having a zeta potential about -35 mV. Thus, it is evident that hydroxide ions physisorbed onto the surface of the nanobubble play a role in the interactions between the molecules present there. Jin et. al. proposed a model for bulk nanobubble stability involving the electrostatic repulsion, terming the pressure due to the electrostatic force as Maxwell pressure. One rationale involving the surface charge density of a bulk nanobubble has been proposed by Ahmed and colleagues that involves electrostatic repulsion balancing the surface tension. In the following, we consider a theory of electrostatic repulsion and what it requires of the conditions imposed for nanobubbles to have the long-term stability that has been observed experimentally. Several applications have been discovered, such as for wastewater treatment, fish farming, shrimp breeding, and hydroponics. These are further substantiated by Agarwal and coworkers, for such specific issues as the disinfection of infected surfaces, the degradation of organic compounds, and the disinfection of the water itself. The effects of increased yield of fish due to higher dissolved oxygen content are summarised by Endo et al..
The usage of hydrogen nanobubbles in gasoline to improve the calorific yield is also reported by Oha et al.. Other projected uses include the use of nanobubbles as contrast agents for the ultrasound imaging of tumours, as reported by Cai and co-workers, as well as reduction and removal of deposits of calcium oxalate, which is similar to the composition of kidney stones in rat kidneys, as presented by Hirose et al. Another application of the nanobubble’s ability to permit salts to crystallize is the design of self-cleaning membranes for desalination of water,fodder growing system which use nanobubbles as electrically conductive spacers and pass current through them to force the salts to crystallize on the nanobubble surface, which will permit easy removal of the accumulated salts. This was demonstrated and presented by Abida et al. The pressure balance of the nanobubble is considered to be given by the Young-Laplace equation, which, as explained above, equates the internal pressure, external pressure and the surface tension. The first of the four forces that we consider in the Young-Laplace equation is internal pressure. It is proportional to the surface area of the nanobubble, and is assigned a positive sign since it acts to increase surface area. The second is the external pressure, given by the hydrostatic pressure acting on the surface of the bubble, which also decreases the surface area and is negative. The third is the surface tension, which acts along the surface area at the molecular level. The surface tension acts to decrease the surface area, hence the radius and size, and can also be assigned the negative sign. However, a fourth force which is thought to be integral to the stability is the electrostatic repulsion between hydroxide ions adsorbed to the surface of the nanobubble, or, possibly in the cloud surrounding the surface. This repulsion seeks to reduce the contact between the ions on the surface of the bubbles, which also acts to increase the distance between the ions, thus increasing the surface area, and therefore results in a positive pressure. The nature of the interaction between ions can be characterized by the expression for Coulombic repulsion. Since one hydroxide ion is of the order of 1 nanometre in diameter, and most nanobubbles are two orders of magnitude greater in size, we can ignore the curvature of the distance between them and take it to be linear. The repulsion should, in theory, affect all neighbouring hydroxide ions, but is assumed to be insignificant beyond the nearest neighbours. We also assume the spatial arrangement of these ions over the surface to be close-packed in nature, since the repulsion is equal in all directions, and they would ideally assume a close-packed formation. This arrangement of ions is shown schematically below, in Fig. 1a, and as shown in Fig 1b it is assumed, due to close-packing, that they assume the formation of a rhomboidal unit cell, of side and diagonal length denoted by x, which will be referred to subsequently as the inter-ionic distance. That the nanobubble shrinks due to outward diffusion of the gas contained within is, of course, undisputed, but the precise methods and the rate of diffusion are highly debated. Previous theoretical studies have always assumed a model with a higher mass transfer coefficient, or longer time scales for the process to account for the reduced rate and the high lifetime of the nanobubble.
However, it is reasonable to suggest that the change in the rate of diffusion can be attributed to two things: the velocity due to the Brownian motion of the nanobubble, and the inhibition of the diffusion due to the adsorbed hydroxide ions on the surface. In this chapter, the possible effects of Brownian motion are examined for the effect on the rate of diffusion that they may possess. Earlier studies have shown that nanobubbles can be formed by supersaturation, where the solubility limit of the gas, when surpassed will permit the gas to precipitate and form bulk nanobubbles as reported by Matsuki and co-workers . The shrinkage of nanobubbles has so far been thought to be governed by Fick’s Laws, since it is a case of how fast the gas can dissolve into the surrounding fluid. Thus, according to the first law, it must be directly proportional to the outward gas flux, but the constant is still the diffusion constant D0 for the diffusion of the gas into water. However, this only holds true where the surface area of the nanobubble remains constant. It is, however, possible, that the outward diffusion is a case of Fick’s second law, since the surface area that is available to the gas to diffuse outward also changes according to size, and that this surface area determines the rate of shrinkage and thus the lifetime of the bulk nanobubble. It is then reasonable to suppose that the cause of the change of surface area available for diffusion is the change in the surface area occupied by hydroxide ions combined with the decreasing radius of the bulk nanobubble. The rationale for the assumption that the hydroxide ions adhere to and are released the nanobubble surface is based on two observations, as mentioned before. Firstly, the observation that all interfaces formed by water are negatively charged, and we consider nanobubbles to be a special case of a gas-water interface which may be charged in the same way. Secondly, the zeta potentials measured for nanobubbles are all negative, indicating that a negative ion present in pure water is responsible for the negative charge, which by elimination is the hydroxide ion. Further observations also indicate higher negativepotentials for more electronegative gases, such as oxygen and nitrogen, than for other reported gases such as argon and xenon as reported by Ushikubo et. al.. That nano- and microbubbles release hydroxide ions as they shrink is a well-known phenomenon. The stabilization and the shrinkage can be considered to be related to the same phenomenon; thus, the ideal case can be taken to be a nanobubble that is newly formed with no hydroxide ions at the surface at the instant of its formation of an interface. Here, the hydroxide ions present in the water immediately surrounding the bubble, in the hydrodynamic layer, adhere almost instantaneously, the time taken for the adsorption to occur being too small in comparison to the overall timescale to be important.