pressure inside gas nanobubbles

According to Laplace equation the following is the pressure inside a gas bubble for soluble gasses:

Pin = Pout + 4ʏ/d

Where Pin = internal pressure, Pout = external pressure, ʏ = surface tension, d = cavity diameter. The expression 4ʏ/d is defined as the excess pressure.

The controversy of nanobubbles existence is based on the fact that as the diameter of the bubble is in the range of nanometers the internal pressure will be very high, significantly reducing their lifespan. By reducing the surface tension utilizing surface-active material the excess pressure can be lowered in order to stabilize the bubbles.

The concentration of surface-active agents may also be used to regulate the bubble size. Such coated nanobubbles are used in the medical field as ultrasound contrast agents and targeted drug delivery. The Laplace equation may not hold at small diameters such as nanobubbles.For nanobubbles the calculated internal gas pressure should cause an almost instantaneously dissolution but as nanobubbles are now known to exist for long periods the existing basic theories may be insufficient. 


Real nanobubbles cannot be seen with the naked eye. Their existence can be demonstrated by laser scattering. 

The figure below (left) shows a green laser passing through a jar of pristine distilled water. As you can observe the laser beam is almost invisible in the pristine distilled water. The figure below (right) shows the same laser beam passing through the same distilled water after using our proprietary nanobubbler for 10 minutes. 

surface charge and surface tension effects on the nanobubbles stability

Surface charge can counter the surface tension preventing high pressure within the nanobubbles.

It may be expected that as the nanobubble shrinks the charge density will increase.

The effect of charges at the liquid/gas interface is that the surface negative charges repelling each other are stretching out the surface of the bubble. Thus, the effect of the charges is to reduce the effect of the surface tension.

The surface tension tends to reduce the surface whereas the surface charge tends to expand it. Equilibrium will be reached when these opposing forces are equal meaning that Pin = Pout.

Pout can be found to be:

Pout = ɸ2/2Dϵ0

Where ɸ = the surface density on the inner surface of the bubble, D = relative dielectric constant of the gas bubble, ϵ = the permittivity of vacuum.

The inward pressure, Pin, due to the surface pressure is given from the Laplace equation:

Pin = 4ʏ/d

Where ʏ = the surface tension, and d = the diameter of the bubble.

Equalizing these two pressures one can determine the charge density at different bubble diameters. For example, for nanobubbles diameters of 10nm, 20nm, 50nm, 100nm and 200nm the charge density is 0.14, 0.1, 0.06, 0.04 and 0.03 e-/nm2 (e-/nm2 = -1.6 –mC/m2).



The dashed red line is an extrapolation of the data.

The surface tension reduction contributes to the stability of nanobubbles.  

long lived presence of nanobubbles in liquids

The likely reason for the long-lived presence of nanobubbles is that the nanobubbles gas/liquid interface is charged.  This charge is introducing an opposing force to the surface tension slowing or preventing nanobubbles dissipation.  

The presence of charges in interface will reduce the internal pressure and the apparent surface tension with charge repulsion acting in the opposite direction to the surface minimization due to the surface tension. 

The charge similarity together with the lack of van der Waals attraction (the cavities possessing close to zero electron density) tends to prevent nanobubbles from coalescence.  

Nanobubbles protect each other from diffusive loss by a shielding effect, effectively producing a back pressure of gas from neighboring bubbles that may be separated by about the thickness of the unstirred layer, which is slowing the dissolution. The slow dissolution will be even slower than expected due to higher osmotic pressure at the gas/liquid interface which is also driving the dissolved gas near the interface back to the nanobubble.

nanobubbles behavior in liquids

Nanobubbles grow or shrink by diffusion according to whether the surrounding solution is over-saturated or under-saturated with a dissolved gas relative to the raised cavity pressure.  

The solubility of a gas is proportionate to gas pressure and this pressure, exerted by the surface tension, is inversely proportional to the diameter of the bubble.  The dissolution process is, therefore, accelerated with an increasing tendency for gasses to dissolve as the bubbles reduce in size.  

The dissolution is also increased by the nanobubbles Brownian motion which aids the removal of any gas-saturated surrounding.  In contrast to the previous theoretical view there is now much evidence that gas filled nanobubbles can exist for significant periods of time in aqueous solutions.

electrostatic interaction between nanobubbles

The electrostatic interaction between nanobubbles can be large enough to avoid coalescence. Electrostatic interaction will slow any rise even more.

The zeta potential is generally negative and mostly independent of the bubble diameter. The zeta potential depends strongly on the pH and the dissolved salt concentrations whereby increased ionic strength reduces zeta potential. As all the bubbles are similarly charged their coalescence is discouraged. The zeta potential of a bubble can be determined from their horizontal velocity in a horizontal electric field:

v = ζϵ/µ

Where ζ = zeta potential, ϵ = permittivity, and µ = dynamic viscosity. 

The zeta potential increases as the bubble diameter decreases and is around -30mV at the micron level. 


summary of nanobubbles properties

A. Longevity

            - Disappearance of buoyant force 

            - Physical stability, persistence (nanobubbles generally don’t dissolve away)

B. Interface Composition

            - Hydrogen bonds are formed at the nanobubble surface reducing gas diffusivity

C. Small carrying capacity that results in controlled gas transfer rates (Biomedical applications)

D. Migration directionality controlled by ultrasonic fields

E. Nanobubble interfaces can be loaded with surfactants

F. Delivery of material by induced rupture utilizing ultrasound fields and/or optical plasmonic fields

G. Seeded nanobubbles can be used as nucleation sites for crystal growth


Nanobubbles are gas filled cavities in a solution (water solution) with a diameter less than 100 nm. Some define nanobubbles as bubbles in a solution with a diameter smaller than 1 µm and larger than 1 nm.  Each bubble is surrounded by an interface with different properties than the bulk solution.  We will refer to bubbles with a diameter less than 1 micron as “ultra-fine bubbles (UFB)” which include the family of nanobubbles as defined above.   

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