How is Fine/Nano bubble generate?
Bubbles are gas-filled cavities within liquids (and solids; here we deal with liquids only). In liquids, bubbles have internal equilibrium pressures at least that of the external environment. Each bubble is surrounded by an interface that possesses different properties to that of the bulk solution. Surfactants can stabilize bubbles of all sizes, but bubbles may also be formed without them. Large bubbles (>100 µ diameter) rise rapidly (> 6 mm ˣ s-1) and directly to the surface. Microbubbles ( 1 µ - 100 µ diameter) provide a higher surface area per unit volume than the commonly seen larger bubbles. They may be produced by numerous methods and have been used for sludge solubilization, water purification, treatment of wastewater, drug delivery and as contrast agent together with ultrasound. l They are not stable for long periods (~ minutes), rising slowly (10-3 - 10 mm ˣ s-1) and indirectly to the surface, but smaller ones (≈ < 20 µ diameter) will shrink to form more effective and stable nanobubbles. Only these tiny bubbles (< 1 µm diameter) are stable for significant periods in suspension (rising at less than 10-2 µm ˣ s-1 but with this counteracted by Brownian motion of greater than 1 µm ˣ s-1), with larger or smaller bubbles disappearing rapidly from aqueous suspensions unless stabilized with surface-active agents. They are normally and commonly present in lower amounts in aqueous solutions. Their presence is necessary as cavitation nuclei in pure water, particularly when this water does not contain any foreign microparticles and the vessel is without any wall defects.
Nanobubbles (for a history) are generally recognized in the current (2018 and earlier) scientific literature as those gaseous cavities with diameters less than a micron. As such cavities (bubbles) are often greater than 100 nm in diameter but the term 'nano' is applied mostly to particles of smaller diameter (< 100 nm, ISO 20480 1:2017), sub-micron bubbles should probably be known as ultrafine bubbles in the future; all bubbles smaller than 100 µm diameter should then be known as 'fine' bubbles. In this website, we use the term 'nanobubble' as it is still more widely used in the literature.
The surface area of a volume of bubbles is in inverse proportion to the bubble diameter. Thus for the same volume of bubble, their surface area (A) increases proportionally to the reduction in bubble diameter (D; A = 6/D); for example, one mL of 100 nm radius bubbles (2ˣ1015 bubbles) has 1000 times more surface (60 m2) than one mL of 0.1 mm bubbles (2ˣ106 bubbles, 0.06 m2).
Basic theory states that the energy cost of bubble formation depends upon the interfacial area, and is governed by the bubble's surface tension. Small bubbles (< 25 µm diameter) have taut inflexible surfaces (like high-pressure balloons) that limit distortion since large bubbles (≈ mm diameter) have flexible surfaces (like low-pressure balloons) and can divide (break up) relatively easily. The buoyancy of larger bubbles will cause them to rise to the surface of aqueous solutions. Stokes' equation is valid for particles at low Reynolds number and governs the rise rate (R = rise rate, m ˣ s-1): a
Nanobubble movement
R = ρgd2/18μ
where ρ = density (kg ˣ m-3), g = gravity (m ˣ s-2), d = bubble diameter (m), and μ = dynamic viscosity (Pa ˣ s); according to this relationship a 2.5 μm diameter bubble rises 100 times slower (≈ 0.2 mm ˣ min-1) than a 25 μm diameter bubble (≈ 2.3 cm ˣ min-1) , and a nanobubble rises much more slowly than its random motion. The real behavior of bubbles is more complex than this, however, with experiments rarely showing good agreement with the Stokes equation. The Brownian movement velocities are given by the equation
where R is the gas constant (J ˣ mol-1 ˣ K-1; kg ˣ m2 ˣ s-2 ˣ K-1 ˣ mol-1), T is the temperature (K), N is the Avogadro constant, η is the dynamic viscosity (Pa ˣ s; kg ˣ m-1 ˣ s-1), r is the averaged particle radius (m) and t is the measurement time (here taken as one second for comparison to the bubble rise velocities).
Bubbles less than 1 μm diameter rise so slowly that the rate is not determinable. This is due to their random Brownian motion and their low buoyancy. Accumulation of denser elements at the smaller bubbles' extensive surfaces may contribute significantly to the low buoyancy of such tiny bubbles. Larger bubbles (25-200 μm diameter) do not obey the above Stokes equation but the Hadamard and Rybczynski equation with terminal velocity 1.5 times the Stokes velocity :
RH-R = 3R/2 = ρgd2/12μ
This is due to interfacial oscillations as the surface area increases, and this surface becomes less taut. Bubbles larger than about 0.2 mm rise at rates proportional to their diameter (Rd=0.2-2 mm = 120 d, m ˣ s-1). Bubbles larger than about 2 mm diameter rise rapidly at almost the same rate irrespective of diameter (Rd>2mm = ≈ 0.25 m ˣ s-1) . Larger bubbles (≈ > 0.2 mm) undergo significant shape changes on rising through the solution due to the frictional resistance of the liquid. All these rise velocities are relevant to low concentrations of bubbles. Where the solution has high bubble concentrations, the bubbles may physically interfere with each other and rise more slowly.
Time-dependent shrinkage of micro-bubbles
In addition to and in competition to the effect of buoyancy, small bubbles (<25-50 µm diameter) shrink (see below), such that the overall behavior of micro-bubbles is complex.
The degree of saturation next to a bubble depends on the gas pressure within the bubble. Smaller bubbles have higher internal pressure (see below) and release gas to dissolve under pressure into the surrounding under-saturated solution whereas larger bubbles grow by taking up gas from supersaturated solution; thus small bubbles shrink, and large bubbles grow (a process known as 'Ostwald ripening').
Evolution of bubbles
The rates of these processes depend on the circumstances. Also as bubbles rise the pressure on them drops due to the depth of the water, and they consequentially grow and rise faster.
The electrostatic interactions between nanobubbles in water are usually significant enough to prevent coalescence and slow any rise. The charges on the bubbles are determined from their horizontal velocity (v, m2 ˣ s-1 ˣ V-1) in a horizontal electric field, where
v = ζε/μ
where ζ = zeta potential (V), ε = permittivity of water (s2 ˣ c2 ˣ kg-1 ˣ m-3), and μ = dynamic viscosity (Pa ˣ s). The zeta potential is generally negative but mostly independent of the bubble diameter. It depends strongly on the pH , and the dissolved salt concentrations (increased ionic strength reduces zeta potential). The similar negative charge on all the bubbles discourages their coalescence. Also, their division is not favored unless there is considerable energy input, with smaller bubbles requiring greater energy. Thus, small bubbles can grow or contract, but rarely coalesce or divide.
Insoluble gasses may form nanobubbles that are stable indefinitely in water. For soluble gasses, the pressure inside gas cavities is inversely proportional to their diameter and given by the Laplace equation,
Pin = Pout +
4γ/d
Pexcess = 4γ/d
where Pin and Pout are the respective cavity internal and external pressures, γ is the surface tension (N ˣ m-1), and d is the cavity diameter (m). The atmospheric pressure and the depth of the bubble govern the external pressure. Thus 10 µm and 100 µm bubbles contain gas at about 1.3 and 1.03 bar respectively in water. Where the external pressure is negative and surfactant is present, such as within long-distance water transport in the xylem of plants, stable water-vapor-containing nanobubbles are formed.
This Laplace equation is simply derived by equating the free energy change on increasing the surface area of a spherical cavity
= γΔA = 4πγ(r+δr)2 - 4πγr2
to the pressure-volume work
= ΔPΔV = ΔP(4/3)π(r+δr)3 - ΔP(4/3)πr3
For nanobubbles the calculated internal gas pressure should cause their almost instantaneous dissolution using early theory , i but as nanobubbles are now known to exist for long periods, this basic theory must be insufficient. It is not certain that the Laplace equation holds at very small radii but it does hold for H2 nanobubbles above 10-nm radius. It has been shown that surface tension may increase almost 20-fold to 1.3 N ˣ m-1 for 150 nm diameter droplets in the absence of other effectors such as surface charge. Thus, the Laplace equation appears correct down to about a nanometer or so, below which a small correction must be applied. However, there may well be further contributions to the work required, due to the removal of surface-bound material, as the surface area contracts that would lower the excess pressure. In the absence of any other surface effects such as solute interactions or charges, the excess pressures expected in a 50 nm radius spherical nanobubble and a 50 nm diameter surface nanobubble (rS = 50 nm, r = 1000 nm), due to the surface tension minimizing the cavity surface, are 5.8 MPa and 0.14 MPa respectively. It has been proposed that supersaturation around the nanobubbles may significantly lower the surface tension, so allowing stable nanobubbles.
The pressure within nanobubbles is affected by other factors and is possibly much lower than expected from the Laplace equation. The gas-liquid interface of bubbles may be deliberately (or fortuitously) coated with surface-active materials, such as protein or detergent, that lower the surface tension and hence the excess pressure so stabilizing the bubbles. The presence and concentration of surface active agents regulate the bubbles size. Such coated microbubbles/nanobubbles are used as ultrasound contrast agents or for targeted drug delivery.
An increase in static pressure on bulk nanobubbles caused their number concentration to decrease but their mean size to increase,. Both these parameters undergo partial recoveries on the release of the pressure.