19.4 Formation of gaseous bubbles in liquids
Description
This article is from the Chemistry FAQ, by Bruce Hamilton B.Hamilton@irl.cri.nz with numerous contributions by others.
19.4 Formation of gaseous bubbles in liquids
Discussions about the behaviour of dissolved gases in liquids, especially
when discussing carbonated beverages, are usually more appropriate in
sci.physics and/or sci.mech.fluids, and there is a good text available [11].
Section 23.9 of this FAQ lists the change in solubility with temperature
for common atmospheric gases in water at near-ambient pressure. As the
temperature increases, the solubility decreases, creating a supersaturated
solution that can result in bubble formation. A similar effect occurs if the
pressure is reduced. The formation of bubbles can be understood in
thermodynamic terms using the Gibbs free energy of the bubble.
Gibbs free energy = -n * R * T ln(C/Cs) + gamma * A
A = Surface area of the bubble.
C = Concentration of gas in the liquid,
Cs = Concentration of gas in the liquid at saturation,
gamma = Interfacial tension between the gas and the liquid
n = Number of moles of gas in the bubble
= (P*V)/(R*T), where P = pressure, and V = volume of a sphere.
R = Gas Constant
T = Temperature
After inserting the expressions for the surface area of a sphere (r = radius)
and number of moles, and differentiating, then we obtain:-
r(mininum) = 2 * gamma / ( P * ln(C/Cs))
This describes the size of a bubble that would continue to grow under the
existing conditions, rather than redissolve. Of course, the expression
assumes homogeneous precipitation of the bubble, and in real life most
bubbles are created heterogeneously. Statistics and kinetics are also
required to determine the rate of formation of bubbles, and predict the
effect of changing parameters such as temperature. As the liquid is warmed,
bubbles may be created faster, as the higher temperatures overcome the
activation barrier - which is the difference between the Gibbs free energy
when r is less than r(minimum), and the Gibbs free energy at r(minimum).
The formation of a bubble also dramatically perturbs the system, even
causing secondary bubbles to form. Secondary bubble formation may be
implicated in the production of copious quantities of froth from shaken,
quickly-opened, carbonated drink containers. The sites for gaseous bubble
formation in supersaturated drinks are typically small particles, or minor
flaws on the smooth surface of the container.
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