Bubble Nucleation: Bubble stability
Bubble Nucleation: Bubble & Droplet Stability
I promised some people in this forum that I would eventually get around to discussing nucleation theory. Rather than try to write and discuss this subject in one blog, I have decided to break it up into several discussions. And as such we shall start with bubble stability. Included here is an introduction to droplet stability (sorry much is this is from a book I wrote a decade or so ago but never published).
In general tensile surfaces are in pressure/mechanical equilibrium and are stable.
However, for both droplets and bubbles, there exists a critical size below which they are unstable 13,14,15, whilst for rising bubbles, there seems to be a size above, which they tend to disintegrate. Generally bubbles become unstable when smaller than micro sizes, while droplets are unstable when in nano sized.
In Fig. 2.9.1 we show a tensile layer, with molecule #1 representing liquid molecules, which are part of the tensile layer and molecule #2 representing liquid molecules away from the tensile layer. Since the cohesive forces are acting upon molecule #1 in five directions down three orthogonal axis. Therefore, the resultant force on molecule #1 is directed into the liquid, perpendicular to the tensile layer, as is shown in Fig 2.9.2. We realize that the cohesive forces act upon bulk liquid molecule #2 (in Fig 2.9.1) in six directions hence there is no net force acting upon molecule #2 (as shown in Fig. 2.9.2).
We may hypothesize that a condition of tensile layer stability is: The cohesive forces act upon the molecules, which constitute the tensile layer, do so in only five directions, when contemplating the problem in three dimension (3-d), i.e. three directions when contemplating in two dimensions (2-d), as illustrated by molecule 1 in Fig 2.9.
Take water as an example and visualize the cohesive bonding of polar liquid molecules, as being due to some alignment of the liquid molecule’s dipole moments. A simple model shows a liquid droplet in 2-d space, with the magnetic dipoles of molecules, being aligned along the tensile layer, as shown in Fig 2.9.3. Although the dipoles are shown to be perpendicular to the tensile layer, they would more likely be aligned parallel to said interface, with the dipole’s longitudinal axis directed into the page. In Fig. 2.9.3, it is obvious that no matter how small the droplet’s radius (rd) becomes, the cohesive forces are always going to act on the molecules, which constitute the tensile layer, in only three directions, in our 2-d diagram which translated into 5 directions in 3-d.
Can the last statement similarly be said for gaseous or vaporous bubbles? Consider the 2-d vaporous bubble illustrated in Fig.2.9.4. Once more a simple perspective shows that the dipoles are perpendicular to the tensile layer, when in fact they might more likely be aligned parallel to it so that their longitudinal axis would be directed into the page. We have no problem similarly visualizing the cohesive bonding acting along the tensile surface, as being due to the alignment of the liquid molecule’s dipole moments. Now, imagine that the bubble’s radius decreases. We realize that at some point, that the cohesive forces which may be associated with the molecule’s dipole moments that constitute the tensile layer, will become felt across bubble.
If the cohesive of the molecules that constitute the tensile layer, are felt across the bubble, then we can expect that the bubble will become inherently unstable consequentially it will be prone to collapse. When the bubble does collapse, then the cohesive forces, acting upon the molecules, are doing so in four orthogonal directions, rather than three orthogonal directions.
Our expectation is: A bubble cannot exist when the magnitude of the bubble’s radius approaches the magnitude of the intermolecular distance (D) or at the very least the distance over which cohesive forces are readily felt. A more thorough understanding might necessitate the analysis of how the electromagnetic fields inside of a particular bubble, changes with the bubble’s radius. All we can surmise at this point is: The electromagnetic fields due to the dipole moments of molecules along the tensile layer should approach zero, as the bubble’s radius approaches infinity. This is of course considering that the liquid’s cohesive forces along the tensile layer are strictly due to dipole attraction. Recent work by the likes Gerald Pollack of whose proposes an EZ layer exists may such an analysis but will not remove the concept of cohesive forces.
Now we must ask: Does bubble’s radius have to approach intermolecular distances (D), in order for the tensile layer to be unstable?
Consider that we have a shrinking stable bubble in 2-d space. We may expect that at some point the dipole moments of the polar molecules along the tensile layer would be felt by 3rd polar molecule away from it, as is illustrated by the arrow in Fig 2.9.6. More precisely, in Fig 2.9.6, we can imagine that the radius of the bubble is sufficiently small that molecule 5 is felt by molecule 8. Similarly, molecules 4 and 10 feel molecule 1, while molecules 11 and 5 feel molecule 2 etc. Certainly as the bubble gets smaller, the influence of the 3rd molecule away increases, therefore our expectation should be that a bubble becomes unstable before: . With this being the case, we may expect that at some point wherein the bubble’s radius is still significantly larger than the intermolecular distances, that the tensile layer may fold up like a squeezed accordion.
If we wanted to fully model at what point do the polar molecules interact with the 3rd polar molecule away from themselves, we would also have to consider the liquid’s Brownian motion. Our expectations will be, as the liquid molecules vibrate to and fro, the interaction between a polar molecule and its 3rd neighboring polar molecule will most readily occur when the two molecules, are closest to each other. Accordingly, any precise analysis should put special emphasis upon the closet possible intermolecular spacing and not simply deal with the mean intermolecular spacing, when determining the stability of a tensile layer.
Furthermore, our model was that of a 2-d bubble. In reality bubbles are three dimensional objects (3-d), therefore a more precise definition would be: A bubble’s tensile layer is stable when the liquid molecules along the tensile layer, only feel cohesive forces of their neighboring liquid molecules in five rather than six directions, with each direction being along one of three orthogonal axis in Cartesian space.
Although we only discussed polar molecules, a similar analysis would apply to bubbles forming in other types of liquids. We might expect that a bubble in an ionic bonded liquid would be unstable at a larger radii than a it would be for a bubble in a hydrogen bonded liquid. Conversely weakly bonded liquids may allow for bubble stability to exist at the smallest bubble radii possible.
Conclusions
We can easily understand why a bubble in a liquid becomes inherently unstable as its radius becomes smaller. This was due to intermolecular bonding between molecules along the tensile not allowing the bubble to remain stable, hence a bubble whose radii is too small will fold up like an accordion. The same reasoning does not explain why nano sized droplets are unstable.
At some point I can in the future discuss droplet stability. I will at this point simply say that droplet stability is due to the energy involved nucleation, while bubble stability is due to the mechanics of cohesive forces.
What I want you to take from this blog is the concept that a bubble must be larger than a given size in order to be stable. In scuba diving (real reason I got into this) nitrogen bubbles (DCI: decompression illness) generally have to be the size of a microbubble or better in order to be considered as being stable.
And just so that you know the science of DCI needs a rethink, that I did decades ago, but then found myself rewriting bubble nucleation followed by thermodynamics. Eventually I plan on discussing how to better understand DCI, but Rome was not built in a day.
Thanks again to everyone who have shown me the courtesy of reading what I write.