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I was wondering if it's possible to have a soap bubble with a varying pressure over its surface? That is, such a bubble would not have constant internal pressure at all points.

I am specifically interested in this for modelling a situation in which a soap bubble is placed in a stream of moving air, or a situation in which a soap bubble is heated, in both of which cases there may be significant variation in external pressure over the surface of the bubble.

If this is possible, does the Young-Laplace equation still hold in some form (eg. at each point on the surface of the bubble)?

Thanks for any responses.

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  • $\begingroup$ Given that you're talking about the Young-Laplace equation, I assume you're not also considering a transient pressure differential and an unsteady (but non-breaking) surface? $\endgroup$ – JMac Aug 2 '18 at 18:54
  • $\begingroup$ I'm considering an unsteady non-breaking surface, certainly - so the bubble isn't stable in shape - I don't know what a transient pressure differential is - basically, I'm just interested in modelling different shapes bubbles could take on when they are placed in a stream of moving air or heated. As regards the Young-Laplace equation, I'm trying to find out whether the derivation here (farside.ph.utexas.edu/teaching/336L/Fluidhtml/…) can be modified for varying pressure; I suppose, yes, that it may have to be abandoned. $\endgroup$ – J8ES94K002 Aug 2 '18 at 19:06
  • $\begingroup$ I'm not gonna lie, I'm not too well versed in the Young-Laplace equation. When I looked it up though, Wikipedia says it is for the interface between two static fluids, so it seems like it would only apply to stable steady shapes. By transient pressure differential I just meant changing; it's not a steady state phenomenon. $\endgroup$ – JMac Aug 2 '18 at 19:09
  • $\begingroup$ It's certainly possible to have an external pressure variation on the surface of the bubble due to external flow, and a local version of the Young-Laplace equation (involving the two local principal radii of curvature at each location) will apply at each location. $\endgroup$ – Chet Miller Aug 2 '18 at 22:31
  • $\begingroup$ Don't forget pressure differential due to gravity. $\endgroup$ – Mike Dunlavey Aug 3 '18 at 0:15
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I would have to say "no". Any pressure differential will cause flow from the high pressure part of the bubble to the low pressure part of the bubble. Since the bubble is so small, such a flow would very quickly equalize the pressure throughout the bubble.

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    $\begingroup$ What if the bubble is quite large? $\endgroup$ – J8ES94K002 Aug 2 '18 at 18:50
  • $\begingroup$ @J8ES94K002, how large did you have in mind? The larges bubble that I have ever seen is no more than approximately 2 feet in diameter, and I still consider this to be small in terms of pressure differentials and fluid flow. $\endgroup$ – David White Aug 2 '18 at 19:09
  • $\begingroup$ I wasn't really sure, but probably around that size (2 feet in diameter) and as you say that, it does seems to confirm the impossibility of such bubbles. $\endgroup$ – J8ES94K002 Aug 2 '18 at 19:23
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It is certainly possible to have bubbles with different pressure with slushing surface going back and forth. We have more likely than not even blown one out.

Consider a vibrating ellipsoid switching its long and short dimensions in a standing wave mode. The second harmony would be 4 quadrants bulging in and out. The third harmony will be 8 zones and so forth.

Then we would have a combination of say first mode and the third mode. With contributing ratios that will merge from say 50% each to some random combination that would minimize the energy of vibration. As an undesired situation, the vibration would become unstable and burst the bubble.

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