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While reading on the Plateau Rayleigh instability of fluid jets, the following thought came to my mind: suppose we have a fluid jet with zero cohesion forces (and therefore zero surface tension) falling under the influence of gravity. My understanding is that since fluid parcels with different vertical coordinate move at different speeds, and there are no intermolecular forces, than the whole jet cannot exist at all! Just think of the molecoles as tiny stones dropped from an orifice at different times - since they all experience uniform acceleration they always keep the same relative speed and therefore get away from each other.

So, in my understanding, surface tension is what keeps the liquid jet a unity and is the cause for it getting narrowed as it is accelerated by gravity. However, after reading the MIT lecture notes on fluid jets that are linked to in the wikipedia article on Plateau-Rayleigh instability, I saw the profile $r(z)$ of the jet depends on the Weber number, which is inversely proportional to surface tension. Therefore, in the limit of zero surface tension and infinite Weber number, I thought one should get uniform cross section of the jet. However, this conclusion is wrong according to a formula from the lecture notes, which states:

$$\frac{r}{a} = (1+\frac{2gz}{U_0^2})^{-1/4}.$$

So my question is how to reconcile this formula with the argument I gave before? Is there a fallacy in my argument?

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dynamically you can estimate the response with zero surface tension by turning up the viscosity. when you do this you'll get a skinny thread of fluid with no tendency to break up into individual droplets- like a dribble of honey dropping from a spoon. It just keeps on getting thinner and thinner.

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  • $\begingroup$ can you please elaborate your answer from a more mathematical point of view? I want to see how the equations settle in the limit of zero surface tension. $\endgroup$
    – user2554
    Feb 27 at 9:56
  • $\begingroup$ no, sorry. this was something I learned from a physicist years ago. $\endgroup$ Feb 27 at 20:37

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