Oscillation frequency of 2D circular drop in an ambient environment

[member 428835]

Hi PF!

Do you know what the natural oscillating frequencies are for a 2D circular drop of liquid in an ambient environment (negligible effects)?

Prosperetti 1979 predicts the frequencies for both a spherical drop and bubble here at equations 5b and 6b. There must be a simpler circular 2D extension, right?

Much appreciated!

 

[Baluncore]

The problem with a 2D model is that the terms for the surface area, volume and mass are all zero.

 

[member 428835]

The problem with a 2D model is that the terms for the surface area, volume and mass are all zero.

A 2D circle for sure exists. I read somewhere that the dimensionless frequency is $\lambda_n = \sqrt{n(n-1)(n+1)}$. I know for sure one exists: just can't recall the circular bubble and drop exactly.

 

[member 428835]

For completeness, I just now read and it seems what I posted in post 3 is correct for a droplet (not a bubble). This is directly given in equation 28 here. Still unsure about the bubble.