Oscillation frequency of 2D circular drop in an ambient environment

Click For Summary

Discussion Overview

The discussion centers on the natural oscillating frequencies of a 2D circular drop of liquid in an ambient environment, with a focus on theoretical predictions and models. Participants explore the applicability of existing equations for spherical drops and bubbles to a 2D context.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant references Prosperetti 1979, suggesting that there should be a simpler extension for 2D circular drops based on existing equations for spherical drops and bubbles.
  • Another participant raises a concern that a 2D model may not be valid, noting that terms for surface area, volume, and mass could all be zero.
  • A different participant acknowledges the existence of a 2D circle and cites a dimensionless frequency formula, but expresses uncertainty about its application to circular bubbles versus droplets.
  • One participant clarifies that the previously mentioned frequency formula is applicable to droplets, not bubbles, referencing a specific equation for further detail.

Areas of Agreement / Disagreement

Participants express differing views on the validity of a 2D model for oscillating frequencies, with some supporting its exploration while others question its feasibility. The discussion remains unresolved regarding the specific frequencies for circular drops and bubbles.

Contextual Notes

Limitations include potential issues with the definitions of surface area, volume, and mass in a 2D context, as well as unresolved distinctions between the behaviors of droplets and bubbles.

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!
 
Physics news on Phys.org
The problem with a 2D model is that the terms for the surface area, volume and mass are all zero.
 
Baluncore said:
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.
 
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.
 

Similar threads

  • · Replies 14 ·
Replies
14
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 8 ·
Replies
8
Views
6K