Oscillation frequency of 2D circular drop in an ambient environment

In summary, the conversation discusses the natural oscillating frequencies for a 2D circular drop of liquid in an ambient environment and the difficulties of predicting these frequencies due to the terms for surface area, volume, and mass being zero in a 2D model. It is mentioned that Prosperetti 1979 provides predictions for a spherical drop and bubble, and there may be a simpler 2D extension for a circular drop. The dimensionless frequency for a circular droplet is given as ##\lambda_n = \sqrt{n(n-1)(n+1)}##, but there is uncertainty about the frequency for a circular bubble.
  • #1
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!
 
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  • #2
The problem with a 2D model is that the terms for the surface area, volume and mass are all zero.
 
  • #3
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.
 
  • #4
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.
 

Related to Oscillation frequency of 2D circular drop in an ambient environment

1. What is the significance of studying the oscillation frequency of 2D circular drops?

The oscillation frequency of 2D circular drops is important in understanding the behavior of liquid drops in various environments, such as in industrial processes or in nature. It can also provide insights into the physical properties of the liquid and its interactions with the surrounding environment.

2. How is the oscillation frequency of a 2D circular drop affected by the ambient environment?

The oscillation frequency of a 2D circular drop is influenced by factors such as the viscosity and density of the surrounding fluid, surface tension, and the presence of any external forces, such as gravity or electric fields. Changes in these parameters can alter the frequency of oscillation.

3. What factors can affect the shape of a 2D circular drop and its oscillation frequency?

The shape of a 2D circular drop is primarily determined by the balance between surface tension and gravity. Other factors that can affect its shape and oscillation frequency include the presence of impurities, temperature, and the properties of the surface on which the drop is placed.

4. How is the oscillation frequency of a 2D circular drop measured?

The oscillation frequency of a 2D circular drop can be measured using various techniques, such as high-speed imaging or laser interferometry. These methods involve tracking the movement of the drop over time and analyzing the frequency of its oscillations.

5. What are the potential applications of understanding the oscillation frequency of 2D circular drops?

Knowledge of the oscillation frequency of 2D circular drops can have practical applications in fields such as microfluidics, where the behavior of liquid drops is crucial for the design of devices and processes. It can also aid in the development of new technologies, such as liquid-based sensors or actuators.

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