What Causes Bubble Oscillation?

In summary, the conversation discusses Gauss's Law and the equations related to it, specifically the equilibrium before and after a bubble is charged. The conversation also mentions the use of Newton's 2nd Law and the consideration of adiabatic pressure changes.
  • #1
kenth
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Homework Statement
A bubble with radius ##R##, mass ##m## and surface tension ##S## has initial pressure inside ##P_i## and outside pressure ##P_0## then charged with surface charge density ##\sigma##, Find the period of the oscillation
Relevant Equations
Gauss's Law, Laplace equation, Newton's Law of Motion
From Gauss's Law

give ##E=\dfrac{\sigma}{2\epsilon_0}##

##\therefore P_e=\dfrac{\sigma^2}{2\epsilon_0}##

Consider at equilibrium (before bubble being charged)

##P_i=P_0+\dfrac{4S}{R}##

Using Newton's 2nd Law

##\Sigma F=m\ddot{R}##

Let ##R+\delta R## be the new radius

Give (after binomial approximation) ##\dfrac{\sigma^2}{2\epsilon_0}+\dfrac{4S\delta R}{R^2}=\dfrac{m}{\pi R^2}\ddot{R}##
I think this should be SHM but the equation doesn't look like it, also do I need to consider the fact that ##P_i## decreases due to change in volume?
 
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  • #2
You need to think of it as an oscillation around the new (i.e. charged) equilibrium. The only reason to bother with the old equilibrium would be to find the amplitude.
And yes, I would suppose the pressure changes adiabatically.
 
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Related to What Causes Bubble Oscillation?

1. What is charged bubble oscillation?

Charged bubble oscillation is a phenomenon in which bubbles of gas or liquid are subjected to an alternating electric field, causing them to expand and contract in a regular pattern.

2. How does charged bubble oscillation occur?

Charged bubble oscillation occurs when an electric field is applied to a liquid or gas containing charged particles, causing the particles to move and collide with each other. This movement creates pressure waves that cause the bubbles to expand and contract.

3. What are the applications of charged bubble oscillation?

Charged bubble oscillation has many applications in various fields, including medicine, materials science, and environmental science. It is used in ultrasound imaging, drug delivery, and wastewater treatment, among others.

4. What factors affect charged bubble oscillation?

The size and charge of the bubbles, the strength of the electric field, and the properties of the surrounding medium all affect charged bubble oscillation. Additionally, the frequency of the electric field and the presence of other particles or impurities can also impact the oscillation.

5. How is charged bubble oscillation studied and measured?

Charged bubble oscillation can be studied and measured using various techniques, such as high-speed photography, acoustic measurements, and spectroscopy. These methods allow scientists to observe and analyze the behavior of the bubbles and the surrounding medium during oscillation.

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