Register to reply

Mass-spring equivalent of microbubbles

Share this thread:
Jan14-13, 06:20 AM
P: 37

The Gilmore equation is associated with bubbles in gas. When equated to a mass-spring system, you get the following results.

[tex]m_{effective}=4\pi R_{0}\rho[/tex]
So the effective mass is given by the liquid volume that the bubble occupies. This is easy for me to see as it's effectively the spherical volume multiplied by the liquid's density.

What I don't understand is the following
[tex]k_{effective}=12\pi\gamma P_{0}R_{0}[/tex]
where [tex]\gamma[/tex] is the ratio of specific heats, and [tex]P_{0}R_{0}[/tex] are ambient pressure and radius respectively. My notes say that this means the effective stiffness is provided by the compressibility of the gas. Could someone please explain how this is the case?

Phys.Org News Partner Physics news on
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Bubbling down: Discovery suggests surprising uses for common bubbles
New non-metallic metamaterial enables team to 'compress' and contain light
Jan14-13, 09:13 AM
P: 1,969
Actually these are gas bubbles in a liquid and not bubbles in gas.
Imagine a spherical bubble of gas of radius Ro and pressure Po and then allow for a small change in volume.
Assume adiabatic transformation and calculate the change in pressure dp due to small change in radius, dr.
Then calculate the force corresponding to the dp on the surface of the sphere.
You'll end up with something that looks like dF = -K dr.

Register to reply

Related Discussions
Mass-spring-mass system rotating about its centre of mass relativistically Advanced Physics Homework 0
Equivalent spring constant.... Introductory Physics Homework 15
Spring Constant given mass, and equivalent mass in free fall from fixed height. Introductory Physics Homework 3
Spring mass spring mass spring - 2 balls oscillations General Math 1
Which of these spring systems is equivalent? Introductory Physics Homework 1