Charged liquid jet instability

[weiwei]

I am dealing with a problem of instability of an infinitely long charged liquid jet. When there is a change is surface profile(which originally is a column with radius R), it surface charge density changes, thus the electric energy change of the liquid jet is E (due to surface charge density change), the charging system (a constant voltage V connected to the liquid jet) has energy change -2E, the paper I am reading just gives this result without proving it. So I am trying my luck here to see if any theorem can explain it.

 

[Andy Resnick]

I am dealing with a problem of instability of an infinitely long charged liquid jet. When there is a change is surface profile(which originally is a column with radius R), it surface charge density changes, thus the electric energy change of the liquid jet is E (due to surface charge density change), the charging system (a constant voltage V connected to the liquid jet) has energy change -2E, the paper I am reading just gives this result without proving it. So I am trying my luck here to see if any theorem can explain it.

Zoiks! This is a tough problem. I found this:

https://web.duke.edu/uphyl/pubs/Chen_11_Springer_EHD_Stability.pdf

It seems to discuss your problem. Good luck!