Bubble cavitation - what does a dash mean?

[rwooduk]

For a bubble in water in equilibrium the supporting forces due to pressure of the gas P_g and vapour P_v in the bubble must equal the crushing forces i.e. the hydrostatic forces P_h and those due to surface tension 2sigma/R₀. So we have

$P_{v}+P_{g}=P_{h}+ \frac{2\sigma }{R_{0}}$

Now we apply ultrasound so the pressure in the liquid is now Ph + Pa where:

$P_{a}=P_{A} sin 2\pi ft$

BUT the ultrasound causes cavitation of the bubble! And when the bubble is largest we have:

$P_{V}>(P_{h}-P_{a}) + \frac{2\sigma }{R_{0}} - P_{g}$

Now my question, he writes the next equation as:

$P_{V}-\frac{2\sigma }{R_{0}}=P_{V}^{'}>(P_{h}-P_{a})$

BUT he doesn't define $P_{V}^{'}$ so I'm a little lost.

Could someone tell me what a dash would generally mean?

It's from p.61 of this paper:

http://gendocs.ru/docs/37/36518/conv_1/file1.pdf

Thanks in advance for any help!

 

[Serena]

Are you sure that the link for your paper is correct?

 

[rwooduk]

Are you sure that the link for your paper is correct?

Ahh i don't think it allows direct linking, its Applied sonochemistry the pdf is directly available here:

https://scholar.google.co.uk/scholar?hl=en&q=applied+sonochemistry&btnG=&as_sdt=1,5&as_sdtp=

 

[Serena]

I am sorry, gendocs.ru doesn't provide a direct link to the PDF from Scholar. Do you know the DOI of this article?

 

[rwooduk]

hmm sorry I tried to upload it here:

http://www.filedropper.com/12_7

 

[Serena]

I think it's just a conventional way to express the threshold value for the coupled vapor pressure and surface tension effects on cavitation.

 

[nasu]

Do you mean the word "dash" or a dash like this "-" (a punctuation mark).
I cannot find it on page 61 of that document.

 

[rwooduk]

I think it's just a conventional way to express the threshold value for the coupled vapor pressure and surface tension effects on cavitation.

Many thanks for your help! The thing that confuses me is that the P_V term for vapour pressure is in the same equation as the P_':

$P_{V}-\frac{2\sigma }{R_{0}}=P_{V}^{'}>(P_{h}-P_{a})$

If the $P_{V}^{'}$ term expresses in part the vapour pressure then why is there a P_V at the other side of the equation?

Thanks again for your help.

Do you mean the word "dash" or a dash like this "-" (a punctuation mark).
I cannot find it on page 61 of that document.

I mean a dash at the top of the symbol, in the paper P becomes P^'