- #1
rwooduk
- 762
- 59
For a bubble in water in equilibrium the supporting forces due to pressure of the gas Pg and vapour Pv in the bubble must equal the crushing forces i.e. the hydrostatic forces Ph 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!
##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!