Analytical approximations for the collapse of an empty spherical bubble

Zitieren

Dateien zu dieser Ressource

Prüfsumme: MD5:1b97393b3f439994e161f0ebe4d52cad

OBRESCHKOW, Danail, Martin BRUDERER, Mohamed FARHAT, 2012. Analytical approximations for the collapse of an empty spherical bubble. In: Physical Review E. 85(6). ISSN 1539-3755. eISSN 1550-2376

@article{Obreschkow2012Analy-22485, title={Analytical approximations for the collapse of an empty spherical bubble}, year={2012}, doi={10.1103/PhysRevE.85.066303}, number={6}, volume={85}, issn={1539-3755}, journal={Physical Review E}, author={Obreschkow, Danail and Bruderer, Martin and Farhat, Mohamed} }

deposit-license Farhat, Mohamed Bruderer, Martin eng Analytical approximations for the collapse of an empty spherical bubble 2013-03-18T15:49:28Z Obreschkow, Danail Bruderer, Martin The Rayleigh equation 3/2Ṙ+RR̈+pρ<sup>−1</sup>=0 with initial conditions R(0)=R<sub>0</sub>, Ṙ(0)=0 models the collapse of an empty spherical bubble of radius R(T) in an ideal, infinite liquid with far-field pressure p and density ρ. The solution for r≡R/R<sub>0</sub> as a function of time t≡T/T<sub>c</sub>, where R(T<sub>c</sub>)≡0, is independent of R<sub>0</sub>, p, and ρ. While no closed-form expression for r(t) is known, we find that r<sub>0</sub>(t)=(1−t<sup>2</sup>)<sup>2/5</sup> approximates r(t) with an error below 1%. A systematic development in orders of t<sup>2</sup> further yields the 0.001% approximation r<sub>*</sub>(t)=r<sub>0</sub>(t)[1−a<sub>1</sub> Li<sub>2.21</sub>(t<sup>2</sup>)], where a<sub>1</sub>≈−0.018 320 99 is a constant and Li is the polylogarithm. The usefulness of these approximations is demonstrated by comparison to high-precision cavitation data obtained in microgravity. 2013-03-18T15:49:28Z Physical review E ; 85 (2012). - 066303 Farhat, Mohamed 2012 Obreschkow, Danail

Dateiabrufe seit 01.10.2014 (Informationen über die Zugriffsstatistik)

Obreschkow_PhysRevE.85.066303.pdf 123

Das Dokument erscheint in:

KOPS Suche


Stöbern

Mein Benutzerkonto