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Collisions of solid particles with vortex rings in superfluid helium

Published online by Cambridge University Press:  23 May 2008

DEMOSTHENES KIVOTIDES
Affiliation:
Center for Risk Studies and Safety, Department of Chemical Engineering, University of California, Santa Barbara, CA 93117, USA
S. LOUISE WILKIN
Affiliation:
Center for Risk Studies and Safety, Department of Chemical Engineering, University of California, Santa Barbara, CA 93117, USA

Abstract

We have performed self-consistent computations of the interactions between a superfluid vortex-ring and a solid particle for two different vortex-ring sizes and over a wide range of temperatures. In all cases, the particle and the vortex eventually separate. For temperature T = 0 K, larger rings tend to trap the particle more effectively than smaller rings. Trying to escape the vortex, the particle follows a spiralling trajectory that could be experimentally detected. The dominant dynamical process is the excitation and propagation of Kelvin waves along the vortices. For T > 0 K, particle–vortex collision induces particle vibrations that are normal to the particle's direction of motion and might be experimentally detectable. In contrast to the T = 0 K case, smaller rings induce larger particle oscillation velocities. With increasing temperature, enhanced mutual friction damping of Kelvin waves leads to the damping of both the intensity and frequency of post-collision particle vibrations. Moreover, higher temperatures increase the relative impact of the Stokes drag force on particle motion.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 1983 Friction on quantized vortices in He II. A review. J. Low Temp. Phys. 52, 189.CrossRefGoogle Scholar
Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 2001 Quantized Vortex Dynamics and Superfluid Turbulence. Springer.CrossRefGoogle Scholar
Bewley, G. P., Lathrop, D. P. & Sreenivasan, K. R. 2006 Superfluid helium: visualization of quantized vortices. Nature 44, 588.CrossRefGoogle Scholar
Brennen, C. E. 2005 Fundamentals of Multiphase Flow. Cambridge University Press.CrossRefGoogle Scholar
Celik, D. & VanSciver, S. W. 2002 Tracer particle generation in superfluid helium through cryogenic liquid injection for particle image velocimetry (PIV) applications. Exp. Thermal Fluid Sci. 26, 971975.CrossRefGoogle Scholar
Crowe, C. T., Sommerfeld, M. S. & Tsuji, Y. 1998 Multiphase Flows with Droplets and Particles. CRC Press, Boca Raton.Google Scholar
Donnelly, R. J. 1991 Quantised Vortices In Helium II. Cambridge University Press.Google Scholar
Donnelly, R. J., Karpetis, A. N., Niemela, J. J., Sreenivasan, K. R., Vinen, W. F. & White, C. M. 2002 The use of particle image velocimetry in the study of turbulence in liquid helium. J. Low Temp. Phys. 126, 327332.Google Scholar
Drew, D. A. & Passman, S. L. 1998 Theory of Multicomponent Fluids. Springer.Google Scholar
Finne, A. P., Eltsov, V. B., Hanninen, R., Kopnin, N. B., Kopu, J., Krusius, M., Tsubota, M. & Volovik, G. E. 2006 Dynamics of vortices and interfaces in superfluid 3He. Rep. Prog. Phys. 69, 31573230.CrossRefGoogle Scholar
Kivotides, D. 2005 Turbulence without inertia in thermally excited superfluids. Phys. Lett. A 341, 193197.CrossRefGoogle Scholar
Kivotides, D. 2006 Coherent structure formation in turbulent thermal superfluids. Phys. Rev. Lett. 96, 175301.CrossRefGoogle ScholarPubMed
Kivotides, D. 2007 Relaxation of superfluid vortex bundles via energy transfer to the normal fluid. Phys. Rev. B 76, 054503.CrossRefGoogle Scholar
Kivotides, D., Barenghi, C. F. & Samuels, D. C. 2000 Triple vortex ring structure in superfluid helium II. Science 290, 777.Google Scholar
Kivotides, D., Vassilicos, J. C., Samuels, D. C. & Barenghi, C. F. 2001 Kelvin waves cascade in superfluid turbulence. Phys. Rev. Lett. 86, 3080.CrossRefGoogle ScholarPubMed
Kivotides, D., Barenghi, C. F. & Sergeev, Y. A. 2005 Measurement of the normal fluid velocity in superfluids. Phys. Rev. Lett. 95, 215302.CrossRefGoogle ScholarPubMed
Kivotides, D., Barenghi, C. F. & Sergeev, Y. A. 2006 a Numerical calculation of the interaction of superfluid vortices and a rigid sphere. J. Low Temp. Phys. 144, 121134.CrossRefGoogle Scholar
Kivotides, D., Barenghi, C. F. & Sergeev, Y. A. 2006 b Physics of solid particles in thermal counterflow. Europhys. Lett. 73, 733739.Google Scholar
Kivotides, D., Barenghi, C. F., Mee, A. J. & Sergeev, Y. A. 2007 a Interaction of solid particles with a tangle of vortex filaments in a viscous fluid. Phys. Rev. Lett. 99, 074501.Google Scholar
Kivotides, D., Barenghi, C. F. & Sergeev, Y. A. 2007 b Collision of a tracer particle and a quantized vortex in superfluid helium: self-consistent calculations. Phys. Rev. B 75, 212502.CrossRefGoogle Scholar
Kivotides, D., Barenghi, C. F. & Sergeev, Y. A. 2008 Interactions between particles and quantized vortices in superfluid helium. Phys. Rev. B 77, 014527.Google Scholar
Kozik, E. & Svistunov, B. 2004 Scale-separation scheme for simulating superfluid turbulence: Kelvin-wave cascade. Phys. Rev. Lett. 92, 035301.CrossRefGoogle Scholar
Nazarenko, S. & West, R. J. 2003 Analytical solution for nonlinear Schroedinger vortex reconnection. J. Low Temp. Phys. 132, 1.CrossRefGoogle Scholar
Poole, D. R., Barenghi, C. F., Sergeev, Y. A. & Vinen, W. F. 2005 The motion of tracer particles in helium II. Phys. Rev. B 71, 064514.Google Scholar
Schwarz, K. W. 1974 Spherical probes and quantized vortices: hydrodynamic formalism and simple applications. Phys. Rev. A 10, 2306.CrossRefGoogle Scholar
Schwarz, K. W. 1985 Three-dimensional vortex dynamics in superfluid 4He: line–line and line–boundary interactions. Phys. Rev. B 31, 5782.CrossRefGoogle ScholarPubMed
Tsubota, M. & Maekawa, S. 1993 Pinning and depinning of two quantized vortices in superfluid 4He. Phys. Rev. B 47, 12040.Google Scholar
Vinen, W. F. & Niemela, J. J. 2002 Quantum turbulence. J. Low Temp. Phys. 129, 213.Google Scholar
Vinen, W. F., Tsubota, M. & Mitani, A. 2003 Kelvin-wave cascade on a vortex in superfluid 4He at a very low temperature. Phys. Rev. Lett. 91, 135301.CrossRefGoogle Scholar
de Waele, A. T. A. M. & Aarts, R. G. K. M. 1994 Route to vortex reconnection. Phys. Rev. Lett. 72, 482.CrossRefGoogle Scholar
Winckelmans, G. S. & Leonard, A. 1993 Contributions to vortex particle methods for the computation of three-dimensional incompressible unsteady flows. J. Comput. Phys. 109, 247.Google Scholar
Zhang, T. & VanSciver, S. W. 2005 Large-scale turbulent flow around a cylinder in counterflow superfluid 4He (He (II)). Nature Phys. 1, 3638.CrossRefGoogle Scholar
Zhang, T., Celik, D. & VanSciver, S. W. 2004 Tracer particles for applications to PIV studies of liquid helium. J. Low Temp. Phys. 134, 9851000.CrossRefGoogle Scholar