%0 Journal Article
%T Trajectory Analysis of Particle Motions in Superfluid Helium-4 Using PTV Method
%A Lizhu Chen
%A Yoshiyuki Tsuji
%J Journal of Flow Control, Measurement & Visualization
%P 76-85
%@ 2329-3330
%D 2022
%I Scientific Research Publishing
%R 10.4236/jfcmv.2022.102005
%X <span style=\"font-family:Verdana;\">This paper describes the use of particle tracking velocimetry to analyze the Lagrangian acceleration of small particles in superfluid helium with varying time increments, </span><span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;\"><img src=\"Edit_1febe78b-f3b5-4dea-88c6-cad8ac41de21.png\" alt=\"\" /></span><em><span style=\"font-family:Verdana;\"></span></em></span><em></em><span style=\"white-space:normal;\"><span style=\"font-family:;\" \"=\"\"><span style=\"font-family:Verdana;\">. The probability density of acceleration exhibits Gaussian properties for </span><span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;\"><img src=\"Edit_fdf82e03-596c-4f17-ba12-c2bfbc191a48.png\" alt=\"\" /></span></span><span style=\"white-space:nowrap;\"><sub><span style=\"font-family:Verdana;\"></span><em><span style=\"font-family:Verdana;\"></span></em></sub></span><sub></sub><span style=\"font-family:Verdana;\">,&nbsp;but displays a lognormal distribution for <img src=\"Edit_746c131f-2bdd-4709-a301-923caa9e8f40.png\" alt=\"\" /></span><span style=\"font-family:Verdana;\">,&nbsp;where </span><span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;\"><img src=\"Edit_1db25d2c-7572-4b20-8973-88d460aaf6fc.png\" alt=\"\" /></span><sub><span style=\"font-family:Verdana;\"></span></sub></span><sub></sub><span style=\"font-family:Verdana;\"> is the migration time characterizing the particle motion. The particle trajectories are well characterized by the Hurst exponent </span><i><span style=\"font-family:Verdana;\">H</span></i><span style=\"font-family:Verdana;\">. For smaller time scales than </span><span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;\"><img src=\"Edit_438151b4-f9b2-4121-aab5-02f2702e81c6.png\" alt=\"\" /></span><sub><span style=\"font-family:Verdana;\"></span></sub></span><sub></sub><span style=\"font-family:Verdana;\">, the trajectories exhibit linear motion (</span><em><span style=\"font-family:Verdana;\"><img src=\"Edit_7cfe244b-9b74-43e6-945b-ec33c770cc16.png\" alt=\"\" /></span></em><span style=\"white-space:nowrap;font-family:Verdana;\"></span><span style=\"font-family:Verdana;\">), but have certain fractal properties with </span><em><span style=\"font-family:Verdana;\"><img src=\"Edit_17dac2ef-690d-4387-984e-cce749cae4fd.png\" alt=\"\" /></span></em><span style=\"font-family:Verdana;\"> for time scales larger than </span><span style=\"white-space:nowrap;\"><span style=\"font-family:Verdana;\"><img
%K Superfluid
%K He II
%K Counterflow
%K Particle Tracking Velocimetry
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=116813