M.Sc Student | Katz Eduard |
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Subject | Orientation of Small Fibers by Means of Different Flows |

Department | Department of Mechanical Engineering |

Supervisors | Mr. Alexander Yarin |

Professor Emeritus Miles Rubin |

The micro-fiber alignment has recently been the focus of numerous research endeavors, because it opens a lot of possibilities in the science and the industries. The objective of this research is to align axisymmetric inertialless micro-fibers by means of different flows.

Motion of a rigid spheroidal inertialless particle (micro-fiber) immersed in a viscous Newtonian creeping flow is described by a particular case of the Jeffery's equation. For the ensemble of micro-fibers completely random initial orientations (white noise) are assumed. Dilute suspensions of micro-fibers with the lengths greater than about 3 microns are considered. Therefore, the rotational Brownian motion of the micro-fibers is negligible. As a result, the micro-fiber dynamics is fully deterministic, albeit affected by their random initial orientation.

Under such conditions, the orientation probability density function for the micro-fibers provides a convenient description of the orientational state. Then the governing equation is the Fokker-Planck equation with the diffusional terms being neglected. The Fokker-Planck equation is solved by the method of characteristics with Runge-Kutta stepping along streamlines for a number of flows of particular interest for applications.

Both potential and creeping flows are considered. The flows are time-independent and involve significant elongational components. The Fokker-Planck equation is solved for several particular cases: jets outflowing from nozzles, flows in wedges, for "infinitely" long and finite micro-fibers. In the latter case the Jeffery's equation allows for formulation of the field terms in the Fokker-Planck equation.

The results show that significant micro-fiber alignment is possible in the flows with dominant elongation or shear components.