טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKatz Eduard
SubjectOrientation of Small Fibers by Means of Different Flows
DepartmentDepartment of Mechanical Engineering
Supervisors Mr. Alexander Yarin
Professor Emeritus Miles Rubin


Abstract

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.