Orientation control of particles and fibers for polymeric liquids and fiber reinforced materials

Molecules in polymeric liquids and fibers in fiber-reinforced materials are modelled using the spheroidal model or the dumbbell model of the Kelvin type. A method is developed to transform the nonlinear governing equation of orientation for dilute suspensions to a system of time-varying linear differential equations. Thereby the finding of the exact solution becomes much easier than before. where the introduced scalar variable z plays a key role both in the finding of the solution and in the formulation of the criterion of strong flow. Moreover, by utilizing the results of the exact solution, the technologically important problem of fiber (or particle) orientation control is further analyzed; hence, the criterion of controllability for a target orientation is established and the allowable set in the space of parameters :is identified. The procedures to choose suitable parameters to perform specific orientation alignment are suggested and demonstrated, and guarantee that the most fibers (or particles) can be controlled to the preferred orientation within a finite time with desired precision.