Dielectric Force Calculation for a Cylindrical Fiber of Finite Length by the Energy Displacement Method

ABSTRACT

A dielectric mobility separator has been used to collect size-separated fibers for toxicity studies of inhaled airborne aerosols. To improve the resolution of fiber length separation inside the dielectric mobility separator, the dielectric force on a fiber must be obtained. Because of the lack of analytical and numerical solutions specific to cylinders, cylindrical fibers are usually approximated by prolate spheroids in such calculations. The objective of this study was to obtain the dielectric force on a cylindrical fiber of finite length using a numerical method and to compare it with numerical and analytical calculations of the dielectric force on a prolate spheroid having the same dimensions and physical properties. First, the electrical potential around a cylindrical fiber in a nonuniform field was calculated by the finite element method. The dielectric force was obtained by displacing the fiber against the field gradient by a small distance and computing the corresponding energy changes (energy displacement method). Simulation results show that the dielectric force on a cylindrical fiber with aspect ratio, β, less than 2 is twice as large as the dielectric force on a prolate spheroid having the same dielectric constant and dimensions. For β between 2 and 10, the ratio of dielectric force on a cylinder to that on a prolate spheroid decreases as β increases.