Transport of small particles in flows

The rotation of a small rigid particle immersed into a Newtonian liquid is described by Jeffery's equation. In this project, we derive the governing equation using a singular asymptotic expansion. Compared to Jeffery's original approach, the systematic asymptotic analysis naturally enables the determination of higher order effects.

In a dilute solution of small particles, the average dynamics is described by a Fokker-Planck equation. If the orientation of the particles can be characterized by a single unit vector, for example in the case of rotationally symmetric ellipsoids, the Fokker-Planck equation is a partial differential equation on the unit sphere. A finite element discretization for this equation has been derived using a projected octahedron mesh.

left: 2D regular mesh; middle: projection onto octahedron; right: central projection onto sphere