Mesoscopic stability and sedimentation waves in settling periodic arrays.
The stability of a periodic array of particles settling in a viscous incompressible fluid under the influence of gravity is investigated in the framework of the point sedimentation model. The simple cubic array is unstable, but the body-centered and face-centered cubic arrays with gravity directed along one of the crystal axes are mesoscopically stable, i.e., they are stable except for very long wavelength in a certain domain of directions of the wave vector. In such mesoscopically stable arrays the instability is suppressed in periodic boundary conditions for systems smaller than a maximum size. In a stable finite system the particles perform small motions about the positions of the regular array, and sedimentation waves propagate through the system.
Felderhof
B U
BU
Institut für Theoretische Physik A, RWTH Aachen Templergraben 55, 52056 Aachen, Germany. ufelder@physik.rwth-aachen.de