Katarina Gustavsson
NADA
KTH
Stockholm
In this talk, we present a numerical method designed to simulate the
dynamics of slender, rigid fibers immersed in an incompressible
fluid. Fiber dynamics is of fundamental importance for
understanding many flows arising in physics, biology and
engineering. One typical example is paper-pulp, where the
micro-structure of the suspension is made up of many fibers in a
fluid. Here, we consider microscopic fibers that sediment due to
gravity.
Our numerical algorithm is based on a non-local slender body
approximation that yields a system of coupled integral equations,
relating the forces exerted on the fibers to their velocities, which
takes into account the hydrodynamic interactions of the fluid and the
fibers. The system is closed by imposing the constraints of rigid body
motion. The fact that the fibers are straight have also been exploited
in the design of the numerical method.
We present results from simulations
including a large number of fibers in a periodic box and discuss averaged
quantities such as mean sedimentation speed and fiber orientation and how
these quantities are affected by cluster formation and vertical
alignment of the fibers. We also
present a more detailed study of how the sedimentation process
depends on cluster size,
cluster density and the orientation of fibers within the clusters.