Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
60<br />
Numerical Simulations of Rigid Fiber Suspensions<br />
K. Gustavsson ∗ , A.-K. Tornberg †<br />
In this talk, we present a numerical method designed to simulate the dynamics<br />
of slender, rigid fibers immersed in an incompressible fluid. Fiber dynamicsisof<br />
fundamental importance for understanding many flows arising in physics, biology<br />
and engineering. One typical example is paper-pulp, where the micro-structure of the<br />
suspension is made up of many fibers in a fluid. Here, we consider microscopic fibers<br />
that sediment due to gravity.<br />
Our numerical algorithm is based on a non-local slender body approximation that<br />
yields a system of coupled integral equations, relating the forces exerted on the fibers<br />
to their velocities, which takes into account the hydrodynamic interactions of the<br />
fluid and the fibers. The system is closed by imposing the constraints of rigid body<br />
motion. The fact that the fibers are straight have also been exploited in the design<br />
of the numerical method 1 .<br />
Numerical simulations performed on a microscale offers the ability to obtain detailed<br />
information regarding the microstructure including interactions of individual<br />
fibers. It is well known that the shape of the particles have a large influence on<br />
the macroscopic properties of the suspensions and when the suspended particles are<br />
slender their orientation strongly affect the rheological properties of the flow. During<br />
sedimentation, a forming of clusters of fibers (flocculation) occurs which enhance the<br />
settling velocity to a value larger than the maximum speed of a single and vertically<br />
aligned fiber.<br />
We present results from simulations including a large number of fibers in a periodic<br />
box and discuss averaged quantities such as mean sedimentation speed and fiber<br />
orientation and how these quantities are affected by cluster formation and vertical<br />
alignment of the fibers. We also present a more detailed study of how the sedimentation<br />
process depends on cluster size, cluster density and the orientation of fibers<br />
within the clusters.<br />
∗ Royal Institute of Technology (<strong>KTH</strong>), Nada, S-100 44 Stockholm, Sweden<br />
† Courant Institute of Mathematical Science, NYU, New York, USA<br />
1 Tornberg A.-K. and Gustavsson K., J. Comput. Phys. To appear (2006).
Change language