Abstracts - KTH Mechanics

DNS of moving solids in viscous fluid : Application to
rheology of complex fluids
P. Laure ∗ ,G.Beaume †‡ and T. Coupez ‡
The orientation of long bodies (one dimension is much prevailing upon the other
two) in liquids of different nature is a fundamental issue in a many problems of practical
interest. In particular for composite material, the addition of spherical particles,
short or long fibers to polymer matrix is well known to enhance the mechanical properties
of composite material. The degree of enhancement depends strongly on the
orientation of the fibers and the distribution or agregation of various particles in the
final product. Then, a better knowledge of the motion of solid particles in polymer
liquids is important for the design of molding equipment and determining the optimal
processing conditions.
We propose a method to simulate fiber motions in flow by using finite element
method with a multi-domain approach of two phases (namely a viscous fluid and
rigid bodies). One must simultaneously solve the Stokes equations (governing the
motion of the fluid having very high viscosity) and the equations of rigid-body motion
(governing the motion of the particles). These equations are coupled through the noslip
condition on the particle boundaries. The rigid-body motion constraint is imposed
by using a Lagrangian multipliers 1 . The main interest of this approach is that it is
not necessary to give an explicit form of drag and lubrication forces acting between
fibers.
However, it is not possible to simulate the motion of even a moderately dense
suspension of particles without a strategy to handle cases in which particles touch.
A collision strategy is a method for preventing near collisions by defining a security
zone around the particle such that when the gap between particles is smaller than
the security zone a repelling force is activated. Different repelling forces are proposed
for spherical particles, but it is more complicated to express it for long fibers 2 . Our
repelling force is based on the physics of elastic collisions occurring in the security
zone 3 .
Finally, computation are made for a large population of particles (fibers alone,
fibers and spheres with different sizes). We point out that it is possible to get informations
on macroscopic properties of fiber suspensions by averaging numerical results
on an elementary volume. In this way, the influence of particle concentration and fiber
aspect ratio on the ”average” viscosity is analyzed.
∗ INLN, UMR 6618 CNRS-UNSA, 06560 Valbonne, France.
† Schneider Electric-Technocentre 38 TEC Grenoble
‡ CEMEF, ENSMP-UMR 7635 CNRS, 06904 Sophia Antipolis, France
1 R. Glowinski et al., Int. J. Multiphase Flow 25, 755 (1999)
2 Y. Yamane et al., J. Non-Newtonian Fluid Mech. 54, 405 (1994)
3 P.Laureetal.,Proc. of Computational Methods for Coupled Problems in Sci. and Eng. (2005)
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