The structure and rheology of fiber suspensions depends on properties of the fibers, their interactions, as well as the flow field to which they are exposed.  Determining the microstructure in general is a challenging task.  We have developed a particle-level simulation technique for studying behavior of flexible fiber suspensions.  

The fibers are modeled as linked, rigid bodies connected by ball and socket joints, as illustrated in Figure 1 below.

The fibers are allowed to bend and twist, but potentials are defined within the joints that resist the bending and twisting.  The fibers experience hydrodynamic drag forces, as well as short-range repulsion and frictional interactions between neighboring fibers.  

Simulations are performed by solving numerically the equations of motion for each fiber in the suspension. This provides the position, shape, and orientation of each fiber as a function of time, which constitutes the desired microstructure.  Once this information is known, macroscopic properties such as the suspension viscosity can be calculated directly.

One of the most interesting results we have observed with these simulations is that under certain conditions, the fibers will tend to aggregate in the absence attractive forces between the fibers.  This is illustrated in Figure 2 below, where snapshots of three different simulation runs are shown. The conditions are the same in each run, except for the coefficient of friction, which increases from left to right [(a) m = 5, (b) m = 10, (c) m = infinity].

The aggregation, or flocculation, occurs by a process known as "elastic interlocking."  In the flow, the fibers are continually being bent and twisted, but are continually trying to spring back to their equilibrium shapes.  As they try to spring back, there motion may be impeded by the presence of other fibers; if the friction forces are sufficiently strong, and if each fiber becomes impeded by several others, they can become "permanently" locked in position.

Fiber stiffness also affects flocculation.  If the fibers are too flexible, they will not aggregate, as illustrated in Figure 3 below (the stiffness decreases from left to right).  This observation is confirmed experimentally, where suspension of aggregated fiber can be dispersed by heating them above the glass transition temperature of nylon, thus decreasing their stiffness.

We are currently examining the effects of various interactions on the structure and rheology these suspensions.