2-D Brownian dynamics simulation (HTML5, javascript)

Above, a suspension Brownian, hard disks is deformed by an oscillatory, simple shear. The disks do not interact hydrodynamically, but are free to diffuse and translate along the shear field streamlines until colliding. The particles become redder when the pressure they experience due to collisions is larger. These stresses show strong correlation in the form of "force chains" when the shear rate and area fraction are sufficiently large. This deceptively simple model gives rise to stunning complexity: structure and dynamics. The same principles represented here are responsible for generating non-Newtonian flow behavior in nearly all microstructured media. Click here to see an analogous simulation in which the suspension is probed via microrheology instead.

In this particular example, the suspension is deformed by uniform, linear shear. The Peclet number describes the ratio of the shear rate, $ \gamma $, to the rate of particle diffusion, $ D / a ^ 2 $, where $ a $ is the particle radius and $ D $ is the particle diffusivity: $\mathrm{Pe}=\gamma a^2 / D$. Likewise, the Deborah number describes the ratio of the oscillation rate of the deformation, $ \omega $, to the rate of particle diffusion: $De= \omega a^2 / D$. Above, the Peclet and Deborah numbers can be varied independently. Because of how the simulation is constructed increasing either will appear equivalent to descreasing the rate of particle diffusion. Hydrodynamic interactions among the particles are neglected, but this effect is easily included by using the Stokesian Dynamics methodology.