50500

#Particles 300

0.010.83

Area fraction 0.75

# 2-D colloidal micro-rheology simulation (HTML5, javascript)

Above, a suspension Brownian, hard disks diffuses freely. If you click on a particle, termed the probe, it can be driven through the suspension by moving the pointer. There are two modes of motion possible: one in which the difference between the particle's center and the pointer prescribes the particle's velocity through the suspension -- fixed-velocity; and another in which this difference prescribes the displacement of a Hookean spring pulling the particle -- fixed-force. The fixed-velocity case is akin to what can be achieved with optical tweezers while the fixed-force case corresponds to an experiment with magnetic tweezers. 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 driven particle makes significant deformation to the suspension structure. The forces on the probe particle, fixed-velocity, or the velocity of the probe particle, fixed-force, are indicative of the viscoelastic properties of the medium this is the fundamental tenant of micro-rheology. 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 deformed via simple shear.

In this particular example, the suspension's equilibrium structure is distorted by the motion of the clicked particle. The length of the arrow extending from the probe is proportional to either its velocity through the dispersion or the external force driving its motion. In either case, a Peclet number describes the importance of this driving impetus relative to the thermal relaxation of the dispersion: $\mathrm{Pe}= U a / D$ (fixed-velocity) or $\mathrm{Pe} = F a / kT$ (fixed-force), where $a$ is the particle radius, $D$ is the particle diffusivity, $kT$ is the thermal energy, $U$ is the particle velocity or $F$ is the force driving particle motion. The simulation is constructed such that the frame of reference travels with the probe particle. When moving with a fixed-velocity, the diffusive motion of the probe is frozen. In contrast, the suspension can be seen to move in a coordinated but random fashion when the probe is driven by a fixed force. This is because the probe is free to diffuse and well as translate. Essentially, in the fixed-velocity mode the probe particle pushes material aside as it translates along a rigidly defined trajectory while in fixed-force mode the probe's motion is compliant and even tortuous. Hydrodynamic interactions among the particles are neglected, but this effect is easily included by using the Stokesian Dynamics methodology.