Microrheology of colloidal dispersions by Brownian dynamics simulations

Abstract

We investigate active particle-tracking microrheology in a colloidal dispersion by Brownian dynamics simulations. A probe particle is dragged through the dispersion with an externally imposed force in order to access the nonlinear viscoelastic response of the medium. The probe's motion is governed by a balance between the external force and the entropic "reactive" force of the dispersion resulting from the microstructural deformation. A "microviscosity" is defined by appealing to the Stokes drag on the probe and serves as a measure of the viscoelastic response. This microviscosity is a function of the Péclet number ͑Pe= Fa/ kT͒-the ratio of "driven" ͑F͒ to diffusive ͑kT / a͒ transport-as well as of the volume fraction of the force-free bath particles making up the colloidal dispersion. At low Pe-in the passive microrheology regime-the microviscosity can be directly related to the long-time self-diffusivity of the probe. As Pe increases, the microviscosity "force-thins" until another Newtonian plateau is reached at large Pe. Microviscosities for all Péclet numbers and volume fractions can be collapsed onto a single curve through a simple volume fraction scaling and equate well to predictions from dilute microrheology theory. The microviscosity is shown to compare well with traditional macrorheology results ͑theory and simulations͒.

Shear Thinning and Local Melting of Colloidal Crystals

“…Using a power-law fit we find that F $ ðv À v c Þ with close to 1=2. This implies ''velocity or shear thinning'' similar to that observed in microrheology studies of dense hard sphere systems [9,22,23,25] and bulk rheology of colloidal crystals [19,20]. Moreover, the v 1=2 behavior has been reported to be directly related to a change in the structure factor, suggesting a change in the local structure [7,8].…”

“…1(d)]. The fluctuations around Ár ss are due the intermittent nature of the probe's motion through the crystal: pushing the encountered particles away and subsequently ''hopping'' from site to site [9,17,18]. The data presented here all correspond to the steady state regime.…”

“…Figure 1(a)-1(c) shows three snapshots of a crystal through which a probe particle is being dragged from left to right at a velocity of 0:25 m=s. As is clearly inferred from the disordered area behind the probe particle, the drag leads to the formation of numerous defects resulting in local melting [9,[15][16][17][18]. Although the colloidal crystal is slightly compressed in front of the probe particle, the crystal remains remarkably intact in this region.…”

“…Driving the probe particle by optical tweezing can lead to three different modes: constant force, constant velocity or a mixed mode [9,14]. At constant force the probe can move around obstacles while at constant velocity the particle will largely resist lateral motions thus leading to significantly larger deformations of the material.…”

“…As a consequence of progressive miniaturization, the effect of the microscopic structure on mechanical properties becomes increasingly significant, which has invoked the development of micromechanical models [3][4][5][6]. Also in complex fluids there are many suggestions that the rearrangement of the local structure is the basis for behavior like shear thickening and thinning [1,2,[7][8][9][10]. The key here is the simultaneous characterization of the external forces and changes in the microstructure.…”