Stokesian Dynamics simulation of Brownian suspensions

Abstract

The non-equilibrium behaviour of concentrated colloidal dispersions is studied by Stokesian Dynamics, a general molecular-dynamics-like technique for simulating particles suspended in a viscous fluid. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Peclet number, Pe, which measures the relative importance of shear and Brownian forces. Three clearly defined regions of behaviour are revealed. There is first a Brownianmotion-dominated regime ( P e < 1) where departures from equilibrium in structure and diffusion are small, but the suspension viscosity shear thins dramatically. When the Brownian and hydrodynamic forces balance (Pe w lo), the dispersion forms a new 'phase' with the particles aligned in 'strings' along the flow direction and the strings are arranged hexagonally. This flow-induced ordering persists over a range of P e and, while the structure and diffusivity now vary considerably, the rheology remains unchanged. Finally, there is a hydrodynamically dominated regime (Pe > 200) with a dramatic change in the long-time self-diffusivity and the rheology. Here, as the Pklet number increases the suspension shear thickens owing to the formation of large clusters. The simulation results are shown to agree well with experiment.

Assembly of vorticity-aligned hard-sphere colloidal strings in a simple shear flow

“…1C). Although the existence of a string structure is consistent with some simulations (13)(14)(15)(16)(17)(18)(19), the orientation of the strings is unexpected: it is normal to the numerically predicted flow direction. To make sure that the vorticity-aligned string structure is not an artifact of our confocal imaging techniques, we perform two numerical and experimental control tests.…”

“…In general, our results in conjunction with previous studies (13)(14)(15)(16)(17)(18)(19)22) help clarify the conditions necessary for obtaining string structures with different orientations in hard-sphere colloidal suspensions. We conclude that: (i) in Brownian dynamics simulations without hydrodynamic couplings between particles, strings form along the flow direction (13)(14)(15)(16)(17); (ii) with confinement that allows no motion in y, the vorticity-aligned string structure does not exist; (iii) with both hydrodynamic coupling and freedom for particles to migrate in y, a string structure with log-rolling strings along the vorticity direction prevails.…”

“…This structure has received much attention since it was first found in a numerical simulation (13). Despite intensive study (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23), however, there is still heated debate over whether such a structure exists in experiments (10,23,24) or is an artifact of certain numerical algorithms (20)(21)(22)(23). In part, this controversy persists due to the lack of experimental techniques that provide direct visualization of the suspension structure.…”

Stationary shear flow around fixed and free bodies at finite Reynolds number

“…In general, there are nonhydrodynamic contributions from interparticle forces and Brownian motion as well (Russel, Saville & Schowalter 1989) and these have been considered both analytically for dilute pair interactions (e.g. by Brady & Morris 1997) and for concentrated systems by simulation (Phung, Brady & Bossis 1996). While we consider only hydrodynamic stresses, for a finite-Reynolds-number suspension the stresslet is not the only contribution.…”

Stress–structure relation in dense colloidal melts under forward and instantaneous reversal of the shear

“…In addition, the first and second normal stresses, together with the osmotic pressure as a function of _ g, must be sought to characterize the stress tensor. The nonlinear functional forms of the shear and normal stresses with the Péclet number, as well as a positive first normal stress and a sign reversed second normal stress, for monodisperse colloidal suspensions at lower and moderately high volume fractions have been reported in Stokesian dynamics simulations of concentrated colloidal suspensions 5 as well as molecular dynamics (MD) simulations of non-Brownian spheres. 6 Similar results have been reported in systems with charge-stabilized dispersion, 7 however the functional dependence in the vicinity of the glass transition are not known.…”