Motion of a rod-like particle between parallel walls with application to suspension rheology

We study the dynamics of elongated axisymmetric particles undergoing shear flow between two parallel planar walls, under creeping-flow conditions. Particles are modeled as linear chains of touching spheres and it is assumed that walls are separated by a distance comparable to particle length. The hydrodynamic interactions of the chains with the walls are evaluated using our Cartesian-representation algorithm Bhattacharya et al., Physica A 356, 294–340 2005b . We find that when particles are far from both walls in a weakly confined system, their trajectories are qualitatively similar to Jeffery orbits in unbounded space. In particular, the periods of the orbits and the evolution of the azimuthal angle in the flow-gradient plane are nearly independent of the initial orientation of the particle. For stronger confinements, however, i.e., when the particle is close to one or both walls a significant dependence of the angular evolution on the initial particle configuration is observed. The phases of particle trajectories in a confined dilute suspension subject to a sudden onset of shear flow are thus slowly randomized due to unequal trajectory periods, even in the absence of interparticle hydrodynamic interactions. Therefore, stress oscillations associated with initially coherent particle motions decay with time. The effect of near contact particle-wall interactions on the suspension behavior is also discussed

Lateral migration of flexible fibers in Poiseuille flow between two parallel planar solid walls

Dynamics of non-Brownian flexible fibers in Poiseuille flow between two parallel planar solid walls is evaluated from the Stokes equations, solved numerically by an accurate multipole code HYDROMULTIPOLE. Fibers migrate towards a critical distance from the wall zc, which depends significantly on the fiber length N and bending stiffness A. Therefore, the calculated values of zc can be used to sort fibers. Three modes of the dynamics are found, depending on a shear-to-bending parameter Gamma. In the first mode, stiff fibers deform only a little and accumulate close to the wall, as the result of a balance between the tendency to drift away from the channel and the repulsive hydrodynamic interaction with the wall. This mechanism is confirmed by simulations in the unbounded Poiseuille flow. In the second mode, flexible fibers deform significantly and accumulate far from the wall. In both modes, the tumbling pattern is repeatable. In the third mode, the fibers are even more curved, and their tumbling is irregular.Comment: 11 pages, 13 figure