Cross‐stream migration of bead–spring polymers in nonrectilinear pore flows

Abstract

AbstractDeterministic cross‐stream migration of FENE dumbbells, cyclic trimers and bicyclic tetramers in nonhomogeneous, nonrectilinear flows representative of tortuous pores is analyzed. Identifying the crucial feature of misalignment between a tumbling dumbbell and the surrounding streamlines, Brunn (1983) showed that the dumbbell model requires three reflections in the bead–bead hydrodynamic interaction (HI) for lateral migration to occur: lower‐order approximations of the HI are insufficient because they lead only to alignment with the flow rather than tumbling. In any orientation the trimer (tetramer) has at least two (three) “bonds” out of alignment with the flow. Radial migration in rotary Couette flow between concentric cylinders occurs in the freely draining limit, and the simplest, first‐order HI is sufficient to cause lateral migration in rectilinear tube flow. Flow through a sinusoidally corrugated pore brings a new convective timescale on which the bead–spring entity moves between converging and diverging flow environments. Since this process outpaces the dumbbell's alignment, even a freely draining dumbbell spends most of its time slightly misaligned with the surrounding streamlines, and migrates toward the walls (higher shear). Tumbling occurs on a much longer timescale, with the dumbbell traveling through many wavelengths of the wall corrugations (and fluctuating in orientation) between successive (rapid) end‐for‐end flips in the shear field. The flipping time seems to scale inversely with the length of the dumbbell. The trimer and tetramer rotate largely as in rectilinear shear, and exhibit somewhat stronger migration for the same bond length. As a simple model of pore entrance effects, net drift in an oscillatory Sampson flow through a thin orifice is also considered.