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 which are solved numerically by the multipole method. Fibers migrate towards a critical distance from the wall z(c), which depends significantly on the fiber length N and bending stiffness A. This effect can be used to sort fibers. Three types of accumulation are found, depending on a shear-to-bending parameter Gamma. In the first type, stiff fibers deform only a little and accumulate close to the wall, where their tendency to drift away from the channel is balanced by the repulsive hydrodynamic interaction with the wall. In the second type, flexible fibers deform significantly and accumulate far from the wall. In both types, the fiber shapes at the accumulation positions are repeatable, while in the third type, they are very compact and non-repeatable. The difference between the second and third accumulation types is a special case of the difference between the regular and irregular modes for the dynamics of migrating fibers. At the regular mode, far from walls, the fiber tumbling frequency satisfies Jeffery's expression, with the local shear rate and the aspect ratio close to N.