Dynamics and Topology of Flexible Chains: Knots in Steady Shear Flows

We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an "open" trefoil knot that the flow unknots and then knots again, sometimes repeating several times. These changes in topology should be reflected in changes in bulk rheological and/or transport properties.Comment: 22 pages, 12 figure

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