Cross-stream migration in dilute solutions of rigid polymers undergoing rectilinear flow near a wall

Kinetic theory is used to investigate cross-stream migration of a rigid polymer undergoing rectilinear flow in the vicinity of a wall. Hydrodynamic interactions between the polymers and the boundary result in a cross-stream migration. In simple shear flow, polymers migrate away from the wall, creating a depletion layer in the vicinity of the wall which thickens as the flow strength increases relative to the Brownian force. In pressure-driven flow, an off-center maximum in the center-of-mass distribution occurs due to a competition between hydrodynamic interactions with the wall and the anisotropic diffusivity induced by the inhomogeneous flow field.

Figure 1

A rigid polymer of length $L$ and aspect ratio $A$ suspended in a shear flow of strength $\dot{\gamma }$. The coordinate $s$ describes positions along the polymer axis, and a no-slip boundary is located at $y=0$.

Figure 2

Transverse velocity ${\dot{r}}_y$ as a function of polymer orientation $\theta ={\cos }^{-1}[p_x∕\left(\sqrt{p_x^2+p_y^2}\right)]$, with $p_z=0$. The inset shows the directional dependence on the polymer angle.

Figure 3

Contribution of the shear flow $\left(\mathrm{Pe}\alpha \right)$ and Brownian torque $\left(72\beta \right)$ to the migration of a rigid polymer in simple shear flow plotted as a function of ${\mathrm{Pe}}_{\mathrm{r}}$.

Figure 4

Center-of-mass distribution for a rigid polymer with $A=10$ in simple shear flow.

Figure 5

Center-of-mass distribution for a rigid polymer with $A=10$ in pressure-driven flow. The height of the channel is $8L$ and $n_T=\int nd{r}_y$.