Flow Behavior of Chain and Star Polymers and Their Mixtures

Abstract

Star-shaped polymers show a continuous change of properties from flexible linear chains to soft colloids, as the number of arms is increased. To investigate the effect of macromolecular architecture on the flow properties, we employ computer simulations of single chain and star polymers as well as of their mixtures under Poiseuille flow. Hydrodynamic interactions are incorporated through the multi-particle collision dynamics (MPCD) technique, while a bead-spring model is used to describe the polymers. For the ultradilute systems at rest, the polymers are distributed uniformly in the slit channel, with a weak dependence on their number of arms. Once flow is applied, however, we find that the stars migrate much more strongly towards the channel center as the number of arms is increased. In the star-chain mixtures, we find a flow-induced separation between stars and chains, with the stars located in the channel center and the chains closer to the walls. In order to identify the origin of this flow-induced partitioning, we conduct additional simulations without hydrodynamic interactions, and find that the observed cross-stream migration originates from a combination of wall-induced hydrodynamic lift forces and viscoelastic effects. The results from our study give valuable insights for designing microfluidic devices for separating polymers based on their architecture.

Keywords: Poiseuille flow; chains; microfluidics; polymers; separation; simulations; stars.

Figure 1

Schematic representation of the channel geometry and resulting flow profile.

Figure 2

(a) Center of mass probability distribution normal to the channel walls, $P_{\mathrm{cm}}\left(x\right)$, for various arm numbers f at rest; (b) Component of the radius of gyration tensor normal to the walls ($G_{xx}$) as a function of center of mass distance x. In both panels, the shaded regions around the curves indicate our measurement uncertainty. The dotted vertical lines indicate the excluded regions of width $R_{\mathrm{g}}$ near the channel walls.

Figure 3

Center of mass probability distribution normal to the channel walls, $P_{\mathrm{cm}}\left(x\right)$, for a chain (left) and a star with $f=30$ arms (right) at various flow strengths ${\mathrm{Re}}_{\mathrm{p}}$, as indicated.

Figure 4

Components of the radius of gyration tensor along (a) the gradient and (b) the flow direction vs. the polymer CM position x. Data shown for a chain (left) and a star with $f=30$ arms (right) at various flow strengths ${\mathrm{Re}}_{\mathrm{p}}$, as indicated.

Figure 5

Components of the radius of gyration tensor averaged over the entire channel vs. flow strength ${\mathrm{Re}}_{\mathrm{p}}$, normalized by the value at rest. Dashed lines show component in flow direction, $〈G_{zz}〉$, and solid lines show component in gradient direction, $〈G_{xx}〉$.

Figure 6

Center of mass probability distribution normal to the channel walls, $P_{\mathrm{cm}}\left(x\right)$, for a mixture of chains ($f=2$) and stars ($f=30$) at (a) rest (${\mathrm{Re}}_{\mathrm{p}}=0$) and (b) under flow (${\mathrm{Re}}_{\mathrm{p}}=6$). Panel (c) shows the system under flow (${\mathrm{Re}}_{\mathrm{p}}=6$), but with hydrodynamic interactions switched off. The volume fraction of polymers is fixed to $\mathsf{\Phi }=0.1$ in all simulations.

Figure 7

Center of mass probability distribution normal to the channel walls, $P_{\mathrm{cm}}\left(x\right)$, for a mixture of stars with $f=18$ and $f=30$ arms at (a) rest (${\mathrm{Re}}_{\mathrm{p}}=0$) and (b) under flow (${\mathrm{Re}}_{\mathrm{p}}=6$). Panel (c) shows the system under flow (${\mathrm{Re}}_{\mathrm{p}}=6$), but with hydrodynamic interactions switched off. The volume fraction of polymers is fixed to $\mathsf{\Phi }=0.1$ in all simulations.