# Flow Behavior of Chain and Star Polymers and Their Mixtures

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model and Simulation Method

## 3. Results and Discussion

#### 3.1. Ultradiulte Conditions

#### 3.2. Polymer Mixtures

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CM | Center of mass |

FENE | Finitely extensible nonlinear elastic |

HI | Hydrodynamic interactions |

MD | Molecular Dynamics |

MPCD | Multi-particle collision dynamics |

PDMS | Polydimethylsiloxane |

PEO | Poly(ethylene oxide) |

WCA | Weeks-Chandler-Andersen |

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**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, $\u2329{G}_{zz}\u232a$, and solid lines show component in gradient direction, $\u2329{G}_{xx}\u232a$.

**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.

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**MDPI and ACS Style**

Srivastva, D.; Nikoubashman, A. Flow Behavior of Chain and Star Polymers and Their Mixtures. *Polymers* **2018**, *10*, 599.
https://doi.org/10.3390/polym10060599

**AMA Style**

Srivastva D, Nikoubashman A. Flow Behavior of Chain and Star Polymers and Their Mixtures. *Polymers*. 2018; 10(6):599.
https://doi.org/10.3390/polym10060599

**Chicago/Turabian Style**

Srivastva, Deepika, and Arash Nikoubashman. 2018. "Flow Behavior of Chain and Star Polymers and Their Mixtures" *Polymers* 10, no. 6: 599.
https://doi.org/10.3390/polym10060599