### Abstract

The conformation of a polymer chain subjected to periodic straining fields of arbitrary amplitude Ω and modulation frequency ω is studied in the Rouse model of polymer dynamics in the high-frequency limit ωτ_{R} ≫ 1 where τ_{R} is the Rouse relaxation time. We specialize to the case of sinusoidal time dependence, but our results are expected to be general. We calculate the dimensionless mean square extension μ of a polymer segment containing s monomers, defined as the ratio of the mean square size to the equilibrium value. For simple shear we find μ = 3 + λ ^{2}f_{1}(φ) for large segments, ωτ_{s} ≫ 1, where τ_{S} is the segment relaxation time, λ ≡ Ω/ω, and f_{1} is a nonuniversal function of the phase, φ ≡ ωt, of the straining field. For small segments, ωτ_{s} ≪ 1, we find μ = 3 + λ^{2}√ωτ_{s}f_{2}(φ) with nonuniversal f_{2}. In extensional flow the extension along the stretching axis is derived: μ = f_{3}(φ, λ) for ωτ_{s} ≫ 1 and μ = 1 + √ωτ _{s}f_{4}(φ, λ) for ωτ_{s} ≪ 1 (again f_{3} and f_{4} are nonuniversal). These results are interpreted in terms of blobs of relaxation time ∼ω^{-1}: the chain of blobs deforms affinely in the flow, but within a blob the polymer has time to relax. In the nonlinear régime (λ ≳ 1) the blobs are strongly distorted and the polymer within a blob relaxes to an elongation well beyond its equilibrium size such that its dimensions vary linearly with number of monomers. In the case of elongational flow, the fluctuations in the velocity field entirely suppress the "yo-yo" instability that has been conjectured to play an important role in the phenomenon of drag reduction.

Original language | English (US) |
---|---|

Pages (from-to) | 2637-2645 |

Number of pages | 9 |

Journal | The Journal of Chemical Physics |

Volume | 92 |

Issue number | 4 |

State | Published - 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of Chemical Physics*,

*92*(4), 2637-2645.

**Polymer deformation in strong high-frequency flows.** / O'Shaughnessy, Ben; Durning, Chris; Tabor, Michael.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 92, no. 4, pp. 2637-2645.

}

TY - JOUR

T1 - Polymer deformation in strong high-frequency flows

AU - O'Shaughnessy, Ben

AU - Durning, Chris

AU - Tabor, Michael

PY - 1990

Y1 - 1990

N2 - The conformation of a polymer chain subjected to periodic straining fields of arbitrary amplitude Ω and modulation frequency ω is studied in the Rouse model of polymer dynamics in the high-frequency limit ωτR ≫ 1 where τR is the Rouse relaxation time. We specialize to the case of sinusoidal time dependence, but our results are expected to be general. We calculate the dimensionless mean square extension μ of a polymer segment containing s monomers, defined as the ratio of the mean square size to the equilibrium value. For simple shear we find μ = 3 + λ 2f1(φ) for large segments, ωτs ≫ 1, where τS is the segment relaxation time, λ ≡ Ω/ω, and f1 is a nonuniversal function of the phase, φ ≡ ωt, of the straining field. For small segments, ωτs ≪ 1, we find μ = 3 + λ2√ωτsf2(φ) with nonuniversal f2. In extensional flow the extension along the stretching axis is derived: μ = f3(φ, λ) for ωτs ≫ 1 and μ = 1 + √ωτ sf4(φ, λ) for ωτs ≪ 1 (again f3 and f4 are nonuniversal). These results are interpreted in terms of blobs of relaxation time ∼ω-1: the chain of blobs deforms affinely in the flow, but within a blob the polymer has time to relax. In the nonlinear régime (λ ≳ 1) the blobs are strongly distorted and the polymer within a blob relaxes to an elongation well beyond its equilibrium size such that its dimensions vary linearly with number of monomers. In the case of elongational flow, the fluctuations in the velocity field entirely suppress the "yo-yo" instability that has been conjectured to play an important role in the phenomenon of drag reduction.

AB - The conformation of a polymer chain subjected to periodic straining fields of arbitrary amplitude Ω and modulation frequency ω is studied in the Rouse model of polymer dynamics in the high-frequency limit ωτR ≫ 1 where τR is the Rouse relaxation time. We specialize to the case of sinusoidal time dependence, but our results are expected to be general. We calculate the dimensionless mean square extension μ of a polymer segment containing s monomers, defined as the ratio of the mean square size to the equilibrium value. For simple shear we find μ = 3 + λ 2f1(φ) for large segments, ωτs ≫ 1, where τS is the segment relaxation time, λ ≡ Ω/ω, and f1 is a nonuniversal function of the phase, φ ≡ ωt, of the straining field. For small segments, ωτs ≪ 1, we find μ = 3 + λ2√ωτsf2(φ) with nonuniversal f2. In extensional flow the extension along the stretching axis is derived: μ = f3(φ, λ) for ωτs ≫ 1 and μ = 1 + √ωτ sf4(φ, λ) for ωτs ≪ 1 (again f3 and f4 are nonuniversal). These results are interpreted in terms of blobs of relaxation time ∼ω-1: the chain of blobs deforms affinely in the flow, but within a blob the polymer has time to relax. In the nonlinear régime (λ ≳ 1) the blobs are strongly distorted and the polymer within a blob relaxes to an elongation well beyond its equilibrium size such that its dimensions vary linearly with number of monomers. In the case of elongational flow, the fluctuations in the velocity field entirely suppress the "yo-yo" instability that has been conjectured to play an important role in the phenomenon of drag reduction.

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M3 - Article

AN - SCOPUS:5544265348

VL - 92

SP - 2637

EP - 2645

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -