### Abstract

We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are generally not zero even if the time average of the shear rate is zero. The validity of the theoretical calculations is confirmed by direct numerical simulations of the Smoluchowski equation. Nonadiabatic effects are also investigated by means of simulations and it is found that the time-integrated stress tensor depends on the speed of the modulation of the shear rate if we adopt the isotropic distribution as an initial state.

Original language | English |
---|---|

Article number | 054903 |

Journal | Journal of Chemical Physics |

Volume | 142 |

Issue number | 5 |

DOIs | |

Publication status | Published - Feb 7 2015 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*142*(5), [054903]. https://doi.org/10.1063/1.4906557

**Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions.** / Yabunaka, Shunsuke; Hayakawa, Hisao.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 142, no. 5, 054903. https://doi.org/10.1063/1.4906557

}

TY - JOUR

T1 - Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions

AU - Yabunaka, Shunsuke

AU - Hayakawa, Hisao

PY - 2015/2/7

Y1 - 2015/2/7

N2 - We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are generally not zero even if the time average of the shear rate is zero. The validity of the theoretical calculations is confirmed by direct numerical simulations of the Smoluchowski equation. Nonadiabatic effects are also investigated by means of simulations and it is found that the time-integrated stress tensor depends on the speed of the modulation of the shear rate if we adopt the isotropic distribution as an initial state.

AB - We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are generally not zero even if the time average of the shear rate is zero. The validity of the theoretical calculations is confirmed by direct numerical simulations of the Smoluchowski equation. Nonadiabatic effects are also investigated by means of simulations and it is found that the time-integrated stress tensor depends on the speed of the modulation of the shear rate if we adopt the isotropic distribution as an initial state.

UR - http://www.scopus.com/inward/record.url?scp=84923771968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84923771968&partnerID=8YFLogxK

U2 - 10.1063/1.4906557

DO - 10.1063/1.4906557

M3 - Article

AN - SCOPUS:84923771968

VL - 142

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 5

M1 - 054903

ER -