### Abstract

A new theory is developed to study the effects of the granularity of a liquid on the diffusion of a large particle in the liquid. Inhomogeneous Langevin equations are expanded in powers of the size ratio between the solvent and large particles. From the expansion, we obtain hydrodynamic equations with new boundary conditions on the surface of the large particle in the first order. The new boundary conditions can be obtained from the radial distribution function between diffusing and solvent particles. The present theory is formulated by perturbation expansion and can thus deal with a large particle. In addition, using analytical solutions of hydrodynamic equations, we consider the effects of solvent particles at an infinite distance in contrast to the case for other methods. The theory is applied to a model radial distribution function, a hard-sphere system, and a Kihara potential system.

Original language | English |
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Article number | 114603 |

Journal | journal of the physical society of japan |

Volume | 81 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 1 2012 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*journal of the physical society of japan*,

*81*(11), [114603]. https://doi.org/10.1143/JPSJ.81.114603

**Perturbation theory of large-particle diffusion.** / Inayoshi, Yuko; Yoshimori, Akira; Akiyama, Ryo.

Research output: Contribution to journal › Article

*journal of the physical society of japan*, vol. 81, no. 11, 114603. https://doi.org/10.1143/JPSJ.81.114603

}

TY - JOUR

T1 - Perturbation theory of large-particle diffusion

AU - Inayoshi, Yuko

AU - Yoshimori, Akira

AU - Akiyama, Ryo

PY - 2012/11/1

Y1 - 2012/11/1

N2 - A new theory is developed to study the effects of the granularity of a liquid on the diffusion of a large particle in the liquid. Inhomogeneous Langevin equations are expanded in powers of the size ratio between the solvent and large particles. From the expansion, we obtain hydrodynamic equations with new boundary conditions on the surface of the large particle in the first order. The new boundary conditions can be obtained from the radial distribution function between diffusing and solvent particles. The present theory is formulated by perturbation expansion and can thus deal with a large particle. In addition, using analytical solutions of hydrodynamic equations, we consider the effects of solvent particles at an infinite distance in contrast to the case for other methods. The theory is applied to a model radial distribution function, a hard-sphere system, and a Kihara potential system.

AB - A new theory is developed to study the effects of the granularity of a liquid on the diffusion of a large particle in the liquid. Inhomogeneous Langevin equations are expanded in powers of the size ratio between the solvent and large particles. From the expansion, we obtain hydrodynamic equations with new boundary conditions on the surface of the large particle in the first order. The new boundary conditions can be obtained from the radial distribution function between diffusing and solvent particles. The present theory is formulated by perturbation expansion and can thus deal with a large particle. In addition, using analytical solutions of hydrodynamic equations, we consider the effects of solvent particles at an infinite distance in contrast to the case for other methods. The theory is applied to a model radial distribution function, a hard-sphere system, and a Kihara potential system.

UR - http://www.scopus.com/inward/record.url?scp=84870234128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870234128&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.81.114603

DO - 10.1143/JPSJ.81.114603

M3 - Article

AN - SCOPUS:84870234128

VL - 81

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 11

M1 - 114603

ER -