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Effective Long-Time Diffusivity of Particles of Arbitrary Shape in an External Orienting Field.

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Title: Effective Long-Time Diffusivity of Particles of Arbitrary Shape in an External Orienting Field.
Authors: Tianyu Yuan1,2 tyyuan777@163.com, Liping Liu1,3 liu.liping@rutgers.edu
Source: Journal of Applied Mechanics. Aug2025, Vol. 92 Issue 8, p1-15. 15p.
Subjects: Brownian motion, Fokker-Planck equation, Particle physics, Mass transfer coefficients, Colloids, Biophysics, Diffusion kinetics
Abstract: Pertaining to the motion of a rigid particle in a flow, several distinct "centers" of the rigid particle can be identified, including the geometric center (centroid), center of mass, hydrodynamic center, and center of diffusion. In this work, we elucidate the relevance of these centers in Brownian motion and diffusion. Starting from the microscopic stochastic equations of motions, we systematically derive the coarse-grained Fokker-Planck equations that govern the evolution of the probability distribution function (PDF) in phase space and in configurational space. For consistency with the equilibrium statistical mechanics, we determine the unknown Brownian forces and torques. Next, we analyze the Fokker-Planck equation for the PDF in the position and orientation space. Through a multiscale analysis, we find the unit cell problem for defining the effective long-time translational diffusivity of a particle of arbitrary shape in an external orienting field. We also show some fundamental properties of the effective long-time translational diffusivity, including rigorous variational bounds for effective long-time diffusivity and invariance of effective diffusivity with respect to change of reference or tracking points. Exact results are obtained in the absence of an orienting field and in the presence of a strong orienting field. These fundamental results hold significant potential for applications in biophysics, colloidal science, and micro-swimmers design. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Effective Long-Time Diffusivity of Particles of Arbitrary Shape in an External Orienting Field.
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  Data: <searchLink fieldCode="AR" term="%22Tianyu+Yuan%22">Tianyu Yuan</searchLink><relatesTo>1,2</relatesTo><i> tyyuan777@163.com</i><br /><searchLink fieldCode="AR" term="%22Liping+Liu%22">Liping Liu</searchLink><relatesTo>1,3</relatesTo><i> liu.liping@rutgers.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mechanics%22">Journal of Applied Mechanics</searchLink>. Aug2025, Vol. 92 Issue 8, p1-15. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Brownian+motion%22">Brownian motion</searchLink><br /><searchLink fieldCode="DE" term="%22Fokker-Planck+equation%22">Fokker-Planck equation</searchLink><br /><searchLink fieldCode="DE" term="%22Particle+physics%22">Particle physics</searchLink><br /><searchLink fieldCode="DE" term="%22Mass+transfer+coefficients%22">Mass transfer coefficients</searchLink><br /><searchLink fieldCode="DE" term="%22Colloids%22">Colloids</searchLink><br /><searchLink fieldCode="DE" term="%22Biophysics%22">Biophysics</searchLink><br /><searchLink fieldCode="DE" term="%22Diffusion+kinetics%22">Diffusion kinetics</searchLink>
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  Label: Abstract
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  Data: Pertaining to the motion of a rigid particle in a flow, several distinct "centers" of the rigid particle can be identified, including the geometric center (centroid), center of mass, hydrodynamic center, and center of diffusion. In this work, we elucidate the relevance of these centers in Brownian motion and diffusion. Starting from the microscopic stochastic equations of motions, we systematically derive the coarse-grained Fokker-Planck equations that govern the evolution of the probability distribution function (PDF) in phase space and in configurational space. For consistency with the equilibrium statistical mechanics, we determine the unknown Brownian forces and torques. Next, we analyze the Fokker-Planck equation for the PDF in the position and orientation space. Through a multiscale analysis, we find the unit cell problem for defining the effective long-time translational diffusivity of a particle of arbitrary shape in an external orienting field. We also show some fundamental properties of the effective long-time translational diffusivity, including rigorous variational bounds for effective long-time diffusivity and invariance of effective diffusivity with respect to change of reference or tracking points. Exact results are obtained in the absence of an orienting field and in the presence of a strong orienting field. These fundamental results hold significant potential for applications in biophysics, colloidal science, and micro-swimmers design. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Mechanics is the property of American Society of Mechanical Engineers and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1115/1.4068183
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 1
    Subjects:
      – SubjectFull: Brownian motion
        Type: general
      – SubjectFull: Fokker-Planck equation
        Type: general
      – SubjectFull: Particle physics
        Type: general
      – SubjectFull: Mass transfer coefficients
        Type: general
      – SubjectFull: Colloids
        Type: general
      – SubjectFull: Biophysics
        Type: general
      – SubjectFull: Diffusion kinetics
        Type: general
    Titles:
      – TitleFull: Effective Long-Time Diffusivity of Particles of Arbitrary Shape in an External Orienting Field.
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            NameFull: Tianyu Yuan
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            NameFull: Liping Liu
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            – D: 01
              M: 08
              Text: Aug2025
              Type: published
              Y: 2025
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              Value: 92
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