{
  "abstract": "Micron-sized particles moving through a fluid are subject to viscous resistance and thermal fluctuations. Beyond steady Stokes friction, colloids also exhibit hydrodynamic memory effects arising from conservation laws of the surrounding fluid. Although fluid-flow problems in complex geometries and confinements are often highly involved, numerical or approximate solutions can be obtained; translating these solutions into closed-form equations of motion for individual colloids, however, is rarely possible. Here, we develop a theoretical framework that provides both underdamped and overdamped colloidal dynamics from the solution of an arbitrary flow problem: (i) Using the Lorentz reciprocal theorem, we express the colloidal equation of motion in terms of the geometry's Green's function and the fluid-flow profile. This formulation yields both the corresponding Stokes drag as well as a Basset-like hydrodynamic memory contribution. (ii) As colloid inertia is often negligible, we furthermore derive the corresponding overdamped (colloid-inertia-less) limit, which inherits the Stokes and Basset-like resistances and additionally gives rise to a spurious drift. We propose applications of this framework to passive and active particles subject to involved confinements and problem geometries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17678",
  "author_total": 3,
  "authors": [
    {
      "name": "Benjamin Sorkin"
    },
    {
      "name": "Günther Turk"
    },
    {
      "name": "Howard A. Stone"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4p474dgn8p864.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17678",
  "fulltext_url": null,
  "id": "4p474dgn8p864",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17678",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3104|Micro and Nano Robotics"
    ]
  ],
  "openalex": "W7213501244",
  "pdf_url": "https://arxiv.org/pdf/2609.17678",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4p474dgn8p864.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:01Z",
      "native_id": "2609.17678",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17678"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Brownian motion with geometry-dependent hydrodynamic memory",
  "title_text": "Brownian motion with geometry-dependent hydrodynamic memory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:01Z",
  "url": "https://research.draconitic.com/paper/4p474dgn8p864",
  "venue": "arXiv",
  "versions": []
}