Abstract
Active suspensions, which consist of suspended self-
propelling particles such as swimming microorganisms,
often exhibit non-trivial transport properties.
Continuum models are frequently employed to
elucidate phenomena in active suspensions, such
as shear trapping of bacteria, bacterial turbulence,
and bioconvection patterns in suspensions of algae.
Yet, these models are often empirically derived and
may not always agree with the individual-based
description of active particles. Here we review the
essential coarse-graining steps to develop commonly
used continuum models from their respective microscopic
dynamics. All the assumptions needed to reach
popular continuum models from a multi-particle
Fokker-Planck equation, which governs the probability
of the full configuration space, are explicitly presented.
In the dilute limit, this approach leads to the mean-
field model (a.k.a. Doi-Saintillan-Shelley model),
which can be further reduced to a continuum
equation for particle density. Moreover, we review
the limitations and highlight the challenges related to
continuum descriptions, including significant issues
in implementing physical boundary conditions and
the possible emergence of singular solutions.
propelling particles such as swimming microorganisms,
often exhibit non-trivial transport properties.
Continuum models are frequently employed to
elucidate phenomena in active suspensions, such
as shear trapping of bacteria, bacterial turbulence,
and bioconvection patterns in suspensions of algae.
Yet, these models are often empirically derived and
may not always agree with the individual-based
description of active particles. Here we review the
essential coarse-graining steps to develop commonly
used continuum models from their respective microscopic
dynamics. All the assumptions needed to reach
popular continuum models from a multi-particle
Fokker-Planck equation, which governs the probability
of the full configuration space, are explicitly presented.
In the dilute limit, this approach leads to the mean-
field model (a.k.a. Doi-Saintillan-Shelley model),
which can be further reduced to a continuum
equation for particle density. Moreover, we review
the limitations and highlight the challenges related to
continuum descriptions, including significant issues
in implementing physical boundary conditions and
the possible emergence of singular solutions.
| Original language | English |
|---|---|
| Number of pages | 19 |
| Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Publication status | Accepted/In press - 14 Apr 2025 |