Force-dependence of the rigid-body motion for an arbitrarily shaped particle in a forced, incompressible Stokes flow
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914231463444480 |
|---|---|
| author | Domínguez, Alvaro Popescu, Mihail N. |
| author_facet | Domínguez, Alvaro Popescu, Mihail N. |
| contents | When a particle moves in a Newtonian flow at low Reynolds number, inertia is irrelevant and a linear relationship exists between velocities and forces. For incompressible flows, any force distribution $\mathbf{f}(\mathbf{r})$ acting in the fluid bulk induces flow and motion only through its solenoidal component. For force distributions that are spatially localized (i.e., vanish sufficiently fast at infinity), we derive the representation of the rigid body motion as an explicit linear functional of $\nabla\times\mathbf{f}$, which complements the usual representation in terms of $\mathbf{f}$. We illustrate the utility of this alternative representation, which has the advantage of having the incompressibility constraint built-in, in avoiding certain ambiguities that arise, e.g., when implementing approximations for swimmers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Force-dependence of the rigid-body motion for an arbitrarily shaped particle in a forced, incompressible Stokes flow Domínguez, Alvaro Popescu, Mihail N. Fluid Dynamics Soft Condensed Matter When a particle moves in a Newtonian flow at low Reynolds number, inertia is irrelevant and a linear relationship exists between velocities and forces. For incompressible flows, any force distribution $\mathbf{f}(\mathbf{r})$ acting in the fluid bulk induces flow and motion only through its solenoidal component. For force distributions that are spatially localized (i.e., vanish sufficiently fast at infinity), we derive the representation of the rigid body motion as an explicit linear functional of $\nabla\times\mathbf{f}$, which complements the usual representation in terms of $\mathbf{f}$. We illustrate the utility of this alternative representation, which has the advantage of having the incompressibility constraint built-in, in avoiding certain ambiguities that arise, e.g., when implementing approximations for swimmers. |
| title | Force-dependence of the rigid-body motion for an arbitrarily shaped particle in a forced, incompressible Stokes flow |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2407.08314 |