pypesh

This repository attempts to find a solution to advection diffusion problem

$$ 0 = \Delta \varphi - \mathrm{Pe} (u \cdot \nabla \varphi) $$

with $\varphi = 1$ for $z \to \infty$ and $\varphi = 0$ on a surface of the sphere and $\mathrm{Pe}$ denoting Peclet number. Final determined value is Sherwood number defined as

$$ \mathrm{Sh} = \frac{\Phi}{ 4 \pi D R}$$

Where $D$ is diffusion constant and $\Phi$ is flux falling onto the sphere.

(a) shows the flow field around the sphere. We use two approaches: (c) pychastic to generate and trace trajcetories of single particles and estimate the probability of hitting, which allows to calculate sherwood number. This however is expenive in time, so for smaller $\mathrm{Pe}$ we used (b) scikit-fem package to handle solving which requires rewriting equations in weak form.

How to cite

If you use pypesh in your research, please cite the associated article:

Turczynowicz, J., Waszkiewicz, R., Lisicki, M., and Somka, J. Bridging advection and diffusion in the encounter dynamics of sedimenting marine snow; arXiv (2025)

https://doi.org/10.48550/arXiv.2504.08992

bibtex @article{Turczynowicz_2025, title = {Bridging advection and diffusion in the encounter dynamics of sedimenting marine snow}, author = {Turczynowicz, Jan and Waszkiewicz, Radost and Lisicki, Maciej and Somka, Jonasz}, journal = {arXiv}, year = {2025}, doi = {10.48550/arXiv.2504.08992}, url = {https://doi.org/10.48550/arXiv.2504.08992} }

Examples

Usage as module

Basic usage ```Python python3 -m pypesh --peclet 1000 --ball_radius 0.9

```

Sample output: Sherwood for given parameters is 12.033892568100546

Usage as package

Install

Bash python3 -m pip install pypesh

Basic usage

Python import pypesh.pesh as psh psh.sherwood(peclet = 10**4, ball_radius = 0.9)

For advanced options go to: https://pypesh.readthedocs.io/en/latest/

License

Copyright (C) 2024 Radost Waszkiewicz and Jan Turczynowicz. This repository is published under GPL3.0 license.

Bibliography

• Bubbles, Drops and Particles; R. Clift, J. Grace, M. Weber (1978)
• Electrochemical measurements of mass transfer between a sphere and liquid in motion at high Peclet numbers; S. Kutateladze, V. Nakoryakov, M. Iskakov (1982)
• Mass and heat transfer from fluid spheres at low Reynolds numbers; Z. Feng, E. Michaelides (2000)
• Heat transfer from spheres to flowing media; H. Kramers (1946)