pypesh 0.1.5

Sherwood number in Stokes flow

advection diffusion solver

This repository attempts to find a solution to advection diffusion problem

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

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

$$\mathrm{Sh}=\frac{\mathrm{\Phi }}{4\pi DR}$$

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

We use two approaches: (a) 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 spaller $\mathrm{Pe}$ we used (b) scikit-fem package to handle solving which requires rewriting equations in weak form.

Usage as module

Basic usage

python3 -m pypesh --peclet 1000 --ball_radius 0.9

Sample output:

Sherwood for given parameters is 12.033892568100546

Usage as package

Install

python3 -m pip install pypesh

Basic usage

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)