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rheomodel

Collection of rheology flow curve models

import lmfit
import rheomodel as rm
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import Markdown, Latex


model=lmfit.Model(rm.HB)
model.param_names
['ystress', 'K', 'n']

x=np.logspace(-3,3)
data=pd.DataFrame({'Shear rate':x,'Stress':rm.TC(x,ystress=10,gammadot_crit=0.1,eta_bg=0.8)})
display(Markdown(data.head().to_markdown()))
Shear rate Stress
0 0.001 11.0008
1 0.00132571 11.1525
2 0.00175751 11.3271
3 0.00232995 11.5283
4 0.00308884 11.76 
res_fit=model.fit(data['Stress'],x=data['Shear rate'],weights=1/data['Stress'])
fig, ax = plt.subplots()
ax.plot(res_fit.userkws['x'],res_fit.data, 'o', label='TC simulated data', color='black')
ax.plot(res_fit.userkws['x'],res_fit.eval(), label='HB fit', color='red')

ax.set_yscale('log')
ax.set_xscale('log')
ax.set_xlabel('$\dot\gamma$ [1/s]')
ax.set_ylabel('$\sigma$ [Pa]')
ax.legend()
ax.set_title('Example Fit');

png

Library structure

  • models.bib : ships with the library and is the bibtex file with the citation for the source of the model
  • models.py : list of python function implementing each model expressed as stress as a function shear rate
  • function.py : library functionality like showing model and citation table
import rheomodel as rm
display(Markdown(rm.library_to_table(rm.library).to_markdown()))
ID author title publisher year address journal volume number pages
newton_1687 Isaac Newton Philosophiæ Naturalis Principia Mathematica Josephi Streater 1687 London nan nan nan nan
ostwald_1929 Ostwald, Wilhelm Über die Geschwindigkeitsfunktion der Newton'schen Viscosität Walter de Gruyter 1929 nan Zeitschrift für physikalische Chemie 102 1 64--79
bingham_1916 Bingham, Eugene C. A new conception of plasticity and viscous flow Elsevier 1916 nan The Journal of the Franklin Institute 181 6 543--552
herschel_bulkley_1926 Herschel, Winslow Hobart and Bulkley, Robert Measurement of consistency as applied to rubber-benzene solutions American Society for Testing and Materials 1926 nan Proceedings of the American Society for Testing Materials 26 2 621--633
carreau_yasuda_1979 Carreau, Pierre J. and Yasuda, Koichi Rheological equations from molecular network theories Wiley 1979 nan Journal of Polymer Science 11 2 371--388
cross_1925 Cross, Malcolm M. Viscosity of Colloids ACS Publications 1925 nan The Journal of Physical Chemistry 29 11 1409--1426
caggioni2020variations Caggioni, Marco and Trappe, Veronique and Spicer, Patrick T Variations of the Herschel--Bulkley exponent reflecting contributions of the viscous continuous phase to the shear rate-dependent stress of soft glassy materials AIP Publishing 2020 nan Journal of Rheology 64 2 413--422 
for ID, model in rm.models.model_dict.items():
    display(ID, Latex(model.latex))
'caggioni2020variations'

$\sigma=\sigma_y+\sigma_y\cdot(\dot\gamma/\dot\gamma_c)^{0.5}+\eta_{bg}\cdot\dot\gamma$

'herschel_bulkley_1926'

$\sigma= \sigma_y + K \cdot \dot\gamma^n$

'newton_1687'

$\sigma=\eta\cdot\dot\gamma$

'ostwald_1929'

$\sigma=K \cdot \dot\gamma^n$

'cross_1925'

$\sigma= \dot\gamma \eta_{inf} + \dot\gamma (\eta_0 - \eta_{inf})/(1 + (\dot\gamma/\dot\gamma_c)^n)$

'bingham_1916'

$\sigma=\sigma_y+\eta_{bg}\cdot\dot\gamma$

!jupyter nbconvert --to markdown README.ipynb
[NbConvertApp] Converting notebook README.ipynb to markdown
[NbConvertApp] Support files will be in README_files\
[NbConvertApp] Making directory README_files
[NbConvertApp] Writing 6852 bytes to README.md