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');

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