Available Rheological models

import sys
import os
sys.path.insert(0,'C:\\Users\\caggioni.m\\Documents\\GitHub\\rheofit')
import rheofit

The rheological models available are intended for fitting flow curves, the shear stress indicated by the symbol \(\sigma\) as a function of shear rate indicated by the symbol \(\dot\gamma\).

rheofit.models.Bingham_model # lmfit model
display(rheofit.models.Bingham_model.model_expression)
help(rheofit.models.Bingham)

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

Help on function Bingham in module rheofit.models:

Bingham(x, ystress=1.0, eta_bg=0.1)
    Bingham model

    Note:

    .. math::
       \sigma=\sigma_y+\eta_{bg}\cdot\dot\gamma

    Args:
        ystress: yield stress [Pa]

        eta_bg : Background viscosity [Pa s]

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.casson_model # lmfit model
display(rheofit.models.casson_model.model_expression)
help(rheofit.models.casson)

$\displaystyle \sigma^{0.5}=\sigma_y^{0.5}+\eta_{bg}^{0.5}$

Help on function casson in module rheofit.models:

casson(x, ystress=1.0, eta_bg=0.1)
    Casson Model

    Note:

    .. math::
       \sigma^{0.5}= \sigma_y^{0.5} + \eta_{bg}^{0.5}

    Args:
        ystress: yield stress [Pa]

        eta_bg : Background viscosity [Pa s]

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.Powerlaw_model # lmfit model
display(rheofit.models.Powerlaw_model.model_expression)
help(rheofit.models.Powerlaw)

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

Help on function Powerlaw in module rheofit.models:

Powerlaw(x, n=0.5, K=0.1)
    Powerlaw model for the stress data

    Note:

    .. math::
       \sigma=K \cdot \dot\gamma^n

    Args:

        K : consistency index [Pa s]
        n : shear thinning index (1 for Newtonian) []

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.HB_model # lmfit model
display(rheofit.models.HB_model.model_expression)
help(rheofit.models.HB)

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

Help on function HB in module rheofit.models:

HB(x, ystress=1.0, K=1.0, n=0.5)
    Hershel-Bulkley Model

    Note:

    .. math::
       \sigma= \sigma_y + K \cdot \dot\gamma^n

    Args:
        ystress: yield stress [Pa]

        K : Consistency index [Pa s^n]

        n : Shear thinning index []

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.TC_model # lmfit model
display(rheofit.models.TC_model.model_expression)
help(rheofit.models.TC)

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

Help on function TC in module rheofit.models:

TC(x, ystress=1.0, eta_bg=0.1, gammadot_crit=0.1)
    Three component model

    Note:

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

    Args:
        ystress: yield stress [Pa]

        eta_bg : Background viscosity [Pa s]

        gammadot_crit : Critical shear rate [1/s]

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.carreau_model # lmfit model
display(rheofit.models.carreau_model.model_expression)
help(rheofit.models.carreau)

$\displaystyle \sigma=\dot\gamma \cdot \eta_0 \cdot (1+(\dot\gamma/\dot\gamma_{c_carreau})^2)^{(n-1)/2}$

Help on function carreau in module rheofit.models:

carreau(x, eta_0=1.0, gammadot_crit=1.0, n=0.5, prefix='carreau')
    carreau Model

    Note:

    .. math::
       \sigma=\dot\gamma \cdot \eta_0 \cdot (1+(\dot\gamma/\dot\gamma_c)^2)^{(n-1)/2}

    Args:
        eta_0: low shear viscosity [Pa s]

        gammadot_crit: critical shear rate [1/s]

        n : shear thinning exponent

    Returns:
        stress : Shear Stress, [Pa]

rheofit.models.cross_model # lmfit model
display(rheofit.models.cross_model.model_expression)
help(rheofit.models.cross)

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

Help on function cross in module rheofit.models:

cross(x, eta_inf=0.001, eta_0=1.0, n=0.5, gammadot_crit=1.0)
    cross Model

    Note:

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

    Args:
        ystress: yield stress [Pa]

        K : Consistency index [Pa s^n]

        n : Shear thinning index []

    Returns:
        stress : Shear Stress, [Pa]