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polykin.transport.rheology¤

mu_PowerLaw ¤

mu_PowerLaw(
    gdot: float | FloatArray, K: float, n: float
) -> float | FloatArray

Calculate the viscosity of a fluid using the Power-Law model.

The viscosity \(\mu\) at a given shear rate \(\dot{\gamma}\) is calculated using the following equation:

\[ \mu = K \dot{\gamma}^{n-1} \]

where \(K\) is the consistency and \(n\) is the flow index.

PARAMETER DESCRIPTION
gdot

Shear rate (1/s).

TYPE: float | FloatArray

K

Consistency (Pa·s^n).

TYPE: float

n

Flow index.

TYPE: float

RETURNS DESCRIPTION
float | FloatArray

Viscosity at the given shear rate (Pa·s).

Examples:

Determine the viscosity of a fluid with a consistency of 10 Pa·s^n and a flow index of 0.2, at a shear rate of 1e3 1/s.

>>> from polykin.transport import mu_PowerLaw
>>> gdot = 1e3  # 1/s
>>> K = 10.0    # Pa·s^n
>>> n = 0.2
>>> mu = mu_PowerLaw(gdot, K, n)
>>> print(f"mu={mu:.2e} Pa.s")
mu=3.98e-02 Pa.s
Source code in src/polykin/transport/rheology.py 
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def mu_PowerLaw(gdot: float | FloatArray,
                K: float,
                n: float
                ) -> float | FloatArray:
    r"""Calculate the viscosity of a fluid using the Power-Law model.

    The viscosity $\mu$ at a given shear rate $\dot{\gamma}$ is calculated
    using the following equation:

    $$ \mu = K \dot{\gamma}^{n-1} $$

    where $K$ is the consistency and $n$ is the flow index.

    Parameters
    ----------
    gdot : float | FloatArray
        Shear rate (1/s).
    K : float
        Consistency (Pa·s^n).
    n : float
        Flow index.

    Returns
    -------
    float | FloatArray
        Viscosity at the given shear rate (Pa·s).

    Examples
    --------
    Determine the viscosity of a fluid with a consistency of 10 Pa·s^n and a
    flow index of 0.2, at a shear rate of 1e3 1/s.
    >>> from polykin.transport import mu_PowerLaw
    >>> gdot = 1e3  # 1/s
    >>> K = 10.0    # Pa·s^n
    >>> n = 0.2
    >>> mu = mu_PowerLaw(gdot, K, n)
    >>> print(f"mu={mu:.2e} Pa.s")
    mu=3.98e-02 Pa.s
    """
    return K * gdot ** (n - 1)