polykin.transport.flow

vt_Stokes

vt_Stokes(
    D: float, rhop: float, rho: float, mu: float
) -> float

Calculate the terminal velocity of an isolated sphere using Stokes' law.

In laminar flow (\(Re \lesssim 0.1\)), the terminal velocity of an isolated particle is given by:

\[ v_t = \frac{D^2 g (\rho_p - \rho)}{18 \mu} \]

where \(D\) is the particle diameter, \(g\) is the acceleration due to gravity, \(\rho_p\) is the particle density, \(\rho\) is the fluid density, and \(\mu\) is the fluid viscosity.

PARAMETER	DESCRIPTION
D	Particle diameter (m). TYPE: float
rhop	Particle density (kg/m³). TYPE: float
rho	Fluid density (kg/m³). TYPE: float
mu	Fluid viscosity (Pa·s). TYPE: float

RETURNS	DESCRIPTION
float	Terminal velocity (m/s).

See also

• vt_sphere: generic method for laminar and turbulent flow.

Examples:

Calculate the terminal velocity of a 500 nm PVC particle in water.

>>> from polykin.transport import vt_Stokes
>>> vt = vt_Stokes(500e-9, 1.4e3, 1e3, 1e-3)
>>> print(f"vt = {vt:.1e} m/s")
vt = 5.4e-08 m/s

Source code in src/polykin/transport/flow.py

def vt_Stokes(D: float,
              rhop: float,
              rho: float,
              mu: float
              ) -> float:
    r"""Calculate the terminal velocity of an isolated sphere using Stokes' law.

    In laminar flow ($Re \lesssim 0.1$), the terminal velocity of an
    isolated particle is given by:

    $$ v_t = \frac{D^2 g (\rho_p - \rho)}{18 \mu} $$

    where $D$ is the particle diameter, $g$ is the acceleration due to gravity,
    $\rho_p$ is the particle density, $\rho$ is the fluid density, and $\mu$ is
    the fluid viscosity.

    Parameters
    ----------
    D : float
        Particle diameter (m).
    rhop : float
        Particle density (kg/m³).
    rho : float
        Fluid density (kg/m³).
    mu : float
        Fluid viscosity (Pa·s).

    Returns
    -------
    float
        Terminal velocity (m/s).

    See also
    --------
    * [`vt_sphere`](vt_sphere.md): generic method for laminar and turbulent flow.

    Examples
    --------
    Calculate the terminal velocity of a 500 nm PVC particle in water.
    >>> from polykin.transport import vt_Stokes
    >>> vt = vt_Stokes(500e-9, 1.4e3, 1e3, 1e-3)
    >>> print(f"vt = {vt:.1e} m/s")
    vt = 5.4e-08 m/s
    """
    vt = D**2*g*(rhop - rho)/(18*mu)

    Re = rho*vt*D/mu
    check_range_warn(Re, 0., 0.1, 'Re')

    return vt