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polykin.kinetics.emulsion¤

kentry_diffusion ¤

kentry_diffusion(
    r: float, Dw: float, f: float = 1.0
) -> float

Radical entry coefficient assuming irreversible diffusion-controlled entry.

The entry coefficient is given by:

\[ k_e = 4 \pi r D_w N_A f \]

where \(r\) is the particle radius, \(D_w\) is the diffusion coefficient of the radical in the aqueous phase, \(N_A\) is Avogadro's number, and \(f\) is an efficiency factor.

PARAMETER DESCRIPTION
r

Particle radius [m].

TYPE: float

Dw

Diffusion coefficient of the radical in the aqueous phase [m²/s].

TYPE: float

f

Efficiency factor.

TYPE: float DEFAULT: 1.0

RETURNS DESCRIPTION
float

Radical entry coefficient [m³/(mol·s)].
See Also

Examples:

Evaluate the radical entry coefficient for a particle radius of 100 nm and a diffusion coefficient of 1e-9 m²/s.

>>> from polykin.kinetics import kentry_diffusion
>>> ke = kentry_diffusion(r=100e-9, Dw=1e-9)
>>> print(f"ke = {ke:.2e} m³/(mol·s)")
ke = 7.57e+08 m³/(mol·s)
Source code in src/polykin/kinetics/emulsion/entry.py 
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def kentry_diffusion(
    r: float,
    Dw: float,
    f: float = 1.0,
) -> float:
    r"""Radical entry coefficient assuming irreversible diffusion-controlled entry.

    The entry coefficient is given by:

    $$ k_e = 4 \pi r D_w N_A f $$

    where $r$ is the particle radius, $D_w$ is the diffusion coefficient of the radical in
    the aqueous phase, $N_A$ is Avogadro's number, and $f$ is an efficiency factor.

    Parameters
    ----------
    r : float
        Particle radius [m].
    Dw : float
        Diffusion coefficient of the radical in the aqueous phase [m²/s].
    f : float
        Efficiency factor.

    Returns
    -------
    float
        Radical entry coefficient [m³/(mol·s)].

    See Also
    --------
    * [`kentry_diffusion_reversible`](kentry_diffusion_reversible.md):
      Related method assuming reversible diffusion-controlled entry.

    Examples
    --------
    Evaluate the radical entry coefficient for a particle radius of 100 nm and a diffusion
    coefficient of 1e-9 m²/s.
    >>> from polykin.kinetics import kentry_diffusion
    >>> ke = kentry_diffusion(r=100e-9, Dw=1e-9)
    >>> print(f"ke = {ke:.2e} m³/(mol·s)")
    ke = 7.57e+08 m³/(mol·s)
    """
    return f * 4 * pi * r * Dw * NA