fronts.D.letd

fronts.D.letd(L, E, T, Dwt=1.0, theta_range=(0.0, 1.0))

Return a LETd diffusivity function.

The LETd diffusivity function \(D\) is defined as:

\[D(\theta) = D_{wt} \frac{S_{wp}^L}{S_{wp}^L + E (1 - S_{wp})^T}\]

with:

\[S_{wp} = \frac{\theta - \theta_r}{\theta_s - \theta_r}\]
Parameters:

  • L (float) – \(L\) parameter for the LETd correlation.

  • E (float) – \(E\) parameter for the LETd correlation.

  • T (float) – \(T\) parameter for the LETd correlation.

  • Dwt (float, optional) – Constant diffusivity factor. The default is 1.

  • theta_range (sequence of two floats, optional) – (\(\theta_r\), \(\theta_s\)), where \(\theta_r\) is the minimum (also known as residual) water content and \(\theta_s\) is the maximum water content. The default is (0, 1). \(\theta_s\) must be greater than \(\theta_r\).

Returns:

D –

Function to evaluate \(D\) and its derivatives:

  • D(theta) evaluates and returns \(D\) at theta

  • D(theta, 1) returns both the value of \(D\) and its first derivative at theta

  • D(theta, 2) returns the value of \(D\), its first derivative, and its second derivative at theta

In all cases, the argument theta may be a single float or a NumPy array.

Return type:

callable

References

[1] GERLERO, G. S.; VALDEZ, A.; URTEAGA, R; KLER, P. A. Validity of capillary imbibition models in paper-based microfluidic applications. Transport in Porous Media, 2022, vol. 141, no. 7, pp. 1-20.