# 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.