EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Modelling gravity-driven fingering in soils having an intrinsic non-zero contact angle (water repellent soils) using the innovative moving-boundary approach

Rony Wallach1 and Naaran Brindt2
Rony Wallach and Naaran Brindt
  • 1Hebrew University of Jerusalem, Agriculture, Food and Environment, Soil and Water Sci, Rehovot, Israel (
  • 2Currently at the Department of Biological and Environmental Engineering, Cornell University, US.

Quantitative and Qualitative description of infiltration into soils in general and initially dry soils in particular those in which the hydraulic properties vary spatial and temporal have been challenging soil physicists and hydrologists. Water repellent soils, whose contact angle is higher than 40° and can even reach values that are greater than 90° (noted as hydrophobic soils) are an example of such challenge cases. Infiltration in these soils takes usually place along preferential flow pathways (noted as gravity-induced fingering), rather than in a laterally uniform moving wetting front. The water content and capillary pressure distributions along these fingers are non-monotonic with water accumulation behind the moving wetting front (noted as saturation overshoot) and a decreasing water content toward the soil surface. Being a parabolic-type partial differential equation, the Richards equation that is commonly used to model flow in soils can't handle such water content/pressure distributions. Many attempts have been made to modify the Richards equation to enable it to model the non-monotonic water content profiles. These attempts that are not based on the measurable soil properties that can highlight the physics that induces the formation of such non-monotonic distribution.  

A new conceptual modelling approach, noted as the moving-boundary approach, will be presented. This approach overcomes the existing theoretical gaps in the quantitative descriptions that have been suggested for the non-monotonic water content distribution in the gravity-induced fingers. The moving-boundary approach is based on the presumption that non-monotonicity in water content is formed by an intrinsic higher-than-zero contact angle. Note that non-zero contact angle have been rarely incorporated in models used for quantifying infiltration into field soils, in spite of the findings that most soils feature some degree of repellency. The verified moving-boundary solution will be used to demonstrate the synergistic effect of contact angle and incoming flux on the stability of 2D flow and its associated plume shapes. The physically-based moving-boundary approach fulfils several criteria raised by researchers to adequately describe gravity-driven unstable flow.


How to cite: Wallach, R. and Brindt, N.: Modelling gravity-driven fingering in soils having an intrinsic non-zero contact angle (water repellent soils) using the innovative moving-boundary approach , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-2647,, 2020


Display file

Comments on the display

AC: Author Comment | CC: Community Comment | Report abuse

displays version 1 – uploaded on 02 May 2020
  • CC1: Comment on EGU2020-2647, Gerrit H. de Rooij, 05 May 2020

    Dear Rony,

    Interesting work. I have thought for a long time that finger formation required a resistance at the wetting front (reflected by a non-zero contact angle) had to be large enough to force the soil to wet up immediately behind the wetting fron to a water content at which the hydraulic conductivity would exceed the infiltration rate. If that is the case, the amount of water offered to the soil can be handled by a fraction of the horizontal cross-section of the soil, and thereforee fingers can form.

    You now created a model that can simulate this and your results seem to corroborate my line of thinking. Thanks for that.

    In your slides you argue that the saturation overshoot cannot be modelled by Richards' equation. I would argue that it is not Richards' equation is at fault, but rather the soil water retention curve that goes into it. If you provide a retention curve with a finite water entry value instead of the asymptotic behavior at some residual water content, Richards' equation should be able to handle this, and your model results seem to support this.

    Your figure with the retention curves shows the effect of the contact angle on the eintire wetting curve, but yet they all seem have an asymptotic dry branch, which requires a zero contact angle. I do not fully understand this. Could you please elaborate on that?

    Thank you,

    Gerrrit de Rooij

  • AC1: Comment on EGU2020-2647, Rony Wallach, 18 May 2020

    Dear Gerrrit

    Thanks for you comment and interest in my research. 

    You argue that Richards equation can handle unstable fingered flow in which satruation overshoot at its tip is formed.  I tend not to agree with your statement.  Richards equation, being a parabolic partial differential (diffusion-type) equaion, can not, by difinition, handle a non monotonic mosture/pressure distribution within the finger that results from the water accumulation behind the finger tip. Indeed, the wetting retention curve varies with contact angle as was demonstrated in Brindt and Wallach, 2017 and 2020 (both in WRR), and affects the invasion of dry pores at the wetting front independent on the equation being used to model the flow.  In fact, the moving boundary model was sucessfuly used to model flow in wettable (zero contact angle) and subcritically water repellent (larger than zero contact angle) without making any adjustments. This gave us the confidence that the model and the associated assumptions are valid for stable and unstable flow alike. 

    If you want to discuss this issue further on, please use my email:

    All the best,