The Moving‐Boundary Approach for Modeling 2‐D Gravity‐Driven Stable and Unstable Flow in Partially Wettable Soils

2020 ◽  
Vol 56 (5) ◽  
Author(s):  
Naaran Brindt ◽  
Rony Wallach
Keyword(s):  
Moving Boundary ◽  
Unstable Flow ◽  
Gravity Driven

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

2020 ◽  
Author(s):  
Rony Wallach ◽  
Naaran Brindt
Keyword(s):  
Contact Angle ◽  
Water Content ◽  
Preferential Flow ◽  
Moving Boundary ◽  
Richards Equation ◽  
Water Repellent ◽  
Wetting Front ◽  
Unstable Flow ◽  
Pressure Distributions ◽  
Gravity Driven

<p>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.  </p><p>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.</p><p> </p>

scholarly journals Modeling gravity driven unstable flow in a water repellent soil

1999 ◽  
Vol 215 (1-4) ◽  
pp. 202-214 ◽  
Author(s):  
H.V Nguyen ◽  
J.L Nieber ◽  
C.J Ritsema ◽  
L.W Dekker ◽  
T.S Steenhuis
Keyword(s):  
Water Repellent ◽  
Unstable Flow ◽  
Gravity Driven

Numerical simulation of experimental gravity-driven unstable flow in water repellent sand

2000 ◽  
Vol 231-232 ◽  
pp. 295-307 ◽  
Author(s):  
J.L Nieber ◽  
T.W.J Bauters ◽  
T.S Steenhuis ◽  
J.-Y Parlange
Keyword(s):  
Numerical Simulation ◽  
Water Repellent ◽  
Unstable Flow ◽  
Gravity Driven ◽  
Experimental Gravity

Stratified flows with vertical layering of density: experimental and theoretical study of flow configurations and their stability

2011 ◽  
Vol 690 ◽  
pp. 571-606 ◽  
Author(s):  
Roberto Camassa ◽  
Richard M. McLaughlin ◽  
Matthew N. J. Moore ◽  
Kuai Yu
Keyword(s):  
Moving Boundary ◽  
Two Dimensions ◽  
Optical Tracking ◽  
Effective Length ◽  
Unstable Flow ◽  
Amplification Rate ◽  
Flow Configurations ◽  
The Stability ◽  
Horizontal Density Gradient ◽  
Stratified Viscous Fluid

AbstractA vertically moving boundary in a stratified fluid can create and maintain a horizontal density gradient, or vertical layering of density, through the mechanism of viscous entrainment. Experiments to study the evolution and stability of axisymmetric flows with vertically layered density are performed by towing a narrow fibre upwards through a stably stratified viscous fluid. The fibre forms a closed loop and thus its effective length is infinite. A layer of denser fluid is entrained and its thickness is measured by implementing tracking analysis of dyed fluid images. Thickness values of up to 70 times that of the fibre are routinely obtained. A lubrication model is developed for both a two-dimensional geometry and the axisymmetric geometry of the experiment, and shown to be in excellent agreement with dynamic experimental measurements once subtleties of the optical tracking are addressed. Linear stability analysis is performed on a family of exact shear solutions, using both asymptotic and numerical methods in both two dimensions and the axisymmetric geometry of the experiment. It is found analytically that the stability properties of the flow depend strongly on the size of the layer of heavy fluid surrounding the moving boundary, and that the flow is neutrally stable to perturbations in the large-wavelength limit. At the first correction of this limit, a critical layer size is identified that separates stable from unstable flow configurations. Surprisingly, in all of the experiments the size of the entrained layer exceeds the threshold for instability, yet no unstable behaviour is observed. This is a reflection of the small amplification rate of the instability, which leads to growth times much longer than the duration of the experiment. This observation illustrates that for finite times the hydrodynamic stability of a flow does not necessarily correspond to whether or not that flow can be realised from an initial-value problem. Similar instabilities that are neutral to leading order with respect to long waves can arise under the different physical mechanism of viscous stratification, as studied by Yih (J. Fluid Mech., vol. 27, 1967, pp. 337–352), and we draw a comparison to that scenario.

Sign in / Sign up

Export Citation Format

Share Document