Abstract
This paper extends the work of van Duijn et al. (2018) where travelling wave solutions for wetting fronts were considered under the presence of only capillary hysteresis effect and only dynamic capillary effect. In this work, we investigate how the gravity driven wetting fronts behave while moving through long vertical homogeneous porous columns, under the combined effect of capillary hysteresis and dynamic capillarity. It is shown that the developed saturation profiles will exhibit non-monotone behaviour if certain parametric conditions are satisfied. The characteristics of the profiles are explained in detail for all the cases. Moreover, parametric conditions that inhibit the fronts from reaching full saturation are laid out. The analysis agrees well with experimental observations. Finally, numerical results are shown that confirm all the theoretical predictions.
| Original language | English |
|---|---|
| Pages (from-to) | 316-341 |
| Number of pages | 26 |
| Journal | Nonlinear Analysis : Real World Applications |
| Volume | 50 |
| DOIs | |
| Publication status | Published - 1 Dec 2019 |
Funding
C.J. van Duijn acknowledges the support of the Darcy Centre of Utrecht University and Eindhoven University of Technology. K. Mitra is supported by Shell (the Netherlands) and the Netherlands Organisation for Scientific Research (NWO) through the CSER programme (project 14CSER016 ) and by the Hasselt University (Belgium) through the project BOF17BL04 . The authors are grateful to Prof. I.S. Pop for many fruitful discussions on the subject. We would also like to thank the anonymous referees for their careful reading of the manuscript and their valuable comments and the editorial board for their effort. Appendix
Keywords
- Capillary hysteresis
- Dynamic capillarity
- Overshoot
- Travelling waves
- Unsaturated porous flow
- Wetting fronts