Abstract
Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a rivulet of fluid with finite width over and through a permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semiwidth or fixed contact angle is determined, and it is shown how the length, base area, and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system. In particular, whereas there is a physically realizable pendant rivulet solution only if the semiwidth does not exceed a critical value, there are physically realizable sessile and vertical rivulet solutions for all values of the semiwidth; moreover, a sessile rivulet with fixed semiwidth has a finite maximum possible length which is attained in the limit of a wide rivulet.
| Original language | English |
|---|---|
| Article number | 104003 |
| Journal | Physical Review Fluids |
| Volume | 6 |
| Issue number | 10 |
| Early online date | 7 Oct 2021 |
| DOIs | |
| Publication status | Published - 7 Oct 2021 |
Acknowledgements
The authors wish to thank Dr. Michael Grinfeld (University of Strathclyde) for his help and support during the course of the present work.Funding
A.S.A. wishes to thank the Ministry of Education, Kingdom of Saudi Arabia and King Abdulaziz University for their financial support of his Ph.D. research at the University of Strathclyde in Glasgow.