Modelling Capillary Rise with a Slip Boundary Condition: Well-posedness and Long-time Dynamics of Solutions to Washburn's Equation
Abstrak
The aim of this paper is to extend Washburn's capillary rise equation by incorporating a slip condition at the pipe wall. The governing equation is derived using fundamental principles from continuum mechanics. A new scaling is introduced, allowing for a systematic analysis of different flow regimes. We prove the global-in-time existence and uniqueness of a bounded positive solution to Washburn's equation that includes the slip parameter, as well as the continuous dependence of the solution in the maximum norm on the initial data. Thus, the initial-value problem for Washburn's equation is shown to be well-posed in the sense of Hadamard. Additionally, we show that the unique equilibrium solution may be reached either monotonically or in an oscillatory fashion, similarly to the no-slip case. Finally, we determine the basin of attraction for the system, ensuring that the equilibrium state will be reached from the initial data we impose. These results hold for any positive value of the nondimensional slip parameter in the model, and for all values of the ratio $h_0/h_e$ in the range $[0,3/2]$, where $h_0$ is the initial height of the fluid column and $h_e$ is its equilibrium height.
Topik & Kata Kunci
Penulis (17)
Isidora Rapaji'c
Srboljub Simi'c
Endre Suli Mathematical Institute of the Serbian Academy Sciences
Arts
Belgrade
Serbia
D. Mathematics
Informatics
F. O. Sciences
4. TrgDositejaObradovi'ca
21000 Novi Sad
M. Institute
U. Oxford
Andrew Wiles Building
W. Road
OX2 6GG
United Kingdom.
Akses Cepat
- Tahun Terbit
- 2025
- Bahasa
- en
- Total Sitasi
- 2×
- Sumber Database
- Semantic Scholar
- DOI
- 10.1016/j.physd.2025
- Akses
- Open Access ✓