Loading...
Please wait, while we are loading the content...
Similar Documents
Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves
| Content Provider | Scilit |
|---|---|
| Author | Levy, Rachel Shearer, Michael Witelski, Thomas P. |
| Copyright Year | 2007 |
| Description | The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerate-parabolic, and admits traveling wave solutions in which the free-surface height is piecewise constant, and the surfactant concentration is piecewise linear and continuous. The jumps and corners in the traveling waves are regularized when the small parameters are nonzero; their structure is revealed through a combination of analysis and numerical simulation. |
| Related Links | https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1189&context=hmc_fac_pub https://www.cambridge.org/core/services/aop-cambridge-core/content/view/456286ABF8743BC9D826E6E3529CDF5B/S0956792507007218a.pdf/div-class-title-gravity-driven-thin-liquid-films-with-insoluble-surfactant-smooth-traveling-waves-div.pdf |
| Ending Page | 708 |
| Page Count | 30 |
| Starting Page | 679 |
| ISSN | 09567925 |
| e-ISSN | 14694425 |
| DOI | 10.1017/s0956792507007218 |
| Journal | European Journal of Applied Mathematics |
| Issue Number | 6 |
| Volume Number | 18 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2007-12-01 |
| Access Restriction | Open |
| Subject Keyword | European Journal of Applied Mathematics Non Linear Dynamics Fluid Dynamics Numerical Simulation Perturbation Theory Free Surface Thin Film Piecewise Linear Surface Tension Traveling Wave |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
