Navier-Stokes solutions for parallel flow in rivulets on an inclined plane
We investigate the solutions of the Navier-Stokes equations that describe the steady flow of rivulets down an inclined surface. We find that the shape of the free surface is given by an analytic formula obtained by solving the equation that expresses the condition of static equilibrium under the act...
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2004
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v_n507_p367_Perazzo http://hdl.handle.net/20.500.12110/paper_00221120_v_n507_p367_Perazzo |
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paper:paper_00221120_v_n507_p367_Perazzo2023-06-08T14:45:57Z Navier-Stokes solutions for parallel flow in rivulets on an inclined plane Gravitation Steady flow Surface tension Free surface Rivulets Navier Stokes equations free surface flow mathematical analysis model Navier-Stokes equations We investigate the solutions of the Navier-Stokes equations that describe the steady flow of rivulets down an inclined surface. We find that the shape of the free surface is given by an analytic formula obtained by solving the equation that expresses the condition of static equilibrium under the action of gravity and surface tension, independently of the velocity field and of any assumption concerning the rheology of the liquid. The velocity field is then obtained by solving (in general numerically) a Poisson equation in the domain defined by the cross-section of the rivulet. The isovelocity contours are perpendicular to the free surface. Various properties of the solutions are given as functions of the parameters of the problem. Two special analytic solutions are presented. The exact solutions suggest that the lubrication approximation, frequently employed to investigate problems similar to the present one, predicts reasonably well the global properties of the rivulet provided the static contact angle is not too large. © 2004 Cambridge University Press. 2004 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v_n507_p367_Perazzo http://hdl.handle.net/20.500.12110/paper_00221120_v_n507_p367_Perazzo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Gravitation Steady flow Surface tension Free surface Rivulets Navier Stokes equations free surface flow mathematical analysis model Navier-Stokes equations |
| spellingShingle |
Gravitation Steady flow Surface tension Free surface Rivulets Navier Stokes equations free surface flow mathematical analysis model Navier-Stokes equations Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| topic_facet |
Gravitation Steady flow Surface tension Free surface Rivulets Navier Stokes equations free surface flow mathematical analysis model Navier-Stokes equations |
| description |
We investigate the solutions of the Navier-Stokes equations that describe the steady flow of rivulets down an inclined surface. We find that the shape of the free surface is given by an analytic formula obtained by solving the equation that expresses the condition of static equilibrium under the action of gravity and surface tension, independently of the velocity field and of any assumption concerning the rheology of the liquid. The velocity field is then obtained by solving (in general numerically) a Poisson equation in the domain defined by the cross-section of the rivulet. The isovelocity contours are perpendicular to the free surface. Various properties of the solutions are given as functions of the parameters of the problem. Two special analytic solutions are presented. The exact solutions suggest that the lubrication approximation, frequently employed to investigate problems similar to the present one, predicts reasonably well the global properties of the rivulet provided the static contact angle is not too large. © 2004 Cambridge University Press. |
| title |
Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| title_short |
Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| title_full |
Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| title_fullStr |
Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| title_full_unstemmed |
Navier-Stokes solutions for parallel flow in rivulets on an inclined plane |
| title_sort |
navier-stokes solutions for parallel flow in rivulets on an inclined plane |
| publishDate |
2004 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221120_v_n507_p367_Perazzo http://hdl.handle.net/20.500.12110/paper_00221120_v_n507_p367_Perazzo |
| _version_ |
1768546570883563520 |