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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Autores principales: Perazzo, C.A., Gratton, J.
Formato: JOUR
Materias:
Gravitation
Steady flow
Surface tension
Free surface
Rivulets
Navier Stokes equations
free surface flow
mathematical analysis
model
Navier-Stokes equations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00221120_v_n507_p367_Perazzo
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00221120_v_n507_p367_Perazzo2023-10-03T14:26:35Z Navier-Stokes solutions for parallel flow in rivulets on an inclined plane Perazzo, C.A. Gratton, J. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Perazzo, C.A.
Gratton, J.
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.
format JOUR
author Perazzo, C.A.
Gratton, J.
author_facet Perazzo, C.A.
Gratton, J.
author_sort Perazzo, C.A.
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
url http://hdl.handle.net/20.500.12110/paper_00221120_v_n507_p367_Perazzo
work_keys_str_mv AT perazzoca navierstokessolutionsforparallelflowinrivuletsonaninclinedplane
AT grattonj navierstokessolutionsforparallelflowinrivuletsonaninclinedplane
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