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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.


Documento: Artículo
Título:Navier-Stokes solutions for parallel flow in rivulets on an inclined plane
Autor:Perazzo, C.A.; Gratton, J.
Filiación:Universidad Favaloro, Solís 453, Buenos Aires 1078, Argentina
INFIP CONICET, Dpto. de Física, Facultad de Ciencias Exactas y Nat., Buenos Aires, Argentina
Palabras clave:Gravitation; Steady flow; Surface tension; Free surface; Rivulets; Navier Stokes equations; free surface flow; mathematical analysis; model; Navier-Stokes equations
Página de inicio:367
Página de fin:379
Título revista:Journal of Fluid Mechanics
Título revista abreviado:J. Fluid Mech.


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---------- APA ----------
Perazzo, C.A. & Gratton, J. (2004) . Navier-Stokes solutions for parallel flow in rivulets on an inclined plane. Journal of Fluid Mechanics(507), 367-379.
---------- CHICAGO ----------
Perazzo, C.A., Gratton, J. "Navier-Stokes solutions for parallel flow in rivulets on an inclined plane" . Journal of Fluid Mechanics, no. 507 (2004) : 367-379.
---------- MLA ----------
Perazzo, C.A., Gratton, J. "Navier-Stokes solutions for parallel flow in rivulets on an inclined plane" . Journal of Fluid Mechanics, no. 507, 2004, pp. 367-379.
---------- VANCOUVER ----------
Perazzo, C.A., Gratton, J. Navier-Stokes solutions for parallel flow in rivulets on an inclined plane. J. Fluid Mech. 2004(507):367-379.