On the Marangoni and gravity flow in an inclined channel of an arbitrary section

[1] Acheson, D. J.,  Elementary fluis dynamics,  Oxford University Press, United Kingdom, 1990, pp. 238-259.

[2] Allen, R. F., Biggin, C. M.,  Longitudinal flow of a lenticular liquid filament down an inclined plane, Phys. Fluids. 17, pp. 287-291, 1974.

[3] Amick, C. J., Properties of steady Navier-Stokes solutions for certain unbounded channels and pipes, nonlinear analysis, Theory, Methods and Applications,  2, pp. 689-720, 1978.

[4] Amick, C. J., Fraenkel, L. E.,  Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types,  Acta Mathematica, 144, 83-152, 1980.

[5] Aris, R., Vector, tensors and the basic equations of fluid mechanics,  New Jersey, Englewood Cliffs, 1962.

[6] Chifu, E., Gheorghiu, C.I., Stan, I., Surface mobility of surfanctant solutions XI. Numerical analysis for the Marangoni and gravity flow in a thin liquid layer of triangular section, Rev. Roumaine Chim., 29, no. 1, pp. 31-42, 1984.

[7] Duffy, B. R., Moffatt, H. K., Flow of a viscous trickle on a slowly varying. The chemical engineering Journal, 60, 141-146, 1995.

[8] Duffy, B. R. and Wilson, S. K.,  A third-order differential equation arising in thin-film flows and relevant to Tanner’s law,  Appl. Math. Lett. 10, pp. 63, 1997.

[9] Gheorghiu, C. I., An  unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics,  Cluj-Napoca submitted to Studia Univ. “Babes-Bolyai”.

[10] Levich, V. G., Physico-chemical hydrodynamics,  Englewood Cliffs. New Jersey, 1967.

[11] Ockendon, H., Ockendon, J. R.,  Viscous Flow,  Cambridge, University Press, 1995.

[12] Towell, G. D. and Rothfeld, L. B., Hydrodynamics of rivulet flow,  AICHE. J., 12, p. 972, 1966.

[13] Wagner, A., Instationary Marangoni convection,  Heidelberg Preprint 94-42 (SFB 359), Univ. Heidelberg.

[14] Wilson, S. K., Duffy, B. R.,  On the gravity-driven draining of a rivulet of viscous fluid down a slowly varying substrate with variation transverse to the direction of flow. Phys. Fluids, 10, pp. 13-22, 1998.

[15] Whitaker, S.,  Effect of surface active agents on the stability of falling liquid films.  I and EC Fundamentals, 3, pp. 132-142, 1964.

[16] Young, G. W., Davis, S. H.,  Rivulet instabilities,  J. Flujid Mech., 176, 1987.

soon