Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid
DOI:
https://doi.org/10.14419/ijet.v7i2.15.11208Keywords:
Power-law fluid, Rivulet, Travelling-wave similarity solution, Thin film.Abstract
Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time  and position , the rivulet widens or narrows according to , where  is velocity of a rivulet, and the film thickens or thins according to a free parameter , independent of power-law index . The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.
Â
Â
References
[1] P. C. Smith. A similarity solution for slow viscous flow down an inclined plane. Journal of Fluid Mechanics, 58 (1973) 275-288.
[2] B. R. Duffy, H. K. Moffatt. A similarity solution for viscous source flow on a vertical plane. European Journal of Applied Mathematics, 8 (1997) 37-47.
[3] S. D. R. Wilson, S. L. Burgess. The steady, spreading flow of a rivulet of mud. Journal of Non-Newtonian Fluid Mechanics, 79 (1998) 77-85.
[4] S. K. Wilson, B. R. Duffy, R. Hunt. A slender rivulet of a power-law fluid driven by either gravity or a constant shear stress at the free surface. The Quarterly Journal of Mechanics and Applied Mathematics, 55 (2002) 385-408.
[5] Y. M. Yatim, S. K. Wilson, B. R. Duffy. Unsteady gravity-driven slender rivulets of a power-law fluid. Journal of Non-Newtonian Fluid Mechanics, 165 (2010) 1423-1430.
[6] S. S. Abas, Y. M. Yatim. Travelling-wave similarity solution for gravity-driven rivulet of a Newtonian fluid with strong surface-tension effect. AIP Conference Proceedings, 1870 (2017) 40037-1-40037-7.
Downloads
How to Cite
Received date: April 6, 2018
Accepted date: April 6, 2018
Published date: April 6, 2018