Unsteady gravity-driven slender rivulets of a power-law fluid

✍ Scribed by Y.M. Yatim; S.K. Wilson; B.R. Duffy

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 651 KB
• Volume: 165
• Category: Article
• ISSN: 0377-0257
• DOI: 10.1016/j.jnnfm.2010.06.017

✦ Synopsis

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle ˛to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < ˛< /2) in the case x < 0 with t < 0, and diverging pendent rivulets (when /2 < ˛< ) in the case x > 0 with t > 0, where x denotes a coordinate measured down the plane and t denotes time. Numerical and asymptotic methods are used to show that for each value of the power-law index N there are two physically realisable solutions, with cross-sectional profiles that are 'single-humped' and 'double-humped', respectively. Each solution predicts that at any time t the rivulet widens or narrows according to |x | (2N+1)/2(N+1) and thickens or thins according to |x | N/(N+1) as it flows down the plane; moreover, at any station x, it widens or narrows according to |t | -N/2(N+1) and thickens or thins according to |t | -N/(N+1) . The length of a truncated rivulet of fixed volume is found to behave according to |t | N/(2N+1) .