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

Research output: Contribution to journalArticle

9 Citations (Scopus)
43 Downloads (Pure)

Abstract

Unsteady gravity-driven flow of a thin slender rivulet of a non-Newtonian power-law fluid on a plane inclined at an angle α to the horizontal is considered. Unsteady similarity solutions are obtained for both converging sessile rivulets (when 0 < α < π/2) in the case x < 0 with t < 0, and diverging pendent rivulets (when π/2 < α < π) 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).
Original languageEnglish
Pages (from-to)1423-1430
Number of pages7
JournalJournal of Non-Newtonian Fluid Mechanics
Volume165
Issue number21-22
DOIs
Publication statusPublished - Nov 2010

Keywords

  • power-law fluid
  • rivulet
  • similarity solution
  • unsteady flow

Fingerprint Dive into the research topics of 'Unsteady gravity-driven slender rivulets of a power-law fluid'. Together they form a unique fingerprint.

  • Cite this