Journal of Fluid Mechanics

The shape and stability of pinned rotating annular menisci

P. D.  Weidman a1p1, S.  Krumdieck a2 and P.  Rouse a2
a1 School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK
a2 Department of Mechanical Engineering, University of Colarado, Boulder, CO 80309, USA

Article author query
weidman pd   [Google Scholar] 
krumdieck s   [Google Scholar] 
rouse p   [Google Scholar] 


Laboratory measurements on the instability of axisymmetric capillary surfaces pinned to the corners of annular grooves of rectangular section rotating at constant angular velocity Ω have been conducted. In stable configurations the fluid contact lines remain pinned to the corners of the groove with contact angles θ1,2 relative to the inner and outer vertical walls. Using water as the test fluid in narrow grooves of nearly constant width, the critical frequency Ωc for instability generally decreases with increasing overfill volume ΔV and mean groove radius. Numerical integration of the describing equation gives the shape of the rotating meniscus as a function of five independent parameters. In the range of contact angles θ1, 2 < π, a comparison of experimental results with numerically computed meniscus profiles suggests three mechanisms for contact line movement based on the effective static advancing (θA) and receding (θR) contact angles for liquid pinned to a sharp corner. Measurements of critical frequencies over a wide range of overfill volumes in six different grooves are in favourable agreement with composite regime diagrams for the critical static meniscus configuration. An interesting feature of this system is the existence of a range of overfill volumes inaccessible to experiments conducted by fixing the overfill volume on a stationary disk and subsequently elevating the disk rotation until contact line movement is observed. Numerical studies showing the effects of Bond number, groove curvature and contact angle hysteresis are presented.

(Published Online April 26 2006)
(Received August 29 1989)

p1 Permanent address: Department of Mechanical Engineering, University of Colorado, Boulder CO 80309, USA.