Q. Chen et al., THE BREAKDOWN OF ASYMPTOTIC HYDRODYNAMIC MODELS OF LIQUID SPREADING AT INCREASING CAPILLARY NUMBER, Physics of fluids, 7(11), 1995, pp. 2631-2639
Complex hydrodynamics near the moving contact line control spreading o
f a fluid across a solid surface. In the confined region near the cont
act line, velocity gradients in the fluid are large and viscous forces
control the shape of the fluid/fluid interface. The present model for
liquid spreading describes the viscous effect on the dynamic interfac
e shape to lowest order in capillary number, Ca. Using videomicroscopy
and image analysis techniques, we have examined the shape of liquid/a
ir interfaces very near moving contact lines for Ca greater than or eq
ual to 0.10 where the interfaces are in capillary depression. We find
that the theory correctly describes the data up to Ca=0.10 for distanc
es from 20 to 400 mu m from the contact line. As Ca increases, the mod
el fails to describe the data in a region near the contact line, which
grows as Ca increases. In this expanding region, the model predicts t
oo large a curvature for the interface. We explore the origins of this
breakdown by examining the fundamental assumptions of the model. The
geometry-dependent part of the solution to O(1) in Ca is sufficient ev
en at Ca=0.44. The breakdown of the model arises from the low order of
the geometry-free part of the perturbation solution and/or contributi
ons to the interface shape from the unique hydrodynamics very near the
moving contact line. (C) 1995 American Institute of Physics.