A Finite Element Method for Free-Surface Flows of Incompressible Fluids in Three Dimensions, Part II: Dynamic Wetting Lines Page: 4 of 43
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Int. J. for Numerical Methods in Fluids
To date, few reserchers have solved three-dimensional free-surface problems
with dynamic wetting lines. This paper extends the free-surface finite element
method described in a companion paper to handle dynamic wetting. A generali-
zation of the technique used in two dimensional modeling to circumvent double-
valued velocities at the wetting line, the so-called kinematic paradox, is presented
for a wetting line in three dimensions. This approach requires the fluid velocity
normal to the contact line to be zero, the fluid velocity tangent to the contact line to
be equal to the tangential component of web velocity, and the fluid velocity into
the web to be zero. In addition, slip is allowed in a narrow strip along the substrate
surface near the dynamic contact line. For realistic wetting-line motion, a contact
angle which varies with wetting speed is required because contact lines in three
dimensions typically advance or recede a different rates depending upon location
and/or have both advancing and receding portions. The theory is applied to capil-
lary rise of static fluid in a corner, the initial motion of a Newtonian droplet down
an inclined plane, and extrusion of a Newtonian fluid from a nozzle onto a moving
substrate. The extrusion results are compared to experimental visualization.
KEYWORDS: three dimensional, free surface, contact lines, wetting lines, simulation, finite ele-
ment method, pseudo-solid mesh motion.
Even with a powerful numerical method of predicting free and moving boundary problems
in three dimensions1, modeling practical problems with dynamic contact lines poses many out-
standing challenges. These contact lines represent the curve in three-dimensional space where
liquid, gas, and solid meet. Wetting problems involve dynamic contact lines in which the liquid is
displacing the gas, or vice versa, along the solid surface. The approaches for treating dynamic
contact lines in two dimensions are not easily extended to three dimensions, both conceptually
Baer et al.
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Baer, T.A.; Cairncross, R.A.; Rao, R.R.; Sackinger, P.A. & Schunk, P.R. A Finite Element Method for Free-Surface Flows of Incompressible Fluids in Three Dimensions, Part II: Dynamic Wetting Lines, article, January 29, 1999; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc684974/m1/4/: accessed April 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.