A finite element method for free surface flows of incompressible fluids inthree dimensions. Part II. Dynamic wetting lines

To date, few researchers have solved three-dimensional free surface problem s with dynamic wetting lines. This paper extends the free surface finite el ement method (FEM) described in a companion paper [Cairncross RA, Schunk PR , Baer TA, Sackinger PA, Rao RR. A finite element method for free surface f lows of incompressible fluid in three dimensions. Part I. Boundary fitted m esh motion. International Journal for Numerical Methods in Fluids 2000; 33: 375-403] to handle dynamic wetting. A generalization 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 l ine in three dimensions. This approach requires the fluid velocity normal t o the contact line to be zero, the fluid velocity tangent to the contact li ne to be equal to the tangential component of web velocity, and the fluid v elocity into the web to be zero. In addition, slip is allowed in a narrow s trip along the substrate surface near the dynamic contact line. For realist ic wetting line motion, a contact angle that varies with wetting speed is r equired because contact lines in three dimensions typically advance or rece de at different rates depending upon location and/or have both advancing an d receding portions. The theory is applied to capillary rise of static flui d in a corner, the initial motion of a Newtonian droplet down an inclined p lane, and extrusion of a Newtonian fluid from a nozzle onto a moving substr ate. The extrusion results are compared with experimental visualization. Co pyright (C) 2000 John Wiley & Sons, Ltd.