Capillary impregnation in a flexible slit: a finite element formulation

Dynamic wetting is an important phenomenon in many applications involving motion of liquid/vapor free surface on a solid surface. Capillary impregnation in a slit is one such important application. Modeling of this application is more challenging in a flexible slit than rigid slit since the solid deformation needs to be accounted in addition to tracking the contact line. Previously, a finite element model has been formulated for predicting dynamic wetting on flexible solids with upstream end of slot coater [S. Madasu, R.A. Cairncross, Effect of substrate flexibility on dynamic wetting: A finite element model, Comput. Methods Appl. Mech. Eng. 192 (2003) 2671–2702] as the prototype. This paper presents an application of that formulation in a moving reference frame for predicting the location of dynamic contact line for capillary flow inside a flexible slit. Arbitrary Lagrangian Eulerian (ALE) mesh motion is used to track the location of the contact line. Two singularities arise at the contact line: (i) in the solid domain due to liquid/vapor surface tension force acting as a line force and (ii) in the liquid domain due to the double-valued velocity. “Navier slip condition” and “Distributed line force condition” are used to relieve the singularities in the solid and liquid domains, respectively. The variation of dynamic contact line position with respect to various parameters such as pressure, contact angle, capillary number and elasticity number are presented for the finite element model and compared with an analytical model. The trends for the variation of length of penetration of liquid for rigid solid with inlet pressure, contact angle and capillary number compare qualitatively with the Washburn’s equation (1).