The 2D calculation domain for film flow problems involves one or two free borders, which are subsequently referred to as free surfaces. The finite element mesh will be deformed throughout the calculation according to the kinematic condition on the free surface.
All conservation equations are averaged throughout the third dimension (that is, the film thickness) and thickness-averaged velocity and temperature values are computed. The film thickness becomes a variable of the flow problem, which is governed by the mass conservation equation. Pressure is no longer a variable of the problem and is eliminated in the momentum equations.
Fluid models can be either generalized Newtonian or viscoelastic, isothermal or nonisothermal. Film models can also be defined within the context of a steady, evolution, or transient case. Furthermore, for viscoelastic flows, both single- and multi-mode differential models are available. It is, however, important to note that only viscoelastic models with a constitutive equation written in terms of the extra-stress tensor, as well as the FENE-P and DCPP models, are available for film casting simulations.
For generalized Newtonian fluids, as described in Generalized Newtonian Flow, the viscosity can depend on the temperature and the second invariant of the rate-of-deformation tensor. These dependences obey algebraic relationships identical to those described in Generalized Newtonian Flow. For nonisothermal flow problems, it is important to recall that the temperature is considered to be constant throughout the film thickness, although the heat loss on both sides of the film can be taken into account.
For viscoelastic flows, since film casting is mainly an extensional flow, it is possible for viscoelastic effects to dominate. See Viscoelastic Flows for information on the available constitutive equations.