variavel0=<b>Marcio S. Carvalho</b> - msc@mec.puc-rio.br PUC-Rio
<b>Gladys Zevallos</b> - gzevallo@mec.puc-rio.br Pontificia Universidade Catolica do Rio de Janeiro
<b>Matteo Pasqualli</b> - mp@rice.edu Rice University
<b>Abstract.</b> Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter and apply a liquid layer to a substrate.  Except at low speeds, the film-splitting flow that occurs in forward roll coating is three-dimensional and results in more or less regular stripes in the machine direction.  This instability can limit the speed of the process if a smooth film is required as a final product.  For Newtonian liquids the stability of the film-split flow is determined by the competition of capillary forces and viscous forces: a critical value of the ratio between these two forces, i.e. the Capillary Number, marks the onset of meniscus nonuniformity.  Non-Newtonian behavior can drastically change the nature of the three-dimensional flow.  At extreme conditions the ribs may grow and form filaments that eventually break in such a way as to form small drops, a phenomenon known as spatter or misting.  Misting is a serious problem in many industrial application and it limits the speed of many processes.  However, the mechanisms by which rheological properties of the liquid act are still a matter of research. In this work, the steady two dimensional film split flow of viscoelastic liquids is analyzed by solving the conservation equations with a differential constitutive model, e.g. Oldroyld-B equation, to describe the mechanical behavior  of the flowing liquid.  The presence of the free surface and the differential constitutive model makes this problem extremely complex.  The equations are solved by the Finite Element Method and Newton`s method.
<b>Keywords.</b> roll coating, free surface flow, Oldroyld-B model, finite element method.