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Simulating Viscoelastic Coating Flows

Newtonian flow simulation using FLOW-3D software
Fig. 1 Case A--Newtonian flow. Color
scale represents pressure

This note is a condensed version of a paper presented by one of Flow Science's developers, Dr. James Brethour, at the 6th European Coating Symposium in Bradford, UK, last month.

Recent releases of FLOW-3D introduced an elastic stress solver that builds upon the methods already incorporated into the code. An extension to the elastic stress model is demonstrated here in an example that predicts the orientation, stretching and relaxation of the solution molecules.

FLOW-3D curtain coating simulation
Fig. 1 Case B--0.05wt.% PEO
solution. Color scale represents
component of elastic stress

Curtain coating is a premetered coating process that is commonly used because gravity provides downward inertia to the coating region which reduces the risk of air entrainment, rather than relying on a vacuum system.

Curtain coating is subject to various defects, one of which is edge defects. At the edge of the curtain, surface tension acts on the sharp curvature present here to retract the curtain in the cross-web direction. This results in a thickening of the applied coating near its edges. In practice, guide wires are commonly employed at these edges to help guide the curtain and minimize the edge defects. However, in the simulations presented here, no guides were considered.

Properties of coating fluids. All use a 20 wt.%
solution of PEG in water as a base

Figure 1 shows the results of these simulations. Case A shows the result for the Newtonian flow, composed of a 20wt.% solution of polyethylene glycol (PEG; molecular weight = 8 x 103 g/mol), while Case B shows the result for a 0.05wt.% polyethylene oxide (PEO; molecular weight = 4 x 106 g/mol) in the 20wt.% PEG solution. In both cases, the capillary number is 1.3. Note that both cases exhibit edge retraction, as surface tension is significant in both cases. However, in the latter case, the edge retraction is the lesser of the two. Physically, this can be explained by the fact that the deformation due to the retraction is resisted somewhat by the elastic stress. Of course, this is only a small part of the story in curtain coating; this elasticity will also serve to destabilize the upstream contact line at higher web speeds.

The results here show a good application for extensions to the elasticity model, which will be available in the next release of FLOW-3D. Continuing work is enhancing the model with more constitutive relations, greater flexibility and more numerical options to reduce computation time.