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Modeling Forward Roll Coating

Printing presses often use a technique referred to as forward roll coating for delivering and applying ink to the printing surface. In this process ink typically flows into a narrow gap between two rotating cylinders. Downstream of the gap, the ink splits into two portions forming coatings the surfaces of the cylinders.

In a well known paper by Coyle, Macosko and Scriven (J.Fluid Mech., (1986), V.171, p.183) an asymptotic analysis is presented for the splitting distance, i.e., the distance from the minimum gap location to the downstream position of the free surface on the centerline between the cylinders. Here we use this prediction as a validation test for FLOW-3D.

The rolls have radii of 2.54cm and a minimum separation of 0.02cm. Their tangential speed in the gap is U=2.0cm/s. A dimensionless flow rate in the gap of 1.3 was specified as an inflow boundary condition. The liquid has a viscosity of μ=0.2poise and surface tension of σ=2.0dyne/cm, resulting in a Capillary number of μU/σ=0.2.  Because of symmetry, only the top half of the flow region was simulated. The complete flow region could easily have been simulated and included rolls with different radii and/or different speeds. The final steady results are shown in the figure above, where only every other velocity vector is displayed to avoid overcrowding. The blue region shows where the horizontal velocity is negative, indicating a pair of counter rotating vortices at the splitting point.

Forward roll coating simulation results with FLOW-3D

The computed splitting distance was 0.50cm versus the asymptotic analysis result of 0.509cm, a very good agreement for a computation that only took 172s of CPU time.