Roll coating is distinguished by the use of one or more gaps between
to meter a continuous liquid layer and to apply it to a continuous
Of the two rolls that make a forward or reverse roll coating gap,
one is often covered
by a layer of more-or-less deformable elastomer. Liquid carried into the converging
side of the nip can develop high enough pressure to deform the resilient cover,
which changes the nip profile and thus alters the velocity and pressure field. This
elastohydrodynamic coupled action is not yet well understood. Theoretical modelling
has to take into account the viscous flow, the roll deformation and the free-surface
effects in order to predict the flow behaviour.
In this work the flow between a rigid and a deformable counter-rotating roll that
shares the same angular speed is described by the lubrication approximation together
with a viscocapillary model, based in the film-flow equation, for the
The deformation of the elastomer layer is modelled by Hookean springs oriented
radially, which constitute a one-dimensional model. The stability of the system to
transverse perturbation is analysed by examining the time-dependent response to
infinitesimal disturbances in order to identify those that grow fastest.
The corresponding system of equations is solved by Newton's method with
first-order continuation. The relationship between coating thickness,
operational parameters (loading force, gap setting, roll velocities, etc.),
liquid properties and the properties
of the cover is reported, as well as the critical capillary number for
onset of ribbing
and wavelengths of the ribbing pattern predicted by the mathematical model. The
results indicate how a deformable cover may be used in order to delay the onset of
ribbing for a desired coating thickness.
In order to validate the theoretical predictions of the
model, the symmetric film-split flows between a pair of rigid rolls and a
of a deformable roll and a rigid one were also analysed experimentally.