In the slot-coater shown below, a coating liquid is extruded through a die and onto a solid sheet, the
“web,” moving with velocity U in the x-direction.
The pressure where the slot meets the web is P
the gap between the web and the die is h.
There is a forward-flow region of length L
and also a liquid-
filled region of length L
in which the tendency for backflow is balanced by the movement of the web.
The flow is fully developed, steady and unidirectional in most of the slot, and gravitational effects are
The coating thickness far from the coater is h
, and any evaporation or cooling that takes
place has a negligible effect on the coating density.
It may be assumed that P
, U, h and L
Derive an expression for the velocity profile v
(y) in the forward flow region.