## Conflicting Flow in Coating

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Coating with a self-metered system is a study of flow dynamics where we are fighting viscous forces. Depending on where the math is being applied, one force rises over another in combination with viscosity. Sometimes you need to be more concerned about elastic forces, sometimes gravity, and sometimes pressure. In the world of slot die coating, having a grasp of pressure-induced forces can lead to strong insights of fluid flow and defect resolution.

So what details of pressure forces are important? To answer this question, we need to look at fluid flow at the exit point of the slot die where the fluid is compressed between the wet lip and the substrate. The wet lip is the front face of the slot die downstream. This is considered the last face of the slot die the fluid sees before releasing onto the substrate and traveling into the cure chamber.

If you consider this microscopic image of the slot die exit, we can label the point where the fluid exits the slot die as “A” and the point downstream that the fluid releases from the slot die to flow onto the substrate as “B”. With this convention in mind we can review flow dynamics as explained by pressure and viscosity flow.

For a given flow rate, the fluid can mathematically be described by the following combination of factors-

V = b3/12μ(ΔP) + U*b/2

Where:

V = fluid flow rate

b = slot die lip opening

μ = viscosity

ΔP = pressure difference

U = substrate speed

The first mathematical part of the expression is the pressure-based component. This pressure-based component is Poisseulle flow typically depicted by a rounded flow pattern resisting the flow created by the substrate movement underneath the fluid.

Couette flow, the drag flow depicted by a triangular flow pattern moving in the direction of substrate movement is the counter balance to Poisseulle flow. These two factors battle for dominance to control the fluid flow behavior as liquid exits the slot die.

The key is to balance the Couette and Poiseulle flow factors for a stable meniscus on the upstream lip and flat, even flow as the fluid coats the substrate. As the coating becomes thinner and thinner, the Poiseulle contribution increases and pressure changes have a larger effect.

So, how does all this math help? Understanding the balance of forces helps explain what to shift if a coating defect is present. As an example, if the pressure at position “B” at the fluid release from the slot die is greater than the pressure at position “A” at the slot die exit, a meniscus will properly form, but if the pressure at position “B” becomes too great, then vortices will form in the flow pattern causing potential coating defects and air entrapment.

Coating thickness in self-metered systems is defined by the fluid flow and the web speed. However, if the localized pressure is stronger at one position over another, then the gaps need to be adjusted accordingly. This gap adjustment in the lip opening requires a shim change or a gap adjustment between the slot die and the substrate. But understanding that this is a localized pressure change allows you to tackle the coating issue with pressure instead of physical gap adjustment. Pulling a vacuum on the upstream side of the slot die will improve the situation and allow for more freedom of gap adjustment.

So now you know what is going on inside the fluid as forces battle for control. If you are having coating defects that need physical movement, flow control, or pressure adjustment – you know where to start.