Looking Behind the Curtain of Coating

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Economies of scale occur when a coated product is manufactured wide, fast and in one pass. Substrates can be manufactured wide and multilayer coating can provided added functionality, but how do you make a coated product faster. The first hurdle is curing (typically the bottleneck of the process). Once you properly size the oven for the application, you need to consider the fluid flow dynamics within the coating system. As the fluid is coated faster and faster, the effects of film split, turbulence and air reek havoc on the coated product and leave a trail of coating defects in the path.

Some coating techniques, however, actually perform better under high speed scenarios. One coating technique that should be considered for high speed applications is curtain coating. Imagine taking a slot die, coating in close proximity, and raising it up in the air to allow the fluid to drop down onto the substrate. This rain shower of liquid can have some advantages, but the advantages can only be realized with higher speeds. Why is that?

The fundamental equation behind the success of a falling curtain of fluid is the dimensionless Weber number-

We = ρQV/σ

We = Weber number

ρ = density

Q = volumetric flow rate

V = impingement velocity

σ = surface tension

The Weber number provides us with the height of the curtain that allows for success. A good starting point is to look for the coating conditions that allow for We > 2. This is considered a stability region for the fluid. As We < 2, the constant flow of fluid breaks up and disintegrates into droplets instead of a sheet. While it is possible to maintain a curtain under many conditions, this gets us started.

Let’s break it down. The Weber number is a ratio of the density, volumetric flow rate and fluid flow rate to surface tension forces. The fluid flow rate is also termed the impingement speed of the fluid – the higher the fluid falls the faster the speed. Line speed and pump work together to develop the coat weight of the product – for a set pump speed (volumetric flow rate), a higher line speed creates a lighter coat weight product. Now, if the fluid is dropped at a high throughput, but the line speed is slow, the coat weight will be high. So if your product requires a light coat weight, you will need to adjust height or flow rate to meet our stability criteria (We > 2). Since density and surface tension are relatively set, volumetric flow rate or height of the curtain are the only variables that can be shifted to land the product in a reasonable coating window.

Now, there are many variables that affect the flow and stability of curtain coating a fluid, but the Weber number stability criteria is a good starting point. The coating window itself is a function of the Reynolds number and the web speed to impingement velocity-

Re = ρQ/μ

Re = Reynolds number

ρ = density

Q = volumetric flow rate

μ = viscosity

U/V

U = web speed

V = impingement velocity

If the U/V ratio is too low, disintegration of the curtain occurs (similar to a low Weber number). At a balance point between Re and U/V, the coating is stable. As U/V increases, we begin to see air be an issue because the line speed overcomes the fluid velocity.

With this handful of variables and simple equations, you can evaluate curtain coating to improve your speed and move into a new realm of coating capability.


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