Blotching in roll coating

Abstract

After thermoforming, plastic parts are stacked for ship**, and these parts tend to stick together. Called nesting, sheet stock is often first coated with a silicone compound before thermoforming to prevent this. The coating usually consists of a small amount of lubricant dispersed in a majority of carrier fluid, and this fluid must then dry before reaching the sheet winder or else the coating blotches. This coupling of coating and drying to determine when to expect blotching is examined. Roll coating involves a dimensionless group called the elasticity number that governs the thickness of the coating to be dried. The drying section involves the evaporation of the coating carrier fluid, and then diffusion into the dry surrounding atmosphere. When analyzing the drying, a new dimensionless group that governs blotching is discovered, called blotchability. The result of this analysis allows practitioners to determine which operating conditions cause blotching, and how to eliminate it. Roll coating uses a deflecting rubber roll to apply vanishingly thin coatings (≤1 μm), an interesting elastohydrodynamic problem.

Appendix: carrier fluid volatility

When a volatile coating dries, it liberates carrier fluid mass, in the form of a gas at the drying surface. This gas moves away from its liberating coating surface, and thus slightly accelerates drying. The drying analysis presented here

$$ \theta_{\text{f}} = {\frac{{\left( {\phi - 1} \right)^{2} }}{4}} $$

(27)

conservatively neglects this, which yields9

$$ \theta_{\text{f}} = {\frac{{x_{\text{s}} \left( {\phi - 1} \right)^{2} }}{4\varphi \sqrt \pi }} $$

(33)

where φ is given implicitly by

$$ x_{\text{s}} = {\frac{{\sqrt \pi \varphi {\frac{{1 + {\text{erf}}\varphi }}{{{ \exp }\left( { - \varphi^{2} } \right)}}}}}{{1 + \sqrt \pi \varphi {\frac{{1 + {\text{erf}}\varphi }}{{{ \exp }\left( { - \varphi^{2} } \right)}}}}}} $$

(34)

and where

$$ x_{\text{s}} \equiv {\frac{1}{{{\frac{{M_{\text{w}} }}{{M_{\text{A}} }}}\left( {{\frac{1}{{w_{\text{s}} }}} - 1} \right) + 1}}} $$

(35)

the molecular weights M _w and M _A are defined in Table 1. When water is the carrier fluid, θ _f from (27) hardly exceeds θ _f from (33) because x _s ≅ 0 and then (33) reduces to (25). For more volatile carrier fluids, equation (25) can significantly overpredict θ _f.