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Reverse roll-coating flow: a computational investigation towards high-speed defect free coating

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Abstract

A finite element Taylor–Galerkin pressure-correction algorithm is employed to simulate a high-speed defect-free roll-coating flow, which substantiates a coating process with a free meniscus surface. Findings are applicable across a wide range of coating sectors in optimisation of coating performance, which targets adaptive and intelligent process control. Industrially, there is a major drive towards using new material products and raising coating line-speeds, to address increased efficiency and productivity. This study has sought to attack these issues by developing an effective predictive toolset for high-speed defect-free coatings. Here, time-stepping/finite element methods are deployed to model this free-surface problem that involves the transfer of a coating fluid from a roller to a substrate (of prescribed wet-film thickness). This procedure is used in conjunction with a set of constitutive equations capable of describing the relevant fluid-film rheology in appropriate detail. Quantities of pressure, lift and drag have been calculated streamwise across the flow domain, and streamline patterns reveal a large recirculating vortex around the meniscus region. Such pressure distributions across the domain display a positive peak which decreases as nip-gap size increases. Further analysis has been conducted, mimicking the presence of a wetting line, whilst varying boundary conditions at the nip. Observation has shown that such inclusion would serve as a relief mechanism to the positive peak pressures generated around the nip zone. Here, through an elasto-hydrodynamic formulation, the elastic deformation of a rubber roll cover (elastomer) has also been introduced, which offers fresh insight into the process with respect to nip-flow behaviour, and allows for the analysis of both positive and negative nip-gaps.

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Notes

  1. Equivalent dimensionally to 2×105 s−1.

  2. Possibly caused by fluctuating holding tension levels.

Abbreviations

Ca :

Capillary number

D :

Rate of deformation tensor

D roller :

Drag on the feed-roller

h F :

Film thickness

K :

Consistency index

L foil :

Lift on the foil-substrate

ℓ :

Characteristic length

m :

Power-law index

n :

Number of time steps

p :

Hydrodynamic pressure

Q :

Flow rate

Re :

Reynolds number

U F :

Foil speed

U R :

Roller speed

t :

Time

U :

Characteristic velocity

u :

Fluid velocity

Δt :

Time step

ρ :

Fluid density

μ :

Fluid viscosity

μ 0 :

Viscosity at zero shear rate

μ ∞ :

Viscosity at infinite shear rate

\(\dot{\gamma}\) :

Shear rate

β slip :

Slip coefficient

β curv. :

Free surface mean curvature

δ :

Slip length

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Acknowledgements

The authors gratefully acknowledge financial support for the present work from EPSRC/CASE studentship and Tata-Steel UK.

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Authors and Affiliations

  1. Institute of Non-Newtonian Fluid Mechanics, College of Engineering, Swansea University, Swansea, SA28PP, UK

    F. Belblidia, H. R. Tamaddon-Jahromi, S. O. S. Echendu & M. F. Webster

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  1. F. Belblidia
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  2. H. R. Tamaddon-Jahromi
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  3. S. O. S. Echendu
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  4. M. F. Webster
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Correspondence to M. F. Webster.

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Belblidia, F., Tamaddon-Jahromi, H.R., Echendu, S.O.S. et al. Reverse roll-coating flow: a computational investigation towards high-speed defect free coating. Mech Time-Depend Mater 17, 557–579 (2013). https://doi.org/10.1007/s11043-012-9204-y

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