Film-splitting flows in forward roll coating

Coyle, Dennis J.; Macosko, Chris; Scriven, L. E.

doi:10.1017/s0022112086001416

Cited by 122 publications

(154 citation statements)

References 37 publications

(27 reference statements)

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“…Roll pairs, for the case when both are rigid and separated by a small distance, or 'positive gap', have been studied exhaustively, both experimentally (Ho & Holland 1978;Benkreira, Edwards &W ilkinson 1981;Malone 1992;Decre, Gailly & Buchlin 1995;Gaskell, Innes & Savage 1998) and theoretically (Greener & Middleman 1975;Ruschak 1982Ruschak , 1985Coyle, Macosko & Scriven 1986, 1990a, b;G a s k e l let al 1995; Gaskell, Savage & Thompson 1998) and there remains little that is not known about the fluid mechanics that underpins them.…”

Section: Compliant Layermentioning

confidence: 99%

A model for deformable roll coating with negative gaps and incompressible compliant layers

et al. 2003

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A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or ‘negative gap’ regime. Predictions are presented for coated film thickness, inter-roll thickness, meniscus location, pressure and layer deformation as the control parameters – load (gap), elasticity, layer thickness and capillary number, $\hbox{\it Ca}$ – are varied. There are four main results: Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio $\nu\rightarrow 0.5$. In particular, they fail to predict the swelling of the layer at the edge of the contact region which increases as $\nu\rightarrow 0.5$; they also fail to locate accurately the position of the meniscus, $X_M$, and to identify the presence, close to the meniscus, of a ‘nib’ (constriction in gap thickness) and associated magnification of the sub-ambient pressure loop.Scaling arguments suggest that layer thickness and elasticity may have similar effects on the field variables. It is shown that for positive gaps this is true, whereas for negative gaps they have similar effects on the pressure profile and flow rate yet quite different effects on layer swelling (deformation at the edge of the contact region) and different effects on $X_M$.For negative gaps and $\hbox{\it Ca}\,{\sim}\,O(1)$, the effect of varying either viscosity or speed and hence $\hbox{\it Ca}$ is to significantly alter both the coating thickness and $X_M$. This is contrary to the case of fixed-gap rigid roll coating.Comparison between theoretical predictions and experimental data shows quantitive agreement in the case of $X_M$ and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.

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Section: Compliant Layermentioning

confidence: 99%

A model for deformable roll coating with negative gaps and incompressible compliant layers

et al. 2003

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“…The gap between the rolls is typically much smaller than their radii (i.e. δ ≡ B 0 /2R ≪ 1) and the appropriate dimensionless scheme is well-established [6]:…”

Section: Lubrication Theory Modelmentioning

confidence: 99%

“…This can be achieved in a simple way by approximating the menisci as arcs of circles whose radii are equal to half the local gap between the rolls. Since the semi-gap is approximated by a parabola [6], this gives…”

Section: Lubrication Theory Modelmentioning

confidence: 99%

“…The domain was tessellated into triangular 'V6/P3' elements, and the free surfaces were parametrized by the 'spine method' [12]. The construction of the mesh followed that used by Coyle et al [6] in forward roll coating -see Wilson [16] for more specific details. The residual equations were solved by Newton iteration in which the Jacobian was inverted using the frontal method [11], and the iterative process was terminated when the largest increment to the solution was less than 10 −6 .…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…In fact there is usually a region of recirculating flow and the first stagnation point lies further upstream [6]. The FE solutions were also used to investigate the flow structure in the film-merge region close to the upstream free surface, and showed that recirculations grew as flow rate increased, until the flow became unsteady and three-dimensional when the flux passed a critical value.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Flow in a double-film-fed fluid bead between contra-rotating rolls Part 1: equilibrium flow structure

Wilson¹,

Gaskell²,

Savage³

2001

Eur. J. Appl. Math

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In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis. The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, ζ, of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of ζ < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when ζ = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general (ζ < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films.

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An Algorithm for Simulation of Steady Free Surface Flows

Ramanan¹,

Engelman²

1996

Int. J. Numer. Meth. Fluids

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An algorithm to simulate steady, viscous free surface flows is presented in this paper. A Picard‐type approach wherein the flow and free surface updates are performed alternately is utilized to iterate for a solution. The procedure is intended for large‐scale two‐ or three‐dimensional problems. A surface‐intrinsic co‐ordinate system which facilities representation of general free surface shapes is used. Using a Galerkin finite element method (GFEM), two free surface updates, namely kinematic and normal stress updates are formulated. It is shown that the effects of surface tension, surface tension gradients and imposition of contact angles can be simulated elegantly within the framework of the GFEM. A novel feature of the updates is that the deformations are sought in a direction normal to the current iterate free surface shape, with the result that the method is ideally suited when used in conjunction with an automatic mesh generator. With the normal stress update a volume constraint can also be imposed. A segregated method is utilized to solve iteratively one degree of freedom at a time for the solution of the flow variables. As a result, the memory and disc space requirements are minimal. Sample problems in extrusion, coating and crystal growth are presented to clearly illustrate the convergence behaviour and accuracy of the algorithm.

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Film-splitting flows in forward roll coating

Cited by 122 publications

References 37 publications

A model for deformable roll coating with negative gaps and incompressible compliant layers

A model for deformable roll coating with negative gaps and incompressible compliant layers

Flow in a double-film-fed fluid bead between contra-rotating rolls Part 1: equilibrium flow structure

An Algorithm for Simulation of Steady Free Surface Flows

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