LIQUID FILM COATING

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LIQUID FILM COATING Scientific principles and their technological implications

Edited by

Stephan F. Kistler Imation Corporation Oakdale Minnesota USA

and

Peter M. Schweizer ILFORD AG Fribourg Switzerland

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

First edition 1997

© 1997 Springer Science+Business Media Dordrecht Originally published by Chapman & Hall in 1997 Typeset in 10/12pt Times by AFS Image Setters Ltd, Glasgow

ISBN 978-94-010-6246-6 ISBN 978-94-011-5342-3 (eBook) DOI 10.1007/978-94-011-5342-3

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the U K Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the U K , or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the U K . Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page.

The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.

A catalogue record for this book is available from the British Library

Library of Congress Catalog Card Number: 96-86101

® Printed on permanent acid-free text paper, manufactured in accordance with ANSI/NISO Z39.48-1992 (Permanence of Paper).

CONTENTS

Colour plates appear between pages 228 and 229

List of contributors

Notation

Introduction

1. Coating science and technology: an overviewStephan F. Kistler and Peter M. Schweizer

Part One: Physics and material interactions of coating processes

2. Capillary hydrodynamics and interfacial phenomenaSteven J. Weinstein and Harvey J. Palmer

3. Wetting: static and dynamic contact linesTerence D. Blake and Kenneth J. Ruschak

4. Surfactants: static and dynamic surface tensionYves-M. Tricot

5. Coating rheology: component influence on the rheological response andperformance of water-borne coatings in roll applicationsJ. Edward Glass and Robert K. Prud'homme

6. The fate of thin liquid films after coatingHaroon S. Kheshgi

Part Two: Methods of investigating coating processes

7. Experimental methodsPeter M. Schweizer

8. Asymptotic methods for the mathematical analysis of coating flowsMarc K. Smith

9. Advances in computational methods for free-surface flowsKostas N. Christodoulou, Stephan F. Kistler and P. Randall Schunk

vii

ix

1

3

17

19

63

99

137

183

207

209

251

297

vi Contents

Part Three: Theory and practice of coating processes

10. Analysis and design of internal coating die cavitiesRobert B. Secor

Chapter II: Premetered coating processes

11a Slot coatingFranz Durst and Hans-Giinter Wagner

11b Slide coatingJules Hens and Willy Van Abbenyen

11c Curtain coatingKimiaki Miyamoto and Yoshinobu Katagiri

lId Surfactant effects in coating processesP. Randall Schunk and L. E. Scriven

Chapter 12: Self-metered coating processes

12a Knife and roll coatingDennis J. Coyle

12b Meniscus roll coatingPhilip H. Gaskell and Michael D. Savage

12c Elastohydrodynamic coating systemsFerdinand R. Pranckh and Dennis J. Coyle

12d High-speed blade coatingCyrus K. Aidun and Nick G. Triantafillopoulos

13. Free-meniscus coating processesP. Randall Schunk, Alan J. Hurd and C. Jeffrey Brinker

14. Spin coatingRonald G. Larson and Timothy J. Rehg

15. Control and optimization of coating processesPeter M. Schweizer

Index

367

369

399

401

427

463

495

537

539

573

599

637

673

709

735

769

CONTRIBUTORS

CYRUS K. AIDUNGeorgia Institute of Technology,Institute of Paper Science and Technology,Atlanta, Georgia, USA.

TERENCE D. BLAKEKodak Limited,Research Division,Harrow, UK.

C. JEFFREY BRINKERSandia National Laboratories,Ceramics Synthesis and Inorganic ChemistryDepartment,Albuquerque, New Mexico, USA.

KOSTAS N. CHRISTODOULOUE.!. Du Pont De Nemours & Co.,Scientific Computing Division,Wilmington, Delaware, USA.

DENNIS J. COYLEGeneral Electric Co.,Corporate R&D,Niskayuna, New York, USA.

FRANZ DURSTFriedrich-Alexander-UniversiHit,Lehrstuhl fUr Stromungsmechanik,Erlangen, Germany.

PHILIP H. GASKELLThe University of Leeds,Department of Mechanical Engineering,Leeds, UK.

J. EDWARD GLASSNorth Dakota State University,Polymers and Coatings Department,Fargo, North Dakota, USA.

JULES HENSAgfa-Gevaert N.V.,Research Laboratories,Mortsel, Belgium(retired).

ALAN 1. HURDSandia National Laboratories,Ceramics Processing Science Department,Albuquerque, New Mexico, USA.

YOSHINOBU KATAGIRIFuji Photo Film Co., Ltd.,Production Engineering & DevelopmentDivision,Minami-ashigara-shi, Kanagawa-ken, Japan.

HAROON S. KHESHGIExxon Research and Engineering Company,Corporate Research,Annandale, New Jersey, USA.

STEPHAN F. KISTLER3M Company,Data Storage Products Division,St. Paul, Minnesota, USA.(Current affiliation: Imation Corp.,Oakdale, Minnesota, USA.)

RONALD G. LARSONLucent Technologies, Bell Laboratories,Murray Hill, New Jersey, USA.(Current affiliation: University of Michigan,Department of Chemical Engineering,Ann Arbor, Michigan, USA.)

Vlll Contributors

KIMIAKI MIYAMOTOFuji Photo Film Co., Ltd.,Production Engineering&Development Division,Minami-ashigara-shi, Kanagawa-ken, Japan.

HARVEY J. PALMERUniversity of Rochester,Department of Chemical Engineering,Rochester, New York, USA.

FERDINAND R. PRANCKHAvery Dennison,Corporate Process Technology,Pasadena, California, USA.(Current affiliation: HPM Corp.,Mount Gilead, Ohio, USA.)

ROBERT K. PRUD'HOMMEPrinceton University,Department of Chemical Engineering,Princeton, New Jersey, USA.

TIMOTHY J. REHGAllied Signal Inc.,Aerospace Equipment Systems,Torrance, California, USA.

KENNETH J. RUSCHAKEastman Kodak Company,Emulsion Coating Technologies,Rochester, New York, USA.

MICHAEL D. SAVAGEThe University of Leeds,School of Mathematics,Leeds, UK.

P. RANDALL SCHUNKSandia National Laboratories,Department of Computational Fluid Dynamics,Albuquerque, New Mexico, USA.

PETER M. SCHWEIZERILFORD AG,Engineering Department,Fribourg, Switzerland.

L. E. (SKIP) SCRIVENUniversity of Minnesota,Department of Chemical Engineering andMaterials Science,Minneapolis, Minnesota, USA.

ROBERT B. SECOR3M Company,Engineering Systems and TechnologyLaboratory,

S1. Paul, Minnesota, USA.

MARC K. SMITHGeorgia Institute of Technology,The George W. WoodrutfSchool of MechanicalEngineering,Atlanta, Georgia, USA.

NICK G. TRIANTAFILLOPOULOSGenCorp Polymer Products,Latex Laboratories,Akron, Ohio, USA.

YVES-M. TRICOTILFORD AG,R&D Department,Fribourg, Switzerland.

WILLY VAN ABBENYENAgfa-Gevaert N.V.,Research Laboratories,Mortsel, Belgium.

HANS-GUNTER WAGNERBASF AG,Ludwigshafen, Germany.

STEVEN J. WEINSTEINEastman Kodak Company,Emulsion Coating Technologies,Rochester, New York, USA.

NOTATION

In each chapter, all the symbols are defined E Young's modulus [N/m2 J orin the text where they first appear. The dilational surface elasticity modulusfollowing list defines the symbols most [N/m]commonly used throughout the book. The El elasticity number [El;: IlUL2/D =list is by no means complete, and a particular 12(1 - V

2 )IlUL2/{Ec5 3}]

symbol may have more than one meaning, Es surface elasticity numberdepending on its local definition. Also, given [Es == 9lTr*/IlU]the large number of authors and the wide F force [NJ; may also be used as arange of subject matters covered, some general-purpose functioninconsistencies were nearly impossible to f focal length [m]avoid. As a general rule, upper-case letters f activity coefficient [ - Jdenote dimensional variables, and lower- 9 gravitational acceleration ofcase letters are used for dimensionless [g = 9.81 m/s2 Jquantities; dimensionless groups are given G Gibbs free energy [JJ or shearby two-letter symbols, the first one being modulus [N/m2 Jupper case. Apart from a few well-marked G' loss modulus [N/m2 Jexceptions, SI units are used throughout the G" elastic modulus [N/m2 Jbook. h dimensionless film thickness

[h == H/LJA surface area [m2 J or Hamacker hoo dimensionless final wet thickness of

constant [J] coated film [h oo == Hoo/LJa Langmuir constant [mol/cm3 ] H film thickness or height [mJBo Bond number [Bo ;: pgL2/a] H oo final wet thickness ofcoated film [mJC concentration [mol/cm3J or HG coating gap [m]

capacitance [A s/VJ Ho reference thickness (e.g., film thicknessCj concentration ofspecies i [mol/cm3J down an inclined slide, half gap inCo bulk concentration [mol/cm3 J roll coating, etc.) [mJCs sub-surface concentration [mol/cm3 ] Jf mean curvature of surface [m - 1JC* reference concentration [mol/cm3J 10 incident radiant energy [JJCi dimensionless concentration ofspecies It transient radiant energy [JJ

i [c i ;: CJC*J J JacobianCa capillary number [Ca == IlU/aJ J Jacobian matrixCaAE critical capillary number at onset of L characteristic, macroscopic length

air entrainment [CaAE == IlUAE/aJ scale [mJD diffusion coefficient [m2/sJ or bending Ld length of boundary layer [mJ

stiffness [D == Ec5 3/{12(1 - v2 )}] La capillary length [La == Ja/pgJ~j binary diffusion coefficient of species M change ofmomentum per unit width

i [m2/sJ [kg/s2 J

x Notation

M mass matrix V(t) volume of fluid body [m3 ]n power law index, or index ofrefraction ~ surface velocity [m/s]n unit normal to a surface V* volumetric flow rate [m3/s]p dimensionless pressure [p := PL/p'u] W coating width in cross-web directionlip dimensionless pressure difference (e.g., em]

bead vacuum) [lip:= liPL/p'u] WA work of adhesion [J/m2]P pressure [~/m2] We Weber number [We := pU2L/a]liP pressure difference (e.g., bead vacuum) X coordinate in main flow direction [m]

[~/m2] y coordinate normal to film flow em]PA ambient pressure [~/m2] Z transverse (cross-web) coordinate em]Pv sub-ambient pressure underneath x, y, z dimensionless coordinates [X/L, Y/L,

coating bead [~/m2] Z/L]Po liquid property number

[Po:= a(p/j.l4g)1 /3]q dimensionless flow rate per unit

Greek letterscoating width [q:= Q/(UL)]Q volumetric flow rate per unit coating (X eigenvalue, impingement angle or

width [m2/s] application angleR residual f3 angle of inclination (measured fromR residual vector horizontal)R radius em] '}' angle of solid corner (e.g., at staticRh hydraulic radius em] separation line)Rm mean radius of curvature em] Y shear rate [S-I]91 universal gas constant Yo reference shear rate [s - 1]

[91 = 8.31JK- 1mol- 1] r surface excess concentrationRe Reynolds number [Re:= pUL/j.l] (adsorption density) [moljm2]S arc length [m] or spreading coefficient r i surface concentration (adsorption

[m~/m] density) of species i [moljm2]s dimensionless arc length [s:= S/L] ro equilibrium adsorption densitySCi Schmidt number for species i [mol/m2]

[SCi := j.l/p~J r* reference surface concentrationSCs surface Schmidt number [mol/m2]

[Scs := j.l/p~s] roo maximum surface excessSt Stokes number CSt = pgL2/j.lU] concentration (adsorption density)t time or surface age [s] [moljm2]t unit tangent to a surface () thickness of substrate, blade orT absolute temperature [K] boundary layer em]T total stress tensor B small parameteru, v dimensionless velocity components f. extension rate [s - 1]

[-] Bo dielectric constant of vacuumU coating/web speed [m/s] [A s/(Vm)]UAE critical coating speed at onset of air Bs dielectric constant of material

entrainment [m/s] [As/(Vm)]V alternative characteristic velocity (e.g., 11 non-~ewtonian viscosity CPa s]

impingement velocity in curtain 110 non-~ewtonianviscosity at referencecoating, metering roll velocity in shear rate CPa s]reverse roll coating, etc.) [m/s] K curvature of curve [m - 1]

Notation xi

K dimensionless curvature of curve °E Young's equilibrium contact angle[K = KL] OR recently receded/receding static

Km dimensionless mean curvature of contact anglesurface [Km = YfL] 00 apparent static contact angle

A. wavelength Em] or dimensionless (dynamic value extrapolated to zeroflow rate in roll coating [ - ] speed)

A." viscosity ratio [A." == 1l2/1l1] Ow local contact angle imposed asA.p density ratio [Ap == P2/P1] mathematical boundary conditionIl Newtonian viscosity [Pas] (J surface tension [N/m]Ils surface dilational viscosity [N s/m] (Jeq equilibrium surface tension [N/m]v Poisson's ratio [ - ] or frequency (Js solvent surface tension [N/m]

[S-l] (J12 interfacial tension between two liquids1t surface pressure [J/m2 ] [N/m]II disjoining pressure [N/m2 ] (JT tension in substrate or bladeP density [kg/m3 ] [N/m]<pi finite-element basis function • viscous stress [N/m2 ]t/Ji finite-element basis function ·w wall shear stress [N/m2 ]

°contact angle ~, , isoparametric coordinates

°A recently advanced/advancing static n frequency [S-l]contact angle OJ dimensionless frequency [OJ == nL/U]

00 apparent dynamic contact angle