Fundamentals of Slot Coating Process

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1 Fundamentals of Slot Coating Process Prof. Marcio Carvalho

2 Introduction Coating process is the main manufacturing step for many different (old) products Adhesive tapes Magnetic tapes and disks Paper Needs: Higher yields and faster production speed; Process improvement and optimization.

3 Coating process is the main manufacturing step for many different (new) products Flexible and transparent electronics Thin / flexible displays: Plasma, LC, OLE, Needs: Uniformity requirements are extremely tight; May need 3 features; Process optimization to minimize film thickness variation.

007) Needs: Complex internal microstructure of each layer;

4 and is the most promising approach to practical fabrication of nanoparticle structures ( Fujita & Yamaguchi, 006) (Prevo and Velev, 007) Needs: Complex internal microstructure of each layer; Industrial production speeds (prototype speeds are microns/sec) Process development.

5 FUNCTIONAL COATINGS AN FILMS Coatings and films produced by depositing a liquid layer and subsequently solidifying it are vital ingredients of many different kind of products. The interior of many coatings and films has to have particular microstructure or nanostructure in order to function as intended, whether optically, photochemically, electronically or mechanically.

6 Fundamental understanding of all steps of the product development and manufacturing is crucial for the product & process optimization SOLUTION FORMULATION COATING PROCESS CONITIONS MICROSTRUCTURE OF COATE LAYER FINAL PROUCT PERFORMANCE

7 Unit Operations of a typical coating line Liquid wets the substrate and forms a thin uniform film; In most cases, the film should be thin and uniform; Limitations on how fast this process can be run.

8 evelopment of Coating Technology EVELOPMENTS WERE RESTRICTE TO EACH INUSTRY SEGMENT FIRST PART OF 0 TH CENTURY, COATING TECHNOLOGY WAS AN ART COATING IS A MULTI-ISCIPLINARY SUBJECT WETTING, SPREAING; AHESION; FLUI MECHANICS AN RHEOLOGY; CHEMISTRY, INTERFACIAL SCIENCE; FROM 1940 S, MATHEMATICAL MOELING AN CAREFUL EXPERIMENTS (NOT ONLY PILOT TRIALS) STARTE TO BE USE TO EVELOP AN IMPROVE COATING PROCESSES COMPETITIVE PRESSURE RIVES THE TECHNOLOGY, IMPORTANT TO ANALYZE THE PHYSICAL MECHANISMS THAT ETERMINES THE SUCCESS OR FAILURE OF THE PROCESS

9 Technological Challenges in the Coating Industry Thinner and more uniform wet coating layer; Reduction of emission of organic solvents more concentrated solutions; New coating liquid formulations and more complex product structure; iscrete and non-continuous coating; Increase in line speed and yields; Adapting existing coating lines for new products;

10 Coating Fundamentals Research Move from not only Know-how (process developement) to also Know-why (process understanding) Need fundamental understanding of the basics mechanisms involved in all phases of the process: liquid preparation, coating, and solidification. Theory Experiments Numerics Need specially developed experimental and numerical tools to be able to study in detail all the mechanisms involved.

11 Flow and microstructure development visualization Slot coating visualization: analysis of bead breakup mechanisms Romero and Carvalho (004) Micro structure development uring drying Cardinal and Francis, AIChE J (011)

12 Computer-aided theory for flow prediction Prediction of failure mechanisms and coating window Tensioned Web coating Roll coating Slot coating Curtain coating

13 Slot Coating Process Fundamentals SLOT COATING IS USE IN THE MANUFACTURING PROCESS OF MANY IFFERENT PROUCTS PRE-METERE METHO: THICKNESS IS SET BY FLOW RATE FLOW UNIFORMITY IN THE COATING BEA IS STRONGLY AFFECTE BY OPERATING PARAMETERS

14 FUNAMENTAL ASPECTS OF SLOT COATING OPERATING CONITIONS GAP FLOW RATE (OR FILM THICKNESS) WEB SPEE IE CONFIGURATION (GEOMETRY) LIQUI PROPERTIES SUCH THAT, FLOW IS TWO-IMENSIONAL STEAY STATE STABLE TO SMALL ISTURBANCES

15 FORCES ARE THE KEY TO UNERSTAN FLOW CONITIONS Example of Flow inside a slot coating bead TURNING FLOW (- FLOW) ALMOST RECTILILNEAR FLOW (RAG + PRESSURE GRAIENT) PRESSURE, VISCOUS, SURFACE TENSION AN INERTIAL FORCES MUST BALANCE TO PERMIT STEAY, - FLOW IF FORCES ARE NOT IN BALANCE, COATING BEA WILL BREAK INTO A 3- FLOW (RIVULETS, RIBBING, ) OR TRANSIENT FLOW CONCEPT OF COATING WINOW

16 THE COATING WINOW IS BORERE BY EFECTS UPSTREAM PRESSURE TOO LOW LIQUI INVAES VACUUM CHAMBER PREMETERE ACTION IS LOST MINIMUM WET THICKNESS THAT CAN BE COATE AT GIVEN SUBSTRATE SPEE Ca V NOT ENOUGH VACUUM UPSTREAM MENISCUS INVAES COATING BEA

17 LOW-FLOW LIMIT: MINIMUM COATING THICKNESS AT A GIVEN SUBSTRATE SPEE ; MAXIMUM SUBSTRATE SPEE AT A GIVEN COATING THICKNESS. Low-flow limit

18 RIBBING RIVULETS

19 COATING WINOW IN PLANE OF VACUUM VS THICKNESS Vac COATING WINOW IN PLANE OF WEB SPEE VS THICKNESS Vac? V H 0 t V H 0 t H 0 t THE FASTER THE WEB SPEE, THE LARGER IS THE MINIMUM WET THICKNESS

20 VISUALIZING THE IFFERENT MECHANISMS OF BEA BREAKUP Romero, Scriven and Carvalho (JNNFM, 004) COATING BEA REGION - FRONTAL VIEW

21 GLASS ROLL SIE PLATE FIBEROPTICS 100m SLOT IE MIRROR CAMERA VACUUM BOX

22 ROLL MOTION FLOW VIEWE THROUGH GLASS ROLL ATMOSPHERIC PRESSURE LOWER PRESSURE VACUUM

23 INVASION OF THE UPSTREAM MENISCUS INVASION OF THE OWNSTREAM MENISCUS

24 (c) EFINITIONS OF OPERATING LIMITS IN SLOT COATING PROCESS

25 LUBRICATION APPROXIMATION MOEL Rectilinear Flow Q P C H s P 1 P 0 H U P U P E H P t = Q / V FLOW IN FEE SLOT Q H 3 s 1 P C P L S E FLOW UPSTREAM Q U 0 3 HU PU P 1 L U E VH U 0 PU P0 P E

26 VISCOUS FLOW IN SLOT COATING CONT. FLOW OWNSTREAM Q Vt t 3 H P 1 H E P L 3 H 1V VH P E P L P E L H P P 1 t = Q / V Couette Poiseuille H IF t P P (for L 0) E H IF t P P P (for L 0) E 1 IF P 1 P 0 P P U amb P E P P 0 P P 1 amb VACUUM IS NEEE, OTHERWISE FLOW BREAKS INTO RIVULETS

27 IMPROVING BEA STABILITY BY VACUUM APPLICATION (BEGUIN, 1954, US PATENT,681,94)

28 THINNER COATING THICKNESS FLOW OWNSTREAM CONT. FLOW IS A COMBINATION OF RAG (COUETTE) AN PRESSURE RIVEN (POISEUILLE) THE THINNER THE COATING THICKNESS, THE STRONGER THE POISEUILLE CONTRIBUTION + = IF t H 3 Couette Poiseuille RECIRCULATION APPEARS UNER OWNSTREAM IE LIP + = Couette Poiseuille

29 RELATION BETWEEN VACUUM AN BEA LENGTH Pvac Pamb L U 1 VL H 6 VL Vac Pamb Pvac t 3 3 H HU THE GREATER THE VACUUM, THE GREATER THE UPSTREAM BEA LENGTH IN THE LIMIT OF NO UPSTREAM COATING BEA MINIMUM VACUUM NEEE FOR GIVEN COATING THICKNESS t Vac min P amb P vac 1VL 3 H THIS REGIME IS UNSTABLE IMPOSSIBLE TO MAINTAIN AS STEAY, TWO-IMENSIONAL FLOW - FLOW BREAKS INTO PARALLEL RIVULETS ON THE WEB H t U L H

THE GREATER THE UPSTREAM BEA LENGTH, THE GREATER THE STABILITY AGAINST RIVULET FLOW, AN THE GREATER THE ABILITY OF THE COATING BEA TO ACCOMMOATE FLUCTUATIONS. CONCERNS WITH RECIRCULATION, IF PRESENT.

30 THE GREATER THE UPSTREAM BEA LENGTH, THE GREATER THE STABILITY AGAINST RIVULET FLOW, AN THE GREATER THE ABILITY OF THE COATING BEA TO ACCOMMOATE FLUCTUATIONS. CONCERNS WITH RECIRCULATION, IF PRESENT. COATING IES HAVE A FIXE UPSTREAM LIP LENGTH THERE IS A MAXIMUM VACUUM THAT CAN BE APPLIE BEFORE THE UPSTREAM BEA BECOMES TOO LONG AN INVAES THE VACUUM BOX WEEPING PREMETERING IS LOST THE RANGE OF VACUUM OVER WHICH SLOT COATER CAN BE OPERATE GIVES EFINES THE COATING WINOW

31 COATING WINOW LOW FLOW LIMIT BASIC MECHANISM WELL ESCRIBE BY VISCOCAPILLARY MOEL Q = V t = Q couette - Q Poiseuille R Q couette = V H 0 / H 0 (1) () t Q poiseuille P - P 1 = / R V AT A FIXE WEB SPEE, MINIMUM THICKNESS OCCURS WHEN Q poiseuille IS MAXIMUM R IS MINIMUM R min H0 t FROM FILM-FLOW EQUATION P P AT THE ONSET OF LOW-FLOW LIMIT 1 max H t /3 P P Ca t V Ca 0.65 H t 3

32 LUBRICATION MOEL CAN BE USE TO PREICT THE RANGE OF OPERABILITY FOR IFFERENT PARAMETERS FLOW NEAR OWNSTREAM FREE SURFACE Landau-Levich eq. 3 V P1 P P t (1) L Young-Laplace eq. P P 1 P R () P E H Geometric relation (meniscus is an arc of circle). H arccos t 1 R (3) Flow under downstream die lip Q Vt 3 H P 1 E P L VH P E Couette Poiseuille P 1VL H P 3 t H R (4) P 1 t = Q / V

33 FLOW NEAR UPSTREAM FREE SURFACE Flow under upstream die lip Q U 0 3 HU PU P 1 ( X E CL ) VH U L U Neglect capillary effect on upstream meniscus P U P 0 P VAC x CL is < 0 P U X CL Couette Poiseuille H U P E x X CL PE P 6V VAC HU (5)

34 FAILURE MECHANISMS (3) X CL L U (1) 0 Capillary number V () X CL 0

35 Free variable: FILM THICKNESS t Maximum film thickness X Failure mechanism (3) : Bead invades the vacuum box CL L U Eq. (4) Eq. (1) P P Eq. (5) P E P VAC 6VL H U U 6VL U 1VL H PVAC 3 t H H U 3 V 1.34 t 3 1VL V VLU VL t PVAC H t HU H 0 (6) tmax is the root of Eq.(6)

36 Minimum film thickness Failure mechanism (1) : ownstream meniscus invades coating bead Or Failure mechanism () : Upstream meniscus invades coating bead Failure mechanism (1) 1 1 t H R R t H Eq. (1) and () 0 Eq. (3) R t V (1) V H V t MIN (7)

37 Failure mechanism () X CL 0 Eq. (4) and () Eq. (5) P VAC PE P VAC 3 V VL t H t H 3 1VL V 1 6VL t P VAC H t H () tmin is the root of Eq.(8) 0 (8) t MIN max t (1) MIN, t () MIN

38 Capillary Number, V / LOW FLOW LIMIT MAXIMUM WEB SPEE AT A GIVEN FILM THICKNESS MINIMUM FILM THICKNESS AT A GIVEN WEB SPEE Stable Unstable Ca V 0.65 H 0 1 t Gap / Film Thickness THE MAXIMUM POSSIBLE WEB SPEE FALLS AS THE WET FILM THICKNESS ECREASES FOR t 0.6 mils; H0 4 mils; 0 cp; 5 dyn/cm V max = 30 ft/min VISCOCAPILLARY MOEL VALI ONLY AT LOW CAPILLARY NUMBER EXPERIMENTS HAVE SHOWN EXAMPLES WHERE THE MOEL FAILS TO PREICT THE CORRECT MAXIMUM SPEE

39 TWO-IMENSIONAL MOEL Navier-Stokes equations FINITE ELEMENT MESH FREE SURFACE FREE SURFACE

40 THINNER COATING THICKNESS THICK COATING: NO RECIRCULATION RECIRCULATION ATTACHE TO FREE SURFACE APPEARS AT H / t 3 0 MENISCUS BECOMES MORE CURVE AS THICKNESS FALLS

41 Position along the web, X(mm) ETAIL OF MENISCUS CONFIGURATION AS THICKNESS FALLS H 0 / t = 4.06 H 0 / t = 5.03 H 0 / t = Position across the bead, Y (mm) AS THE GAP-TO-THICKNESS RISES, THE MENISCUS BECOMES MORE CURVE AT THE TURNING POINT (H 0 / t = 5.33), THE ANGLE BETWEEN THE IE AN THE FREE SURFACE IS ALMOST ZERO BEA BREAKS INTO RIVULETS

42 Capillary Number, V / Capillary Number, V / 10 P = 0 NO INERTIAL EFFECTS Viscocapillary Model Navier-Stokes Gap / Film Thickness EFFECT OF INERTIA 1 Viscocapillary Model P = 0 P = 381 P = 76 P = Gap / Film Thickness

43 Position along the web, X (mm) ETAIL OF MENISCUS CONFIGURATION AS COATING SPEE RISES Ca = 0.1 Ca = 0.31 Ca = 0.73 Ca = Position across the bead, Y (mm)

44 Capillary Number, V / Capillary Number, V / INERTIA CAN BE USE TO COUNTERACT THE RECEING ACTION OF THE OWNSTREAM MENISCUS AN ELAY THE ONSET OF THE LOW FLOW LIMIT EXPERIMENTS 10 (Carvalho and Keshghi, 000) MOEL Viscocapillary Model P = 0 P = 381 P = 76 P = 95.5 Extended Coating Window 1 Condition used to coat at: = cp, t = 0.5 mils, V = 30 ft/min Gap / Film Thickness 0.1 Coating window presented in the literature Gap / Film Thickness Viscocapillary Model = 13 cp = 17 cp = 75 cp = cp COATING WINOW OF THE PROCESS IS LARGER THAN THE ONE REPORTE PREVIOUSLY IN THE LITERATURE CAN COAT THINNER BY GOING FASTER!

45 Current Coating Fundamentals Challenges Minimization of film thickness variation for more uniform films; Better understanding of coating of particulate suspensions for more complex film structures; Better understanding of multilayer coating process for more complex film structures; iscrete and patch coating; Examples of recent advances and how they can help the coating industry...

46 Current Coating Fundamentals Challenges Minimization of film thickness variation for more uniform films; Better understanding of coating of particulate suspensions for more complex film structures; Better understanding of multilayer coating process for more complex film structures; iscrete and patch coating; Examples of recent advances and how they can help the coating industry...

radius is not constant, Mechanical vibrations, Coating thickness oscillation h( t) h0 hmsin( t ) Goal

47 Transient Response of Coating Flow Romero e Carvalho (CES, 008), Perez e Carvalho (JEM, 011) Production lines are subjected to perturbations (even if very small ) Gap oscillation H( t) H 0 H msin( t) Roll radius is not constant, Mechanical vibrations, Coating thickness oscillation h( t) h0 hmsin( t ) Goal Optimize slot coating process to minimize film thickness variation due to ongoing disturbances of process conditions;

48 Solution Method Finite Element Method Implicit time integration Newton s method

49 Transient Response f 1Hz f 50 Hz H(t) h(t)

50 Amplification factor is a function of frequency of the imposed disturbance process conditions geometry of die lip Effect of Coating Gap Effect of Vacuum pressure

51 imensionless Vacuum Pressure Amplification factor at a given frequency can be mapped as a function of process conditions. 40 0,3 0,3 0,5 0,7 f 3Hz , ,5 1,5 0,4 0,,0 0,,5 3,0 Gap / Thickness 3,5 4,0 0,4 Amplitude of film thickness oscillation may be reduced by a factor of 5 just by adjusting process conditions.

52 Contour plot of amplification factor as a function of gap and vacuum pressure f 3Hz Solution has been implemented in a production line at Fuji Film, Japan. Boundary Constraint Optimization algorithm. ) ( ) ( ) ( ) ( 1 ) ( x f x x b x x H x x x x q T T ( 0 ) x f H ) ( 0 x b f

53 imensionless Vacuum Pressure imensionless Vacuum Pressure Amplification factor map is a strong function of die lip geometry. 40 0,3 0,3 0,5 0,7 40 0, 0,4 0,6 0, , , ,5 1,5 0,4 0,,0 0,,5 3,0 Gap / Thickness 3,5 4,0 0, ,5 0,1 0,1,0,5 3,0 Gap / Thickness 3,5 4,0 0,3 ie lip geometry may also be optimized to reduce film thickness oscillation.

54 Slot Coating of Particle Suspensions In many applications, coating liquid is a particle suspension. Common approach is to study the flow as Newtonian or non-newtonian with the liquid viscosity evaluated based on the avarage particle concentration. Experimental evidences show that suspensions of particles assume very non-uniform concentration distributions in nonhomogeneous shear flow. Local variation of viscosity and surface tension may change the flow pattern and consequently the process limits.? Particle suspension Coating process Coated film Final particle distribution on the coated film may not be uniform and have a strong effect on the drying process and product performance.

55 MATHEMATICAL MOEL OF COATING FLOW Momentum conservation - + ( ) + T pi c v v v v - 0 Mass conservation Particle Transport BCs along interface v = 0 v c N 0 n v 0 n T n N 0 c n c s s c ) ( s s as first approximation

56 Particle Transport / Bulk v c N 0 Total flux of particles due to different migration mechanisms Assume neutrally bouyant spherical, rigid particles; Neglect Brownian diffusion particle size > 0.5 m; iffuse flux model for particle migration proposed by Phillips et al (PF, 199); Particle migration by two mechanisms: N N c N 1. Spatially varying particle-particle interaction frequency N c k c a c. Spatially varying liquid viscosity N c a k c k c a d c dc

57 Viscosity Model Empirical viscosity model for concentrated suspension developed by Krieger: S 1cc 1.8 m s c c m - suspension viscosity. - continuous phase viscosity. - volume fraction of particles. - maximum packing fraction of particles. In this work: s 1cP; c m 0.68 c0 0.4 ( c0) 60cP

58 SOLUTION METHO Unknown physical domain is mapped to a fixed reference domain; Mapping is described by a set of differential diffusion equations: The set of PE is solved by Galerkin s / Finite Element Method; Need to modify system in order to compute derivative of shear rate (second derivative of velocity field) eformation rate tensor is treated as an independent field that is also expanded in terms of finite element basis functions: G v tr( v I I)

walls; Flow is lubricated; Possible particle agglomeration. Upstream gap: Particles migrate towards zero shear rate layer.

59 RESULTS V 0.1m/s ; 60dyn/cm ; H 100m ; 1cP ; k 1. ; k 1.8 s c Inlet condition: uniform concentration profile: c ( x ) c Feed Slot: Particles migrate towards the middle of the feed slot (zero shear rate) Low particle concentration at the walls; Flow is lubricated; Possible particle agglomeration. Upstream gap: Particles migrate towards zero shear rate layer. Lower particle concentration at die lip; Flow is lubricated; Upstream meniscus position is shifted; Effect on low vacuum limit.

60 THINNER COATING THICKNESS Film thickness (flow rate) has a strong effect on deformation rate distribution under the die lip; Consequently, it has a strong effect on the particle concentration in the coating bead and final coated layer; t H 0 + = const Couette Poiseuille Almost rectilinear flow Couette (drag) + Poiseuille (pressure gradient) t H 0 3 Couette + = Poiseuille 0 t H = 0 Couette Poiseuille

High particle concentration at center of feed slot is convected to final coated layer.

61 Concentration H 0 Film thickness equal to half of the gap t 50m Flux related to shear rate gradient is zero. Weak particle migration after feed slot. High particle concentration at center of feed slot is convected to final coated layer. Concentration field at coated layer Region of high particle concentration in the middle of the coated layer. Possible effect on final structure and drying process y

film. Concentration field at coated layer Region of high particle concentration on the top of the coated layer.

62 c Film thickness close to one-third of the gap H 0 t 37m 3 Strong flux towards the zero-shear rate layer attached to the die lip; High particle concentration attached to the die lip is convected to top of the coated film. Concentration field at coated layer Region of high particle concentration on the top of the coated layer. Possible effect on final structure and drying process y

; High concentration gradient in the free surface Strong Marangoni effect? 0.

63 c Film thickness less than one-third of the gap H 0 t 14m 3 Recirculation under the the die lip; High concentration inside the recirculation (near close packing) particle agglomeration?; High concentration gradient in the free surface Strong Marangoni effect? 0.43 Region of high particle concentration on the top of the coated layer y

64 Final Remarks Slot coating fundamentals is well understood for two-dimensional, steady-state operation coating window studies; Fundamental understanding pays off objectives need to be well defined for industrial use Coating research is addressing current and more complex issues faced by the coating industry;

66 Thank you! You are welcome to visit PUC and Rio de Janeiro

Highlights Interaction across industrial sectors and between academia and industry www.iscsts

org) In Cooperation with: The European Coating Symposium and The Japan Coating Symposium Special sessions focused on energy Vendor Exhibit Welcome Reception Networking Sessions Short Course.

deposition and solidification of thin liquid films.

67 Highlights Interaction across industrial sectors and between academia and industry Sponsored by: The International Society of Coating Science and Technology ( In Cooperation with: The European Coating Symposium and The Japan Coating Symposium Special sessions focused on energy Vendor Exhibit Welcome Reception Networking Sessions Short Course. Extended Abstract book The ISCST Symposium provides a forum for researchers with both academic and industrial perspectives on coating science and technology to discuss the latest research on the deposition and solidification of thin liquid films. The Symposium features contributions on both fundamental and applied research by many of the experts in the field from Europe, Asia, and the Americas. The Symposium format is designed to provide opportunities for networking and for the exchange of information between scientists and engineers who are working on coating process and materials development and manufacturing. Symposium Chair: Prof. Marcio Carvalho, PUC-Rio, msc@puc-rio.br Symposium Co-Chair: r. Brent Bell, W.L. Gore & Associates Inc., brbell@wlgore.com ISCST President: Prof. Andrew Hrymak, The U. of Western Ontario, ahrymak@uwo.ca Symposium Facilitator: Ms. Ashley Wood, AIMCAL, ashley@aimcal.org

PHYSICS OF COATING TENSIONED-WEB OVER SLOT DIE

PHYSICS OF COATING TENSIONED-WEB OVER SLOT DIE A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Eungsik Park IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR