Misting in Forward Roll Coating: Structure Property Processing Relationships

Transcription

1 Doctoral Defense University of Minnesota October 27, 24 Misting in Forward Roll Coating: Structure Property Processing Relationships vs. App. Extensional Viscosity, Pa-s GRAVITY EFFECT Hencky Strain Michael S. Owens PhD. Advisors: L. E. Scriven & C. W. Macosko Coating Process Fundamentals and Microstructured Programs Department of Chemical Engineering & Materials Science University of Minnesota, Minneapolis, 55455, USA

2 FORWARD-ROLL COATING + + Several methods to pre-meter the applied or wet thickness roll direct-rigid roll offset-rigid The goal is to apply a UNIFORM film 5-roll offset-deformable

3 COATING DEFECTS + + Uniform thickness no defects Periodic variation in thickness Ribbing Formation of droplets Misting What is misting and why do industrial coaters care?

4 WHAT IS MISTING? Generation of liquid droplets upon splitting liquid through a gap or nip. Occurs at high roll velocities Mist consists of particle Diameters < 5 μm Health, quality, cleanup, and cost issue. What is the state of the misting literature?

5 MISTING LITERATURE A STATE OF DISARRAY STRUCTURE Linear polymer solutions Mist RISES Branched polymer solutions Mist FALLS BUT Dilute, entangled, MW, extent of branching,..? PROPERTY Elasticity said to raise misting BUT Relative to what? PROCESSING Misting rises and falls with process conditions BUT What are the physics, mechanism(s), Relative significance of process conditions controlling mist concentration? Empirical treatments BUT no solutions or understanding

6 THESIS GOALS Mist Mechanisms & mist concentration at the film-split Relevant Flow Visualize high-speed events Establish technique for measuring mist Characterize low viscosity weakly elastic liquids challenge modern rheometers Physics Solution Rheology High MW branched polymers model structures Surface Tension Newtonian Non-Newtonian HOW WAS MIST CREATED VISAULIZED AND MEASURED? Polymer Structure Linear Polymers Branched Polymers Optimal Conditions Processing Conditions Control physics by process

7 What is known about misting of simple coating liquids? MIST MEASUREMENT PAN FED TWO-ROLL COATER Roll diameter,.2 & 5.2 cm Roll velocity, m/min Velocity ratio,.-3. Rubber diameter, 6 SHORE-A Roll clearance, Negative by wt. FLOW VISUALIZATION High-speed cameras,,-6, frames/sec. Positive roll clearance, Easily-viewed length scales 45-9 o views, Cross-web direction MIST MEASUREMENT Aerosizer DSP TM, Sampling location, Sampling flow rate, Sampling time Tube length Drop count, size, and mass concentration. 8 cm from film-split 2.5 L/min 3 minutes 2 cm

8 NEWTONIAN LIQUIDS Misting of Newtonian silicones occurs at high roll velocities But only misting of non-newtonian materials has been studied Instabilities prior to misting have been studied (Vinjamur 22, ISCST) but Evolution of misting instabilities has not been defined Mist has not been characterized (number, size, mass) Physics is not understood What is the Newtonian misting mechanism?

9 EVOLUTION OF MISTING NEWTONIAN LIQUIDS Smooth coating transitions to one with ribs as capillary number is raised ηv Ca σ = Viscous Drag Surface Tension As roll velocity is raised ribs are dragged downstream and septa form A septum slides atop a rib oscillates in the cross-web and downstream directions As velocity is raised septum is dragged downstream thins cross-web edge detaches and breaks-up SEPTA EDGE THICKENS EXTENDS THINS BREAKUP MODELING 3-D UNSTEADY FLOW IS TOUGH: GO TO EXPERIMENTS

10 MISTING PHYSICS MATERIALS MATERIAL VARIABLES (η, σ) ωr σ ηo η uε Septum becomes unstable as it thins; h + R Viscous drag causes thinning BUT surface tension resists unstable drop count Drop count 3x 6 2x 6 x 6 PDMS PPG GLYCEROL / WATER 92 m/min BREAKUP EDGE THICKENS EXTENDS THINS Drop size, μm Surface tension.5.6 Shear viscosity, m/s Capillary number Critical thickness reached leading to edge detaching Surface tension pinches it BUT viscosity slows breakup drop size WHAT ABOUT PROCESS VARIABLES?

11 2.x 6 MISTING PHYSICS ROLL VELOCITY As roll velocity is raised Viscous drag from a rib pulls a septum downstream Extensional rate rises Septum Breaks More Often mpa-s 23 mpa-s Extensional Rate, s - 2x 7 x 7 5x ε ~ V.9 Roll Velocity, m/min Drop count.5x 6.x 6 5.x 5 75 mpa-s Drop size, μm Roll velocity, m/min Capillary number Mass ~ number x (diameter) 3!!

12 MISTING PHYSICS SPEED RATIO Roll velocity ratio (V /V 2 ) h h 2 IN FORWARD ROLL COATING V = V 2.7, h = thickness V = roll velocity As velocity ratio rises local thickness rises and Extension rates fall Less likely to rupture FEWER DROPS Drop count 2.x 6.6x 6.2x 6 8.x 5. AVERAGE VELOCITY CONSTANT.7 V droplet # ~ V Roll velocity ratio What about the average roll diameter?

13 Extensional rate, s - 3x 7 2x 7 x 7 MISTING PHYSICS ROLL DIAMETER 9 m/min. ε ~ D 2 At equal roll velocity Large roll rotates slowly η o ω viscous drag Septum not as easily extended Extensional rate falls as septum retreats Rate to critical thickness falls Roll diameter, m. RATE FALLS WITH /( εd ) 2 Mist concentration, mg/m D=. m D=.5 m Need to consolidate misting data Roll speed, m/min

14 MATERIALS Silicone Polypropylene glycol Glycerol / water Surface tension, σ mn/m Shear viscosity, η 75 2 mpa-s PROCESS Average roll velocity, m/min Roll velocity ratio, -3 Separation velocity, D =..5 m. ε = 45, s - SIMPLIFY MISTING TRENDS V V / V 2 ε D Mist concentration, mg/m LINEAR SCALE ηv σ Misting Number V 2 2 ( Dε ) ( V / V2 ).7 Correlates misting of Newtonian liquids What about polymer solutions?

15 POLYMER SOLUTIONS Addition of linear polymer known to increase mist (Glass & Fernando 84, Roper 97, MacPhee 97) Addition of branched polymer known to lower mist (Chung97, Gelarden98, Clark, ) Relative to what? Mechanism for paint spatter in polymer solutions filament breakup Flow field downstream of film-split is both shear and extensional Isolate extensional rheology with Newtonian shear rheology How does molecular architecture control: Mechanism(s), Rheology, Mist concentration?

16 Low Ca EVOLUTION OF MISTING DILUTE POLYMER SOLUTIONS Ribs become extended Smooth coating Develops ribs AS CAPILLARY NUMBER, ηv Ca As Ca is raised further Filaments form slide atop ribs develop beads, then break leaving mist σ OR Break at roll ends and retract Form LARGE droplets, IS RAISED Form septa Slide atop ribs Hole forms grows radially detach a filament OR Break at midplane retract leave no mist Rheology Misting?

17 EXTENSIONAL RHEOLOGY COATING SOLUTIONS Viscosity, Pa-s ROTATING CLAMPS FIBER SPINNING OPPOSED NOZZLES ROTATING CYLINDERS FILAMENT STRETCHING ROD PULLING CAPILLARY THINNING For low-viscosity coating liquids CAPILLARY THINNING

18 MOTOR CAPILLARY THINNING Capillary pressure squeezes bridge Viscous and elastic stresses slow thinning Diameter measured vs. time Fit to a working equation viscosity and relaxation time No transducer needed low viscosity solutions HIGH SPEED VIDEO 2. NEWTONIAN LIQUIDS.6 POLYMER SOLUTIONS DIAMETER, mm.5..5 (2 X ) σ D ( t) = D t 6η. s TIME, ms DIAMETER, mm D( t) = D exp( t / 3λ)

19 8 CAPILLARY THINNING EXPERIMENTAL DATA Diameter, mm Extensional Rate, s λ = 5 ms Time, ms Time, ms All data obtainable with surface tension and measured diameter! Diameter falls exponentially w/ time Extensional rate approaches a constant BUT Is determined by force balance of Surface tension and elastic stress App. Extensional Viscosity, Pa-s GRAVITY EFFECT IS IT ACCURATE? Viscosity rises x Newtonian value Hencky Strain

20 CAPILLARY THINNING INDEXER OR RHEOMETER? Polystyrene oligomer: Picolastic A-5, η = 33 Pa-s at 25 o C Polystyrene polymers:.8 M (PDI =.2) 6. M (PDI =.2) c* = overlap concentration Model elastic liquids 6. M Dilute solutions defined below c* c** more conservative estimate of dilute solution (Graessley 98) c** ~.c* λ(c) non-dilute behavior Experimental error at low conc. Capillary Thinning is an Indexer Relaxation time, seconds. Shear relaxation times.8 M -2 - c/c** Compare apparent elasticity of coating solutions vs. misting

21 Relaxation time, ms EXTENSIONAL RHEOLOGY OF LINEAR PEO SOLUTIONS Molecular Wt. kg/mol 5 η λ ~ PEG:Water:PEO ~ 5 35ms 2mPa σ ~ 52 55mN/m - s Concentration, ppm Characterize drop size, drop count, and concentration vs. Relaxation time

22 Drop diameter, μm NEWTONIAN MIST CHARACTERIZATION 5%GLYCEROL : WATER : PEO η = 5 mpa-s, σ = 6 mn/m, Misting Number ~ V = 92 m/min Drop count x 6 8x 5 6x 5 4x 5 2x 5 NEWTONIAN V = 92 m/min Relaxation time, ms Relaxation time, ms As relaxation time is raised DROP SIZE RISES & DROP COUNT FALLS Mist concentration, mg/m COATING WINDOW V = 92 m/min Competition determines misting window Relaxation time, ms

23 Mist concentration, mg/m 3.. COATING WINDOW Roll speed m/min Relaxation time, ms Coating window SHRINKS at roll speed is raised Literature Branched solutions reduce mist Linear polymers increase mist NO! IS BRANCHED BETTER THAN LINEAR AND IF SO WHY?

24 THESIS GOALS Mist Mechanisms & mist concentration at the film-split Extensional flow Newtonian Polymer solution Smooth ribs Septa mist OR Smooth ribs Septa filaments-> mist Misting Number Misting Window Capillary Thinning Relaxation time Solution Rheology Newtonian Strain Hardening Experiments And Molecular models Polymer Structure Linear Polymers Branched Polymers High MW branched polymers model structures Formulation specific Processing Conditions

25 POLYDIMETHYLSILOXANE (PDMS) POLYMER SOLUTIONS Clark et al. 22 Polymer additive for reducing mist Chain Extension Chain Branching Branches On Branches RANDOM BRANCHING

26 Normalized Signal, volts BRANCHING ANALYSIS MULTI-ANGLE LIGHT SCATTERING Linear silicone Branched silicone Retention Volume, mls Branched PDMS very polydisperse.56 Radius of Gyration, nm Linear PDMS Branched PDMS 5.x 5.x 6.5x 6 2.x 6 2.5x 6 Mw, g/mol Compare Rg vs. MW Branching Ratio Rg BRANCHED Rg LINEAR 5.x 5.x 6.5x 6 2.x 6 2.5x Mw, g/mol BRANCHING RISES AS RATIO FALLS High Mw fraction dominates rheology Define concentration where Rg OVERLAP 25% of overall Mw ACTIVE.2 wt% branched polymer Is 5ppm active.

27 35 BRANCHED VS. LINEAR DILUTE PDMS RHEOLOGY App. Extensional Viscosity, Pa-s Linear λ = 4 ms Branched λ = 7 ms Branched No Elasticity Detected LOW MW 8 kg/mol HIGH MW 66 kg/mol INTERMEDIATE MW 44 kg/mol Hencky Strain Lower molecular weight LINEAR SOLUTION has LONGER relaxation time and MORE strain hardening Do branched solutions have fewer but more drops than linear?

28 BRANCHED VS. LINEAR PDMS 2x 6 Newtonian Branched polymers 5 ppm η =28mPa-s 3.5 Linear polymers 5 ppm η =28mPa-s Drop count x 6 Linear polymers 5 ppm η =28mPa-s Drop diameter, μm NEWTONIAN Branched polymers 5 ppm η =28mPa-s Mw, kg/mol Mw,kg/mol Linear polymer solution has fewer droplets of larger size than branched polymer at equal Mw WHY? Model systems by computation

29 MOLECULAR MODEL Dilute solutions no polymer/polymer interactions R 2 end-to-end distance R g 2 SIMPLIFY AS 2 BEADS CONNECTED BY SPRING BEAD IS POINT OF VISCOUS DRAG SPRINGS REPRESENT POLYMER ELASTICITY FORCE FORCE BLOWS UP MAXWELL SPRING OLDROYD-B GEISEKUS STEADY-STATE FENE MODELS Non-linear spring law to describe Finitely extendible reality CHAIN EXTENSION INFINITE CHAIN EXTENSION HOOKEAN SPRING Doesn t allow for Branched polymer structures

30 GENERAL CONNECTIVITY Goal: To design a framework that describes all possible molecular architecture and gives a coarse description of chain contour. Solution: Connectivity matrix or Incidence array Bead, i N Spring, i N- Bead, i N Spring, i N- Can easily design: stars, combs, loops, dendrimers, branches-on-branches, ect.

31 BEAD-SPRING CHAINS Contour represented by series of beads and springs Viscous Non-linear Coarse-grained? Brownian Force elastic force chain contour Force * OTHER FORCES MAY INCLUDE Solvent / Polymer interactions Hydrodynamic interactions Conformation dependant drag Chain interactions if not dilute

32 BROWNIAN DYNAMICS EQUATION OF STATE Brownian force is a time and spatially random Force exerted by the solvent on the chain k T dr 2 (/ 2) i i 3 2 T k T B 3 λ λ 6 i B ~ = v ri + λi λ ni dt b 2 i + ζ 2 t Rate-of-Change Bead solvent owing velocity k λi λ i ζδ of bead position velocity by Bead velocity owing to owingvelocity Bead Non-Linear Force from Extension of Spring exerted randomto on forces beads Solve for bead positions (r by the solvent i ) by Euler integration λ i is a ratio of bead to separation to their maximum allowed separation Ensemble Average of the Polymer Stress (spring separation) And Polymer Relaxation Time Stress, τ - τ Time

33 Relaxation time, seconds MODEL DILUTE POLYMER SOLUTIONS Polystyrene Boger liquids Capillary thinning Mw =2, 6, 2 M Anna et al. JOR 2 T-star PS Linear PS Relaxation time Brownian Dynamics Simulations Linear Polymers STAR POLYMER Molecular weight, g/mol Number of beads ~ MW Relaxation time rises with molecular weight λ Linear > λ branched Corresponds to stress How does stress correspond to mist mechanism?

34 Linear gives less mist than branched MOLECULAR STRUCTURE CONTROLS MISTING Breakup mechanisms Increasing polymer stress or relax n time σ R = τ Solvent + τ Polymer High polymer stress stabilizes filaments AND Capillary Force Acting to Squeeze Filament Newtonian Viscosity Resists Pinching Polymer Elastic Stress Resists Pinching Linear polymer gives greater stress than branched at equal Mw

35 NEWTONIAN x 6 STRUCTURE PROPERTY OPERATIONAL DIAGRAM STRAIN-HARDEN Drop count SEPTUM EDGE FAILURE BREAK-UP MECHANISM SEPTUM EDGE RUPTURE FILAMENT EXTENDED BREAKUP MECHANISMS Increasing Mw Decreasing branching Relaxation time, ms

36 NEWTONIAN CONCLUSIONS Mechanism Ribs septum edge failure mist Mass concentration of mist summarized by Non-dimensional misting number Optimal Material/Process design High surface tension Low viscosity Large rolls Speed ratio Short-term solution: Polymer solutions Change the mechanism by which mist is formed Long-term solution: Different Coating Technique Mist concentration, mg/m LINEAR SCALE Change the technique so instabilities leading to mist do not form Misting Number

37 DILUTE POLYMER SOLUTION CONCLUSIONS Mechanism Ribs septum hole growth filament Mass concentration of mist defined by Misting Window beads-on-string drops single bead big but few drops breaks and retracts no drops COATING WINDOW Optimal Material/Process design.5 Low surface tension. Low viscosity Weak elasticity.5 Large rolls. Speed ratio Relaxation time, ms Short-term solution: Semi-dilute and entangled solutions Mist concentration, mg/m 3 V = 92 m/min Low surface tension w/ more elasticity to get new window no drops Long-term solution: Different Coating Technique Slot/tensioned web or reverse roll coating

38 FUTURE WORK Does another coating window exist? Mist concentration, mg/m COATING WINDOW V = 92 m/min Relaxation time, ms COATING WINDOW Entangled solutions Slinging New coating window (Practical and Fundamental interest) 3-D CFD of septa mist & septa filaments mist (Physics of misting) Misting of viscoelastic-plastic inks? (Practical and Fundamental interest) What is the origin of error(s) during elastocapillary thinning? Fluid mechanics and equilibrium shape analysis (Fundamental and commercial interest) Brownian dynamics of multiple chains in extensional flow (Fundamental and practical) entanglements of dilute solutions interchain hydrodynamics Fluorescently tagged chains in experiment and PIV to follow capillary thinning dynamics

39 Advisors, ACKNOWLEDGMENTS Chris Macosko and Skip Scriven Committee members, Marcio Carvalho, Satish Kumar, Tim Lodge Conspirators in Coating Process Fundamentals and Microstructured Polymers Programs 2-24 Summer Undergraduate Research Participants Friends and family, The non-academics