# 3.2.2. Noakes et al. (2002) “Streak-line Defect Minimization”¶

Noakes, C.J., Gaskell P.H., Thompson, H.M. and Ikin J.B. “Streak-line defect minimization in multi-layer slide coating systems”, Trans IChemE Part A, vol 80, 2002.

## 3.2.2.1. Abstract¶

This paper looks at the computational and experimental minimisation of streak-lines in slide coating systems.

The Problem: Eddies occur in critical regions which cause streaklines

The Solution: Minor geometrical adjustments and/or changes to wetting characteristics - especially in relation to static contact angles can:

• eliminate the occurrence of eddies

• reduce significantly associated surface deposit growth

• avoid formation of streak lines

## 3.2.2.2. Introduction¶

Problem for coating - avoid defects in:

• Liquid preparation

• Deposition

• Drying

The source of the defect:

• The bulk flow

• Instability - forced (uneven pumping) or self-excited (ribbing)

Stable operating conditions $$\Rightarrow$$ deposit-generated defects

Liquid layers are formed by:

1. Pumping liquid out of two feed slots down an inclined surface

2. Liquid being transferred from the slide lip to a moving web/substrate, stabilized by a small suction pressure

Avoid:

• Streak line defects

• Band defects

Streak-lines caused by:

• Nicks/non-uniformities in the coating head

• Particles trapped in feed slots

• Build up of deposits

Banding caused by:

• Uneven flow

• Poor web handling

• Presence of a wavy contact line

Fluid dynamics reasons for streak-lines:

• Existence of eddies

Eddies cause:

• Trapped foreign particles

• Bubbles

• Solid deposits

Eddies occur in:

• In static contact line

Eddies affected by:

• Slide inclination

• Magnitude of static contact angle

• Cleaning of the slide lip

Particle trapping caused by:

• Lack of interfacial tension

• Break off of solid deposits at upper exit slot

Correlation exists between:

• Streak-line defects

• Surface deposits

• Flow structure in vicinity of exit slots

### 3.2.2.2.1. Aims of current study¶

1. Link between deposit-generated streak-line defects and nature of associated underlying flow structure

2. Provide data to assist in predicting whether defects will occur

Physics Investigated:

• Single and multi-layer flows

• Effect of slot exit

• Slide lip geometry

• Phenomena of back-wetting caused by static contact line migration past the upper slot corner

## 3.2.2.3. Experimental Methods¶

• Single layer slot flow $$\Rightarrow$$ upper slot exit

Experimental results:

1. Free surface profiles

2. Visualization of streamlines

3. Velocity distributions

### 3.2.2.3.1. Two dimensional flow apparatus¶

Geometry variation:

• Square edge

• Chamfered edge

Method for visualization:

• Hydrogen bubble technique

• Local velocities measured by including a chopper in the illumination

• Deposit growth mimics by injecting a hardening agent into the flow

### 3.2.2.3.2. Cylindrical flow apparatus¶

Variables:

• Surface finish

• Top corner profile

• Step height

### 3.2.2.3.3. Method for visualising specific regions¶

• Bouncing probe method used to calculate surface profile at slot exit

• Upper meniscus: Same method used in bead forming region between lip and moving web

• Lower meniscus: Illumination with a sheet of light from a laser diode source

• Profile of interface was determined by casting a shadow of a surface bubble track (the lower layer scattered light, which helped)

• Streakline formation was assessed by: coating many rolls under known conditions and recording the average number of sharp streak-lines per unit width.

## 3.2.2.4. Mathematical Modelling¶

### 3.2.2.4.1. Overall equations and assumptions¶

Assumptions:

• Isothermal

• 2D

• Incompressible

• Inelastic

• Coating liquids are often shear thinning however these effects are small - so assuming a Newtonian fluid is valid

Equations:

• 2D Navier-Stokes

• Continuity Equation

Dimensionless Numbers:

• Reynolds Number

• Stokes Number

Complications:

• Presence of free surfaces

• Internal interfaces

For multi-layer systems, only a double layer system is considered as it shows the key features, namely:

• Upper and lower free surfaces

• One internal interface

• Presence of both static and dynamic contact lines

Approach is a Galerkin weighted residual formulation

### 3.2.2.4.2. Single-layer slot exit flow¶

Geometry:

• Chamfered downstream corner

• Raised back slot

• Modified slot exit channel

Non-dimensional version of Navier-Stokes, length scale and velocity scale are:

• Slot width

• Flow rate per unit width / Slot width

The velocity profile at the inlet is given by:

• 1D form of Navier-Stokes Equations

Outlet boundary obtained using:

• Stress evaluation method

Two cases:

1. Static contact line is pinned at the corner, while static contact angle at slot exit is predicted

2. Static contact angle is specified, while static contact line is predicted

### 3.2.2.4.3. Double-layer slot exit flow¶

More complex than single-layer slot exit flow, it has:

• Internal interface - the nature of the boundary conditions which apply at an internal static contact line still remains a matter of debate

• Inter-layer diffusion occurs

Assume:

• Diffusion process is negligible

• No interfacial tension - velocity is continuous, but pressure discontinuous

Difficulty:

• Lack of interfacial tension results in an over-specified problem if the contact angle is imposed

Solution 1:

• If interfacial contact line is known to locate close to the corner, the preferred course of action is to pin it there

• If interfacial contact line locates away from the corner, solutions include:

• geometric extrapolation

• imposition of pressure continuity

• imposition of small interfacial tension which decays to zero within a short distance downstream, this enabling the specification of a contact angle

Macroscopic flow field is independent of the choice of method, however adding small interfacial tension was chosen

Boundary conditions:

• Velocity profile at slot inlet is obtained as for single layer case

• Outflow determined by using stress evaluation method for 2 layers

• Inflow at upper slot determined from solution of 1D Navier Stokes solution

Boundary conditions:

• Inlet velocity profile obtained from 1D solution to Navier-Stokes equations

• Zero traction condition applied at outlet

Physics:

• Simplification is possible via lack of internal contact line

• Lower free surface meets slide feed device at static contact line

• Lower free surface meets moving web at dynamic contact line

• Static contact line is rarely pinned to the tip of the slide feed device, so is computed

• Static contact angle is prescribed

Difficulty:

• No slip hypothesis breaks down near dynamic contact angle

Solution:

• Dynamic contact angle is prescribed

• This allows slip between the web and the liquid close to the dynamic contact line

## 3.2.2.5. Results¶

### 3.2.2.5.1. Single layer slot exit flow¶

Eddy physics:

• The top, layer forming slot can be responsible for disturbances

• Flow near the static contact line would be recirculating in nature

• Agreement between theory and experiment is good

• A slow recirculation near the contact line is predicted when a high backstep is used

Experimental proof of eddy presence causing streak lines:

• Gelatin containing hardening agent introduced into flow

• Hardened deposit found in eddy generating region

• Mechanism for generating streaklines was the gradual formation of brittle deposit due to long residence time associated with eddy presence.

• Deposits were dislodged by periodic cleaning to form minute fragments, which then produced streaklines

Back wetting: migration of contact line upstream:

• Even a small increase in flowrate causes back wetting

Implications of back wetting:

• Can cause the contact line to be other than straight

• Can cause recirculation near the static contact line

• Both of the above are potential for defect formation

Axi-symmetric rig:

• Question What are the maximum sustainable flow rates before back wetting occurs for three different slot exit designs?

Method 1 in axi-symmetric rig:

• Cut back the top face to form a sharper edge

• Use a hydrophobic coating on the top face

• Approximately double the maximum sustainable flow rate before back wetting occurs

• Sharp top edge is impractical, due to hazard and difficult machining

Method 2 in axi-symmetric rig:

• Height of slot is reduced

• Upstream of slide coated to prevent back wetting

• Causes static contact angle to increase to about 90 degrees

• Substantial reduction in deposit growth

• Question How is the flow structure affected by flow properties?

• Reducing viscosity increases eddy size near downstream slot exit

• Increasing flux also increases eddy size

Operability diagram:

• Parameters: Reynolds Number and Capillary Number

• Indicates operability window for a particular slot geometry

• Desirable range: Low Re and Medium to High Ca

Operability diagram $$\Rightarrow$$ to coat a low viscosity liquid, the slot geometry must be changed to enable eddy free regime

Geometric changes:

1. Chamfered slot exit $$\Rightarrow$$ recirculations are going to be small

2. Stepped slot:

• Decrease in liquid velocity and its associated momentum due to widening the slot in turn leads to a reduction in size of eddies

• Widening slot on upstream side is better than widening slot on downstream side

• Sharp step may generate eddies $$Rightarrow$$ widening slot gradually or using chamfer is better

### 3.2.2.5.2. Slot exit flow for two merging layers¶

Comparison with numerical simulations and:

1. Two layer flow experiments for the case of a chamfered slot with identical layers of aqueous glycerine

2. Free surface and internal interface profiles for flow out of a chamfered slot

Good comparison.

A parametric study showed that fluxes and viscosities have greatest influence on flow structure:

• When upper flux $$\lt$$ lower flux, then increases in upper flux cause minimal change

• When upper flux $$\lt$$ lower flux, then eddies occur upstream

Geometric study:

• Small chamfer reduces size of downstream eddy

• Larger chamfers reduce size of upstream and downstream eddies to undetectable sizes

Curved diffuser:

• Flow is free from eddies

• Layer thicknesses change smoothly without humps observed previously

Why don’t they use curved diffusers? Too expensive? Hard to clean/manufacture?

Maybe it’s the sharp edge - could be a hazard?

Validation of numerical model against:

• Experimental upper and lower free surface profiles

Eddies can occur in bead forming region and are increased by:

• Coating gap increase

• Suction applied to lower meniscus is increased

Eddies cause:

• Prolonged residence time of coating liquid within the recirculation region, resulting in deposits forming at the lip face

• The deposits become grazed and break off by the passage of the web splices

• This leads to sharp streak lines

The model requires:

• Sufficiently refined computational mesh in the lower free surface region

Physics:

• Correlation between primary eddy strength and number of sharp streaklines per metre width

Affected by:

• Static contact angle

• Maintain a lip free of mechanical imperfections

• Ensure the surface properties of the lip are such that a high static contact angle is possible

• Lip radius is also an important factor

## 3.2.2.6. Conclusions¶

• surface deposit growth at both slot exits and the bead forming region

and..

• streak line defects

1. Eddies close to the static contact lines are the cause of the deposit growth

2. Two key parameters that determine flow structure:

• Liquid viscosity

• Flux

### 3.2.2.6.1. In slot exit region¶

• To minimise/prevent eddies modify slot exit geometry using curvature, chamfers and/or a diffuser

### 3.2.2.6.2. In bead forming region¶

• An area close to static contact line at the junction of the lower free surface and underside of lip surface is where eddies form

• Eddies will exist near the static contact line if the static contact angle is less than 40 degrees $$\Rightarrow$$ regular cleaning of the surface of the underside lip region is needed to avoid solid deposition

• Or increase static contact angle with a pre-surface treatment, thus weakening eddy structure.