Formulation, characterisation and flexographic printing of novel Boger fluids to assess the effects of ink elasticity on print uniformity

A model printing ink should not only exhibit strict rheological traits but also have adequate drying performance and a suitable surface tension to prevent excessive wetting or dewetting on the substrate, while in the current work also enabling the observation of viscous fingering. Model elastic fluids such as polyethylene glycol and polyethylene oxide solutions (Dontula et al. 1998) have relatively high surface tensions at low viscosities (Yu et al. 2006) while oil-based polystyrene solutions (Anna and Mckinley 2001) exhibit difficulties upon drying and thus are not suitable for printing. As such, this work presents a new class of water-based printable Boger fluids that may be formulated to a range of elasticities and viscosities. These fluids were formulated by blending polyvinyl alcohol (PVA) of molecular weight 20 − 30 × 10³ g/mol with polyacrylamide (PAM) of molecular weight 5 − 6 × 10⁶ g/mol from Acros Organics. PVA and PAM have been shown to be miscible over a range of concentrations (El-din et al. 2003) however constitute no reported flexographic ink or Boger fluid known to the authors. Solutions of each polymer in deionised water were mixed at various concentrations to produce blends of a similar shear viscosity. Table 1 shows the final composition of each ink and Table 2 displays their measured physical properties. In order to colour the solutions, E122 azorubine dye (FastColours LLP) was dissolved in water and added to each at a solid content of 0.05 wt%.

Shear viscosity measurements were carried out on a Malvern Bohlin rotational rheometer with a 40 mm, 4^∘ cone and plate geometry between shear rates of 100 and 0.1 s^− 1.

Viscoelastic measurements were carried out on a TA Instruments AR-G2 with a 60 mm aluminium parallel plate geometry. In light of the extensional flows present in flexography, a purpose built capillary breakup extensional rheometer (CaBER) was used to characterise the uniaxial extensional properties of the inks with a plate diameter, D ₀, of 3 mm. An initial aspect ratio of 0.43 was used for all inks with final aspect ratios of 1.1 for ink N and 1.2 for inks E1, E2 and E3 to ensure surface tension-driven filament formation and breakup. Filament breakup was captured with a FastCam high-speed camera at between 1000 and 4000 frames/s depending on breakup time. From the recorded images, mid-filament diameter D _{m i d} (t) was extracted and used to calculate apparent extensional viscosity η _E : where σ is the ink surface tension and X is a dimensionless variable dependent on the tensile force and radius of the filament (Tuladhar and Mackley 2008). For Newtonian fluid breakup, X is taken to be 0.7127 as determined by Papageorgiou (1995) while for elastic breakup, X = 1 due to the axial symmetry of the filament (McKinley and Tripathi 2000). Furthermore, elastic filament breakup may be modelled with where D ₁ is mid-filament diameter just after extension, t is time and λ _E is the fluid characteristic relaxation time for the elastocapillary thinning action (Bazilevsky et al. 1990). The Bond number \(Bo={\rho }gD_{mid}^{2}/\sigma \) may be used to quantify the relative magnitudes of gravitational and surface tension forces, where ρ is the ink density and g is gravitational acceleration; gravitational effects are considered to be unimportant for B o < O(0.1) (McKinley and Tripathi 2000; Clasen 2010). A pynometer was used to obtain fluid density and surface tension was determined dimensionally via the pendant drop method (Bidwell et al. 1964) using images captured with the FastCam high-speed camera and analysed with ImageJ image processing software.

Flexographic printing of the model inks was carried out on an IGT F1 Printability Tester lab-scale printing press. Solid area printing plates capable of producing full area, featureless coverage (defined in the field as 100% nominal coverage) at a width of 3 cm were selected to assist in the analysis of print uniformity. The substrate used was 330 μm white polyethylene terephthalate (PET), the anilox volume was 24 cm³/m² and the print velocity was 0.2 m/s. Once printed, samples were dried at room temperature and then digitised with an Epson Perfection V700 scanner at 1200 dots per inch. Quantification of the uniformity of digitised prints was carried out by calculating the total area to total circumference ratio of features in a selected area of each print 600 × 600 pixels in size. At the edges of the relief printing plate, an air-ink interface exists leading to the formation of ancillary viscous fingers of varying sizes and orientation. Therefore, sample areas were taken sufficiently away from edges to avoid such boundary effects and within the first 10 cm of the print—during the first inked revolution of the printing plate—for consistent ink transfer. Subsequent image analysis was carried out with Wolfram Mathematica software (Wolfram Research Inc 2015). Total feature area was calculated by binarising the image with Otsu’s cluster variance maximisation method (Otsu 1979) while gradient edge detection provided the total feature circumference. Edges in a radius of three pixels were recorded, thus maintaining the detection resolution required for the features of interest while reducing the influence of noise. The ratio of total area to total circumference may therefore serve as a concise quantification of the overall relative size of the print features and thus a measure of its uniformity. The binarisation and edge detection processes are illustrated for a selected sample area in Fig. 2.

The shear viscosity of each ink is shown in Fig. 3 with low-torque and secondary flow limits marked by dashed lines (Ewoldt et al. 2015), while effects from the latter were not observed. All inks display near constant viscosities with shear rate above the low-torque limit and their mean values, calculated from linear fits of stress and shear rate, are displayed in Table 2. Small-amplitude oscillatory shear measurements taken at a controlled stress of 0.5 Pa—within the linear viscoelastic range (LVR) of each ink—are displayed in Fig. 4 with the LVR determined by amplitude sweeps at 1 Hz. As the viscosities of the inks are similar, the viscous moduli G ^″ are also such, while the elastic moduli G ^′ are seen to increase with concentration of PAM. Modulus G ^′ of ink N was too low to be accurately measured, as would be expected for a Newtonian sample. This rise in elasticity may be attributed to the increasing presence of the long, flexible polymer chains of the high molecular weight PAM. The low-torque limit of the rheometer was surpassed for all measurements, while the raw phase angle reached a maximum of 155^∘ at the highest frequency and was otherwise below 150^∘, suggesting reliability regarding inertial affects (Hudson et al. 2017). Such verification was particularly necessary due to the low viscosity of the inks. Furthermore, the dynamic viscosity η ^′ = G ^″/ω (Barnes et al. 1989), included in Table 2, shows consistency with η and upholds the viscometric similarity of the fluids.

Extensional characterisation using the CaBER technique further demonstrates the trend of increasing elasticity with PAM content. A sequence of images from the filament breakup of ink N and the most elastic ink E3 are shown in Fig. 5 at selected times with brightness adjusted for visual representation. The typical curvature of the Newtonian filament is evident while the axially symmetric filament formed by ink E3 is characteristic of elastic breakup (Mckinley 2005) and was qualitatively similar for inks E1 and E2. The filament breakup time for each fluid, shown in Fig. 6, increases with PAM content, and the PAM-containing inks all show exponential decay characteristic of such behaviour before breakup occurs due to the finite extensibility of the polymer chains (Anna and Mckinley 2001). Relaxation times for each fluid, presented in Table 2, were obtained from the fitting of Eq. 2 to the exponential filament decay and therefore elastocapillary regimes of the elastic inks (Sousa et al. 2017) which occurred with B o < 0.013, suggesting minimal gravitational effect. The increase of λ _E with PAM content confirms that its addition greatened ink extensional elasticity. After an initial retardation, likely due to gravitational drainage, ink N demonstrates a more linear decay where B o ≤ 0.02, betraying Newtonian characteristics (McKinley and Tripathi 2000) with an apparent extensional viscosity of 0.11 ± 0.01 Pa⋅s as described by Eq. 1. This is slightly higher than the Trouton ratio η _E = 3η would predict for Newtonian fluids of such a shear viscosity η and may be due to non-negligible inertial and gravitational forces retarding the fluid breakup in light of ink’s low viscosity and elasticity (McKinley and Tripathi 2000; Rodd et al. 2005).

The constant shear viscosity and measurable shear and extensional elasticity of the presently formulated inks E1, E2 and E3 imply they may be considered Boger fluids.

Non-uniformity consistent with the viscous fingering phenomenon was observed in prints of all inks formulated and representative samples of each print are shown in Fig. 7 with their brightness adjusted to enhance feature visibility. Significant variation can be seen in the nature of the patterns produced from the four inks. Prints from the Newtonian ink exhibit near continuous, periodic striping in the printing direction with a visually counted wavenumber of approximately 2 mm^− 1. As the ink elasticity is increased, the striping becomes less continuous while the feature orientation remains in the printing direction. Area-circumference feature analysis of 600 × 600 pixel areas of the prints conveniently quantifies this uniformity change as the ink elasticity is increased and is plotted with extensional relaxation time λ _E in Fig. 8 with that of Newtonian ink N taken to be zero. The area-circumference ratio, fitted with a negative exponential growth, decreases with λ _E , indicative of the apparent reduction in feature size with elasticity. Furthermore, this ratio also decreases with ink elastic modulus G ^′, seen inset in Fig. 8 fitted with an exponential decay. Error bars represent the standard deviations of the respective quantities, with those of the calculated ratio reflecting its sensitivity to print variation.

The presence of an elastic component in the ink through the introduction of PAM appears to disrupt the continuous striping during printing causing—at the two lower concentrations—shorter printed features without greatly impacting their width. Such a variation of print uniformity would likely affect the conductivity of a print with a functional ink which may also be directionally dependent, particularly in the case of the striping Newtonian ink. Prints of E3, the ink with the greatest degree of elasticity, however exhibit a somewhat different topology, with significantly narrower features in a more forked configuration that nonetheless continue the trends of decreased area-circumference ratio with elasticity seen in Fig. 8. This convergent forking is present, though to a much lesser extent, in prints of the other inks and also appears to increase with elasticity. The striping disruption may be linked to the elastic influence on filamentation during the separation of the printing plate and the inked substrate, a notion consistent with aforementioned reports regarding roller processes that fluid elasticity leads to smaller filaments (Ercan 2001) and that they are longer and more stable (Fernando and Glass 1988). This is supported by the correlation of extensionally measured elasticity through CaBER, a filament thinning process, and print feature size displayed in Fig. 8 which not only characterises non-uniformity in a roller process but extends it to a real printing scenario on a flexographic press with model inks. Notably, this is the first known reporting of a flexographically printed Boger fluid and given the similarity of the capillary number for the printing of all fluids—between 0.100 and 0.107—the present work highlights the limitations of this parameter for the relation of rheological properties and print outcome for elastic inks. Elastocapillary number E c = λ _E σ/η l, a dimensionless parameter characterising elastic and capillary effects (Mckinley 2005), given here with extensional relaxation time, may therefore be a relevant quantity in this context, where an appropriate length scale l is required. Assuming a 40% transfer of ink from the anilox to the printing plate (Cherry 2007), a film thickness of 9.6 μm would be expected at the nip, implying E c ∼ 10⁴ for the three elastic inks, increasing with λ _E , and B o ∼ 10^− 5 suggesting flow strongly dominated by elastic and surface tension forces. Given the controlled viscosity and surface tension of all four inks, this is consistent with the perception that the print variation observed may be attributed to the effects of ink elasticity on flow in the flexographic process and highlights the possibility of tuning rheological parameters for desired printing patterns.

Further understanding and characterisation of the patterning demonstrated in this work is not only of interest in printed electronics but could also be of use in other applications such as security printing where the random nature of the features may be matched with a digital signature for use on secure documents (Anderson 2008).