*2.1. Gravure Printing*

Gravure printing is a mature manufacturing method that has been employed for high throughput image printing since the 19th century [27]. Gravure printing is achieved in four phases, as shown in Figure 2a,b [27,34]. First, ink is poured on a rotating gravure roll and fills the recessed cells in the roll [40]. Second, a doctor blade removes the excess ink from the roll, leaving only an ink thickness corresponding to the depth of the cell [40]. Third, the ink is brought in contact with a substrate, which is itself being rolled at the same speed as the gravure roll, and the ink is pulled from the roll onto the substrate as a result of adhesive forces between the ink and the substrate and the ink's surface tension [27,40]. Finally, the print will stabilize on the substrate and spread based on the theoretical contact angle that the liquid–gas interface makes to the substrate, which is determined by Young's equation. *cosθ<sup>c</sup>* = *γsg*−*γsl γlg* , where *γsg*, *γsl*, *γlg* are the surface energies for solid–liquid, liquid-gas, and solid-gas, respectively [27,50,51]. Although this is true for all direct printing methods, it is particularly important for gravure printing because gravure patterns consist of individual cells which must spread into each other to form a cohesive print [52]. In addition, print resolution, quality, and speed are primarily limited by the complex fluid dynamics occurring when excess ink is removed by the doctor blade [51]. Printing faults during this phase are broadly characterized by two processes: lubrication residue and ink drag out [27,53]. First, the doctor blade will always leave a small residual ink layer on the roll, and this layer's thickness must be substantially reduced to prevent electrical shorts and erroneous material depositions [27]. The doctor blade's efficiency depends heavily on the relative magnitudes of viscous forces and surface tension. This relationship is captured in the capillary number *C<sup>a</sup>* = *viscous f orces sur f ace tension* = *µU σ* , where *µ* is the ink viscosity, *U* is the print speed, and *σ* is the ink surface tension [51].

At high capillary numbers, the residual thickness is often unacceptable [27]. Therefore, reducing print speed and ink viscosity is essential in limiting lubrication residue. Second, the doctor blade may pull ink out of the cells as it passes and deposits the ink on the roll in a process termed drag out [53]. This process has been analytically and empirically shown to depend heavily on capillary flow, which is limited at high capillary numbers [51,52]. In this condition, the print velocity is too high compared to the capillary flow characteristic velocity for drag out to occur [27]. Therefore, high capillary numbers prevent drag out and low capillary numbers limit lubrication residue. In practice, achieving a capillary number of Ca ≈ 1 is necessary for high-quality gravure printing, although the ideal capillary number also depends on pattern geometry, orientation, substrate wetting, and print thickness [54]. Because these interactions are often complicated to determine analytically a priori, especially with viscoelastic inks, many researchers optimize their process with statistical design of experiments techniques, such as analysis of variance and Taguchi methods [51]. Figure 2c depicts results from one such experiment to determine the optimal ink viscosity and cell spacing for a process with a fixed speed (3 m/min) [53]. Three graphene inks were formulated with various viscosities (i), and single dots were printed (ii–iv), with the low viscosity ink (iv) producing an unlevel print with an extended residue tail [53].

In addition to optimizing the ink rheology and substrate wetting, the cell pattern is crucial in achieving high-resolution prints [55]. Printing continuous lines, which is referred to as Intaglio printing, is avoided because the drag-out effect is amplified with long prints oriented in the printing direction [56]. In order to produce high resolution, level prints, minimizing cell dimensions is critical [27,52,53]. As shown in Figure 2c, previously discussed 2.5 Pa·S ink was also printed with cell spacings of 50 µm (v), 25 µm (vi) and 5 µm (vii), and the line uniformity increased significantly with a decrease in cell spacing [53]. Further increasing resolution and quality in gravure printing is complicated, however, because traditional print head fabrication methods, such as electromechanical and laser engraving, are unable to produce cells with dimensions < 10 µm, and they are also likely to produce additional roughness on the gravure roll near the cell as a result of the engraving process [52,53]. Therefore, recent works have employed silicon microfabrication techniques to design very

high-resolution gravure rolls [53]. For instance, Secor et al. used photolithography to design a silicon-based gravure roll capable of producing high resolution trace <30 µm with conductivities >10,000 S/m [53]. To further reduce trace widths, Lee et al. experimented with various cell depth profiles under the hypothesis that curved cell walls would reduce drag out [52]. As shown in Figure 2d, a curved gradient pattern was able to reduce print width by 65%, yielding a final pattern of <10 µm [52]. These recent developments in high resolution and high throughput gravure manufacturing, combined with the novel advances in printable, conductive nanomaterial inks discussed in Section 3, make them well suited to numerous bioelectronics applications, including multilayer circuit fabrication and sensor manufacturing, such as the sweat sensor demonstrated in Figure 2e [40]. However, gravure printing also presents very high startup costs, incurs high costs to prototype, places rigid requirements on ink rheology, and often requires substrate surface modifications in order to achieve optimal printing [17,27,57].
