Selective Evaporation at the Nozzle Exit in Piezoacoustic Inkjet Printing

In practical applications of inkjet printing the nozzles in a printhead have intermittent idle periods, during which ink can evaporate from the nozzle exit. Inks are usually multicomponent where each component has its own characteristic evaporation rate resulting in concentration gradients within the ink. These gradients may directly and indirectly (via Marangoni flows) alter the jetting process and thereby its reproducibility and the resulting print quality. In the present work we study selective evaporation from an inkjet nozzle for water-glycerol mixtures. Through experiments, analytical modeling, and numerical simulations, we investigate changes in mixture composition with drying time. By monitoring the acoustics within the printhead, and subsequently modeling the system as a mass-spring-damper system, the composition of the mixture can be obtained as a function of drying time. The results from the analytical model are validated using numerical simulations of the full fluid mechanical equations governing the printhead flows and pressure fields. Furthermore, the numerical simulations reveal that the time-independent concentration gradient we observe in the experiments is due to the steady state of water flux through the printhead. Finally, we measure the number of drop formation events required in this system before the mixture concentration within the nozzle attains the initial (predrying) value, and find a stronger than exponential trend in the number of drop formations required. These results shed light on the complex physiochemical hydrodynamics associated with the drying of ink at a printhead nozzle, and help in increasing the stability and reproducibility of inkjet printing.

Figure 1

(a) A schematic of the employed ink channel with the ink chamber, restrictor, feedthrough, and nozzle. The ink channel is driven by a piezoelectric actuator attached to a flexible membrane, with compliance $C_a$. Also indicated are the inertances of the restrictor $I_r$, the feedthrough $I_f$, and the nozzle $I_n$. The arrows indicate the direction of the flow rate in the restrictor $Q_r$, the feedthrough $Q_f$, and the nozzle $Q_n$. The pressure in the ink chamber is indicated by $P_{\mathrm{ch}}$, the pressure in between the feedthrough and nozzle is $P_f$, and the Laplace pressure at the meniscus is $P_m$. The compliance of the ink $C_{\mathrm{ink}}$ in the ink chamber and the flow rate through the ink chamber $Q_{\mathrm{ch}}$ are also indicated. (b) The driving waveforms and their corresponding piezo signals as recorded by the oscilloscope. The region that is used for the extraction of the ringdown frequency and decay rate is highlighted in red. The actuation pulses are indicated above the graph. (c) A schematic of the experimental setup. The printhead is driven by a 1-2-$1\text{μ}\mathrm{s}$ trapezoidal pulse. Subsequently, the piezo connections switched to the readout circuit to probe the ringdown of the ink channel acoustics. A light source back illuminates the jetted droplets and images are captured by a high-speed camera. (d) A typical drop formation process with no drying time.

Figure 2

Lumped element model of the ink channel shown in Fig. 1 where the restrictor, feedthrough, and nozzle are composed of a mass and a damper. The ink chamber and meniscus are both represented by a spring.

Figure 3

(a) Real part of the total impedance given by Eq. (15) with a 10 wt% glycerol concentration in all components of the printhead (blue), with double the viscosity in the nozzle (red), and half the surface tension in the nozzle (green). (b) Driving pulse (red) with the corresponding ringdown signal for the 10 wt% glycerol experiment (yellow) with no drying time, and the analytical model (blue).

Figure 4

Schematic of the evaporation phase (not true to scale). The printhead geometry is assumed to be axisymmetric. Water evaporates into the gas phase, leaving behind an enhanced glycerol concentration. Water is replenished by diffusion and convection through the entire system towards the nozzle, as indicated by the gray arrow.

Figure 5

Schematic during the probe pulse and in the jetting phase (not to scale). The axial restrictor flow is solved on a one-dimensional (1D) radial mesh, the chamber pressure is approximated by the ordinary differential equation (ODE) of Eq. (31) and only the part comprising of the feedthrough, nozzle, and the droplet formation is solved by the full flow and compositional equations. The color gradient from blue to red sketches the increase in glycerol concentration.

Figure 6

Snapshots from numerics and the corresponding experiment for the droplet formation process with a drying time of 100 ms (video available online [71]). The numerical simulations provide two color schemes inside the liquid: the left-hand side of the nozzle shows the velocity profile while the right-hand side shows the glycerol concentration. The water evaporation rate is around $100\mathrm{g}/({\mathrm{m}}^2\mathrm{s})$. Snapshots (a),(b) show the nozzle before droplet formation, and (c)–(f) show the droplet formation process. (g) Snapshot at the same time as (f) but for the case of 1.5 ms drying time. (h) Demonstrates the actuation pulses (blue) and numerical pressure signal in the ink chamber (red), where the time instants of the snapshots are also indicated.

Figure 7

Experimentally measured (a) ringdown frequency and (b) decay rate of the ringdown signal of the probe pulse for different drying times at 38% relative humidity (RH) and 0% relative humidity.

Figure 8

Ringdown frequency and decay rate obtained from experiments (open o), analytical model (filled o), and numerical simulations ($△$). The colorbar indicates the average glycerol concentration inside the nozzle for the analytical and numerical models. The arrows at A point towards the experimental results obtained at $0\mathrm{\%}$ relative humidity. The arrow at B points toward the results from the manually closed nozzle.

Figure 9

(a) Evolution of the glycerol concentration in the nozzle during drying time. The numerical results ($\mathrm{△}$) show the average glycerol concentration for two different nozzle lengths: the geometrical length of the nozzle (blue) and an effective nozzle length (yellow). The experimental ringdown frequency and decay rate are converted to a glycerol concentration in the nozzle using the analytical model (o). The numerical snapshots above the figure show the glycerol concentration in the nozzle and the feedthrough at the indicated drying times. (b) Results from the numerical simulations showing the difference between the flow rates of water out of the nozzle (through evaporation $Q_{w,\mathrm{evap}}$) and through the boundaries between the other regions (through advection and diffusion $Q_w$). The different colors indicate the region boundaries as illustrated in the inset.

Figure 10

(a) The resonance frequency of the ringdown signal for the first 1000 droplets that form after different drying times. (b) The number of droplets that have to be jetted before the resonance frequency is back to within 0.5% of the resonance frequency without drying, on a log-log scale.