FIRING INK FROM THE PRINT HEAD

Creating acceptable prints requires two steps: (1) getting ink to fire reliably from a print head onto paper, and then (2) getting ink to behave in a desirable manner on paper. In the first part of this chapter, the inkjet printing process is discussed: how is ink ejection impacted by ink properties? What are typical impediments to reliable drop ejection?

Drop Ejection Cycle

The ejection process of an ink drop from a thermal inkjet (TIJ) print head begins as an electrical pulse is applied to a resistor. Within ∼2–5 microseconds, the resistor surface reaches a temperature of

Fig. 1. Ejection cycle of a thermal inkjet (TIJ) print head.

∼200–300◦_{C, ink near the resistor surface boils, and the resulting}

high pressure (∼100 times atmospheric) vapor bubble pushes ink through a nozzle. Ink is then drawn by capillary action from an ink reservoir to refill the chamber. See Fig. 1.

Conversely, in a piezoelectric inkjet (PIJ) head, the deflection of a membrane drives ink through each nozzle — schematics of the various configurations used in PIJ heads can be found else- where.1, 2 The timescale for PIJ drop ejection is similar to that in a TIJ head (Fig. 1), thus, both are capable of firing ∼10 000 to 30 000 drops from a nozzle each second. Typical nozzle diameters (d = 10−50 µm), ink viscosities (η = 1−5 centipoise), ink surface tensions (σ = 20−50 dyne/cm), and ink densities (ρ = 0.9−1.1 g/ml) are fairly similar for the TIJ and PIJ printers for office and home use. The resulting key fluidic parameters for such print heads are sum- marized in Table 2.

Clearly, fluid inertia is important in drop ejection, since Re >> 1; however, flow is still considered to be in the laminar regime, as the

Table 2. Typical fluidic parameters for ink drop ejection from TIJ and PIJ print heads.

Drop weight w= 2−50 nanograms (ng) Drop ejection velocity v= 5−15 m/sec Reynolds Number
fluid inertia viscous forces  Re= ρdv η = 50−500 Weber Number
fluid inertia surface forces  We= ρdv 2 σ = 20−300

onset of turbulence in tube flow typically occurs for Re ≥ 2000.3

Furthermore, the ratio√We/Re (also called the Ohnesorge number and represented as η/ρdσ) is ≤ 1 for flow in inkjet heads, thus surface forces are as important, or even more important, than viscous forces in the drop ejection process. The impact of ink viscosity and surface tension on drop weight and drop velocity has been studied both experimentally4_{and computationally.}5_{Though these relation-}

ships depend in a complex way on other factors such as flow channel geometry in the print head, it is generally found that increasing ink viscosity leads to decreasing drop weight and drop velocity. In TIJ print heads, thermal energy transfer to the ink stops as soon as a vapor bubble forms, placing practical limitations on the amount of energy that can be imparted to an ink drop. Hence, TIJ heads are primarily limited to inks of low (1–5 cp) viscosities. In con- trast, the mechanical displacement of the membrane in a PIJ head can be more readily extended to provide enough energy to eject inks with viscosities up to ∼50 cp. However, with such high vis- cosities, the maximum firing frequency is reduced, to accommodate the decreased rate of ink refill into the firing chamber.

Drop Break-up

Rapidly (∼10−50 µsec) after ejection, an elongated column of ink breaks into distinct spherical drops, typically a large head and a few smaller satellites (Fig. 2). Satellite drops can cause problems. Because they decelerate faster under viscous air drag than the larger, main droplet,4satellites may not make it to the intended spot on paper in the time (∼100 µsec) typically allotted. As a result, satellite drops can either end up in undesirable locations on the paper, or equally as bad, they can deposit on the internal components of the printer. Though satellite and aerosol droplet formation is complex, in general, liquid atomization studies show that smaller, finer droplets form as the Weber and Reynolds numbers increase6_{— i.e., for faster flows, and}

for fluids with lower ink viscosity and surface tension. Because many ink surfactants can take longer than 100 µsec to migrate to the liquid/air interface, it is possible that ink dynamic surface tension

~20 sec ~40 – 50 sec ~70 – 80 sec main drop main satellite smaller satellites, aerosol droplets ~20µsec ~40 – 50µsec ~70 – 80 µsec main drop main satellite smaller satellites, aerosol droplets

Fig. 2. Typical drop break-up dynamics from an inkjet print head.

plays a role in both drop break-up and spreading.7_{One ink formu-}

lation approach to prevent aerosol employs small amounts of high molecular weight polymers in inks, to apparently increase the ink extensional viscosity, and thus resist the formation of long liquid fil- aments.8Some PIJ heads employ subtle vibrations of the drive mem- brane to control the position of the meniscus at the ink/air interface, thereby helping drops break off cleanly.9_{Overall, drop break-up is}

a complex subject, and to fully understand it as a function of ink composition, a high speed camera will be useful.

Ink on the Orifice Plate — Puddling

Inevitably, some of the ejected ink ends up on the “orifice plate,” (the outside of the print head, near the nozzles). Large ink puddles near the nozzle can rob a newly formed drop of its momentum, causing misdirection, or complete inhibition of firing. Hence, less ink on the orifice plate is desirable. While print head modifications, such as using non-wettable material for the orifice plate, or employing coun- terbores around nozzles,10 _{can help keep the orifice plate clean, ink}

composition also plays a role. In particular, the use of fluorosurfac- tants in inks has been shown to prevent puddling.11_{The mechanism}

fluorinated hydrophobes in such molecules prefer the ink/air interface to the ink/solid interface, thus reducing ink surface tension without promoting wetting on the orifice plate. It is also possible that a fluorosurfactant’s ability to dramatically lower the ink surface tension may help suppress surface tension gradients, thus pre- venting Marangoni flows that would promote ink spreading out of nozzles, onto the orifice plate.

Resistor Fouling — Kogation and Decel

TIJ print heads present the complication that, over time, deposits can form on resistors, reducing the efficiency of heat transfer to the ink, and thus lowering drop weights and drop velocities over a print head’s life. This phenomenon is referred to as “kogation.” Though the chemistry of deposit formation is complex, one key parameter is the solubility of various solutes in the ink. During each firing, roughly ∼0.02 ng of fluid is vaporized over a resistor to generate a ∼20 ng ink drop. Nonvolatile ink components, in the 0.02 ng of ink, such as dyes and pigments, are left behind. If not readily redissolved or redispersed, such solutes can accumulate on resistors. The rate of redissolution of solutes is important — slowly redissolving com- ponents on resistors can give rise to a transient kogation-like phe- nomenon referred to as “decel,” short for “deceleration.” As the name implies, inks exhibit drop velocity decreases with firing. However, after resting for a period of seconds to minutes, the drop velocity may return to its initial value upon firing again, only to subsequently decrease again. See Fig. 3.

Furthermore, certain compounds in inks may have special affinity for resistor surfaces. For example, trace inorganic compounds are suspected to undergo electroless plating-like deposition on the tan- talum oxide covering resistors, and thus the use of sequestering agents is common.12 _{Ink formulation strategies to prevent resistor}

deposits have focused on including components in the ink that sup- posedly passivate the resistor surface, or slowly etch the surface.12,13

In the latter case, a balance must be struck between stripping away unwanted deposits, and corroding resistor materials.

# of firings # of firings drop vel oc it y drop v e lo cit y kogation irreversible drop velocity decrease.

decel reversible drop velocity decrease. firing stopped firing resumed # of firings # of firings drop vel oc it y drop v e lo cit y kogation
irreversible

drop velocity decrease.

decel
reversible drop

velocity decrease.

firing stopped

firing resumed

Fig. 3. The effect of resistor fouling problems (kogation and decel) on drop velocity.

Nozzle Plugging — Decap

Water evaporates rapidly from ink in inactive, uncapped nozzles. Such water loss can result in dramatic changes in the physical prop- erties, and the phase behavior, of ink in exposed nozzles, which in turn can lead to poorly firing or completely plugged nozzles. To mit- igate these effects, low-volatility “humectant” co-solvents are added to commercial inkjet inks, at levels ranging anywhere from 5 to 50% of the total ink weight. Much work goes into picking the right com- bination of co-solvents in inks, so that a print head can have a long “decap time” or “idle time”; that is, the head can be left inactive and uncapped for prolonged periods, but still shoot drops accurately when firing commences.

Resistance to the diffusion of water in the ink channelsRink ≈ L

Dwater,ink



is usually ∼100 times greater than the resistance to the transfer of water from ink to the air phase at the nozzle opening 

Rair ≈ _Dwater,airδM



, since the mass transfer boundary layer thickness between the liquid and air phase (δM) is usually of the same mag-

nitude as the diffusion path length in ink channels (L), but the dif- fusion coefficient of water in air (Dwater,air) is ∼100 times greater

than the diffusion coefficient of water in the ink (Dwater,ink). As

water loss from a print head is ink-diffusion limited, a substantial water concentration gradient develops in ink channels. At typical

ambient relative humidities ranging from 30–80%, the equilibrium weight percent of water in exposed nozzles is estimated to range from∼5–30% respectively.14_{Furthermore, this water concentration}

gradient develops rapidly — the timescale for evaporation is t ≈ L2_/D

water,ink, and for typical ink channel of length L = 50 µm, and

assuming Dwater,ink ≈ 5 × 10−6cm2/sec, this means that the ink in

the nozzle region is equilibrated with the atmosphere in as fast as 5 seconds. The situation is depicted in Fig. 4.

Certainly, dealing with water loss is essential to formulating waterborne inks for inkjet printing. It is important to understand how ink properties, such as viscosity, as well as the solubility of various components, change with water concentration. This is true for both TIJ and PIJ heads — because PIJ heads can be designed to eject more viscous inks, PIJ inks often employ slightly higher loadings of solutes such as pigments and polymers, and thus may exhibit a greater tendency for complications, like precipitation, as water evap- orates. Furthermore, water concentration gradients in ink channels have been shown to give rise to the rapid migration of charged

Fig. 4. Cross-section view of the nozzle region and ink channels of an inkjet print head, showing the sharp water concentration gradient that evolves at an inactive, exposed nozzle.

pigment particles out of nozzles,15,16_{thus water loss can impact the}

composition of inks in nozzles in complicated ways. Overall, while the guiding principles above are employed to develop inks with good decap performance, ultimately some empiricism is involved. Other Things that Block Nozzles

The narrow (∼10−100 µm) ink channels in inkjet print heads can be easily obstructed. For example, air bubbles can lodge in channels, preventing ink flow. Surfactants used in the inks can sta- bilize bubbles, thus anti-foaming agents are sometimes added to inks to prevent excessive bubble formation/foaming. Furthermore, microorganisms can block ink channels. Thus, biocides are com- monly added to inks.12 _{Finally, pigmented inks add the additional}

complication that large (>500 nm) pigment particles may settle in nozzles, especially if print heads are inactive for prolonged periods. Thus, dispersions must be fine enough such that settling is not a major issue.