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Journal of the European Ceramic Society 31 (2011) 2543–2550
Inkjet printing ceramics: From drops to solid

B. DerbySchool of Materials, University of Manchester, Oxford Road, Manchester M13 9PL, UKAvailable online 16 February 2011
Abstract
Inkjet printing is a powerful microfabrication tool that has been applied to the manufacture of ceramic components. To successfully fabricate ceramic objects a number of conditions must be satisfied concerning fluid properties and drop placement accuracy. It has been proposed that fluids are printable within the bounds 1 < Z < 10 (where Z is the inverse of the Ohnesorge number) and these limits are shown to be consistent with ceramic suspensions delivered by piezoelectric drop-on-demand inkjet printers. The physical processes that occur during drop impact and spreading are reviewed and these are shown to define the minimum feature size attainable for a given printed drop diameter. Finally the defects that can occur during the drying of printed drops are reviewed (coffee staining) and mechanisms and methodologies to reduce this phenomenon are discussed.
Keywords: Inkjet printing; Shaping; Drying; Suspensions
1. Introduction
Inkjet printing has major commercial applications in graph-ics output and other conventional printing operations. However, there has been developing interest in using inkjet printing to manufacture components with applications for: displays,1 plas-tic electronics,2 rapid prototyping,3 tissue engineering,4 and ceramic component manufacture.5 A significant and fundamen-tal difference between these new applications and the more widespread application of printing text or images is the behaiour of the printed ink droplets on the printed substrate. Most images are constructed by the deposition of discrete droplets and, in order to optimise resolution and contrast, these droplets are iso-lated and do not contact each other. In contrast, many of the new applications for inkjet printing envisage the manufacture of continuous 1-, 2-, or 3-dimensional structures (1-, 2-, or 3-D). Such structures require a continuous distribution of material and this necessitates contact and adhesion between individual drops after printing.Inkjet printing constructs objects by the precision placement of picolitre volumes of liquid and thus the initial interac-tion between printed material and a substrate is a liquid/solid interaction. Ultimately, the printed deposit undergoes a solid-ification process that can occur through solvent evaporation,

temperature induced solidification/gelation or chemical reac-tion.Considerations of the relative timescales of drop spreading and solidification indicate that there will be a significant period of time after printing when a liquid is present on a surface6 and thus the morphological stability of coallescing liquid films must be examined, as must the effects of the solidification process.

There has been a considerable number of publications on the use of inkjet printing in the manufacture of ceramics.7–17 These prior studies have used all inkjet drop generation technologies (continuous, thermal drop-on-demand and piezoelectric drop-on-demand) to successfully produce ceramic objects using both solvent evaporation and phase-change solidification. Industrial inkjet printing technology now uses piezoelectric drop-on-demand (DOD) generation technology and this is the chosen method for most applications in printing functional materials. The physical operation of these different printing technologies

and the reasons for the choice of piezoelectric DOD printing have been discussed in detail elsewhere6,18; hence here we will

confine our considerations to this technology. We will also only consider the printing of ceramic inks that solidify through sol-vent evaporation. Despite earlier work demonstrating that it is possible to successfully print cm scale objects using a wax based phase change ceramic ink,11–13 ceramic inks contain relatively low volume fractions of solid and thus there is considerable shrinkage and potential for distortion during dewaxing and sintering.14

In order to fabricate ceramic objects using inkjet printing, it is necessary to satisfy a number of requirements. First there is
a need to produce stable ceramic suspensions with defined fluid properties such that they can be passed through a droplet gener-ator and form regular drops. Second, these suspensions need to be delivered onto a substrate or onto a previously printed layer of solidified ceramic ink, with drops in sufficient proximity to each other to allow them to interact and form desired 2-D features. Next, the printed ceramic ink must undergo phase transition to a solid deposit. Finally, to produce 3-D structures the deposi-tion and drying/solidification processes need to be repeated on a layer of pre-deposited and dried material. Here we will consider each of these requirements and their optimization for the direct printing of ceramics.
2. Ceramic inks
Manufacturers of DOD inkjet printing equipment normally state a range of viscosity and surface tension within which inks may be successfully printed. However, this information is nor-mally provided for the benefit of formulating graphics inks and may not be directly applicable to the development of ceramic inks. This is because inks containing a significant volume frac-tion of ceramic particles in suspension have much higher density values than typical graphics inks, which typically have densities in the range 800–1000 kg m−3 and the behaviour of a fluid during printing depends strongly on its inertial behaviour.
The fluid rheological requirements for a printable ink are determined by the physics and fluid mechanics of the drop gen-eration process.6,18 The behaviour of fluids during inkjet printing can be represented by the Reynolds, Weber and Ohnesorge num-bers (Re, We, Oh):
Re = vρa , (1a)
η
We = v2ρa (1b)
,
γ
√ η
Oh = We = (1c)
,
Re (γρa)1/2
where ρ, η and γ are the density, dynamic viscosity and surface tension of the fluid respectively, v is the velocity and a is a characteristic length.Fromm identified the Ohnesorge number, Oh, as the appro-priate grouping of physical constants to characterise drop generation in an inkjet printer.19 Oh is independent of fluid velocity and is commonly used in analyses describing the behaviour of liquid drops. However, in Fromm’s publication, he defined the parameter Z = 1/Oh and from a simple model of fluid flow in a drop generator of simplified geometry, he pro-posed that Z > 2 for stable drop generation.19 Reis extended this through numerical simulation and proposed the following range, 10 > Z > 1, for stable drop formation.20 If Z < 1, viscous dissipa-tion prevents drop ejection from the printer and if Z > 10, droplets are accompanied by unwanted satellite drops. Jang et al. studied the DOD printability of a number of fluid mixtures of ethanol, water and ethylene glycol. Through this they explored a range of values of Oh and determined that the range of printability was
Fig. 1. Fromm’s parameter Z (Z = 1/Oh) influences the printability of fluids. Dashed lines identify the limits for printability proposed by Reis et al.20 Experi-mental points are plotted for a number of ceramic suspensions/inks: grey symbols indicate successful inkjet printing, black symbols indicate that no drops were formed, and white symbols indicate the presence of satellite drops along with the main printed drop.
4 < Z < 14,21 which is very similar to that determined by Reis’s numerical simulation.
There is now a substantial body of literature describing the inkjet printing of a number of ceramic suspensions and other fluids for non-graphics applications; unfortunately not all publications report sufficient information on the rheologi-cal properties of the ceramic suspensions to test this proposed criterion for printability in all cases. Fig. 1 presents such data that either reported the value of Oh (or Z) or reported sufficient data that it is easily calculated. The vertical dashed lines on the figure at Oh = 1 and Oh = 10 represent the limits for stable inkjet printing calculated by Reis.20 The experimental data is presented from eight fluid systems with a grey symbol indicat-ing the successful printing of individual drops, a black symbol indicates that fluids with these properties could not be printed, and finally a white symbol shows the cases where a fluid drop was successfully ejected but accompanied by one or more satel-lite drops. It is useful to separate these data into two sets: fluid systems 1–6 were delivered using piezoelectric DOD printers, while fluid systems 7 and 8 were delivered using a thermal DOD printer. The data obtained from experiments using piezoelectric DOD printing shows reasonably good agreement with Reis’s model, however that obtained in the one study using a thermal DOD printer shows very poor agreement,17 at least with the upper bound for the prediction of the onset of satellite drop for-mation. Özkol considered that one reason for the discrepancy between Reis’s prediction and their results could be the differ-ence in actuation between piezoelectric and thermal DOD inkjet droplet generators.17
The hypothesis that changes in actuation explain the dif-ferent behaviour observed between thermal and piezoelectric DOD inkjet printing is supported by an experimental study of drop and satellite formation in a piezoelectric DOD printer by Dong et al.22 They found that the drop formation mechanism and the conditions under which a given fluid formed satellites is also controlled by the shape and amplitude of the driving
pulse applied to the piezoelectric actuator. The driving pulse
in DOD printing is also known to control both the size of the ejected drop and its velocity.12,22,23 Reis demonstrated that for

the formation of drops using highly loaded ceramic suspensions, acoustic phenomena are important and that there are maxima in inkjet performance that correlate with acoustic resonances in the printhead.23 These are particularly important consider-ations given that typical industrial DOD printheads operate in the kHz regime. Other studies of inkjet printing for applications in graphics also emphasise the importance of acoustic phenom-ena and the need for these to damp before the drop generator is refilled prior to delivering subsequent drops.18 Indeed the shape and form of the actuating waveform is considered an important aspect of the design of piezoelectric DOD printing systems.
However, from Fig. 1, we can see that for the studies that used piezoelectric DOD printers, Reis’s criterion for a printable fluid20 seems to show reasonable agreement with data and it is also in broad agreement with the only explicit study of inkjet printability of fluids by Jang et al.21 Thus despite a possible oversimplification of the conditions that lead to the formation of satellite drops, we suggest the condition 10 > Z > 1 (where Z = 1/Oh) can be used as a guide to the development of fluids for ink jet printing.
The suitability of a fluid for inkjet printing can be roughly assessed by its Ohnesorge number. However there are other lim-its of fluid behaviour that impose additional limits to practical drop generation. In order to generate a small radius drop, the sur-face tension and associated Laplace pressure must be overcome before a drop can be ejected from a printer. Duineveld proposed that this can be described by a minimum value of the Weber number, We > 4, below which there is insufficient fluid flow to overcome surface tension.24 A final bound to printability is given by the onset of splashing that occurs if a drop hits the substrate with velocity above a critical threshold. From the work of Stowe and Hadfield,25 this occurs when We1/2Re1/4 > 50. These limit-ing bounds define a region of the parameter space of We and Re, within which DOD inkjet printing is possible.5,6 Fig. 2 shows
Fig. 2. Inkjet printing is practical for a limited range of fluids and printing con-ditions. This is illustrated here in a parameter space defined by axes of Reynolds and Weber numbers. Based on a diagram originally published in Ref. 5.
this parameter space and the region suitable for DOD inkjet printing. Drop velocity increases diagonally, as indicated and has lower and upper bounds that are defined by the appropriate limits of drop ejection and splashing, orthogonal to velocity is the Ohnesorge number, which defines the limits of the fluid prop-erties, thus Fig. 2 can be considered representing a guide to the limits of both fluid characteristics and drop dynamics consistent with the practical use of piezoelectric DOD inkjet printing.
3. Drop impact, spreading and coalescence
As discussed earlier, an important aspect of inkjet printing in manufacturing technology is the process by which adjacent drops interact to form a solid. In all cases the liquid drop will interact with a solid substrate. Following deposition there will be a period when the drop’s shape is controlled by fluid pro-cesses prior to solidification. Thus an important consideration is the appropriate time constants that apply to the mechanisms of surface spreading and solidification. Here we are confining our discussion to solidification through evaporation. Given that droplet solidification time scales are normally in the regime of around 1 s and droplet deposition rates are >1 kHz, we need to consider the interaction between many liquid droplets on the surface of the substrate. It is possible to use interlacing and sequential printing passes to deposit isolated drops, allow them to solidify and then fill in the gaps to produce a printed plane. However, this
methodology produces an irregular deposit with poor surface roughness for each printed layer,9 with a conse-quent risk of defects from poor penetration of the liquid. If printing occurs with appropriate drop spacing to allow over-lap before solidification, the interaction between adjacent liquid drops and the consequent influence of surface tension will tend to produce smooth surfaces and eliminate possible defects between solidified drops.
When a liquid drop impacts a planar substrate it will deform and spread to cover the substrate, ultimately achieving an equi-librium sessile drop configuration. Yarin has recently reviewed the impact of drops over a size and velocity range that intersects those relevant to DOD printing.26 The typical range of drop size (radius from 5 to 50 mm) and velocity (1 < v < 10 m s−1) is
such that the initial deformation of the drop will be controlled by dynamic impact and viscous dissipation processes.6,18,26 How-
ever, this initial stage of drop deformation is expected to have finished after a few ms and subsequent spreading to equilibrium will be driven by capillary forces.27 A schematic representa-tion of the timescales associated with drop deformation after impact is presen