Position Analysis of the Atomiser Unit of an Aerosol-on-Demand

Jet-Printhead by means of Computational Fluid Dynamics

Martin Ungerer, Tim P. Walter and Ingo Sieber

Institute for Automation and Applied Informatics, KIT, Hermann-von-Helmholtz-Platz 1,

76344 Eggenstein-Leopoldshafen, Germany

Keywords: Computational Fluid Dynamics, Modelling, Simulation, Tolerancing, Additive Manufacturing,

Aerosol-on-Demand.

Abstract: In this paper we present position analysis of the atomiser unit of a newly developed concept of a printhead

for Aerosol-on-Demand (AoD) jet-printing using fluid dynamical modelling and simulation. In our concept

of the AoD printhead, the ink is atomised by ultrasonic excitation and focussed by a sheath gas in a converging

nozzle. Critical for the functioning of the AoD printing process is a proper positioning of the atomiser unit

inside the printhead. Using computational fluid dynamics (CFD), we present a position analysis of the

atomiser unit with respect to axial misalignment and tilting.

1 INTRODUCTION

Printing processes have been discussed for a few

decades with regard to their potential applications for

additive manufacturing of electronics, also referred to

as printed electronics (PE) or functional printing (Cui

2016; Gengenbach et al. 2020). In contrast to

conventional, subtractive processes for electronics

fabrication, PE enables an optimised material usage

and thus less waste (Dyson 2022). Inks that contain

functional dielectrics, semiconducting or conducting

materials are printed onto a substrate in layers

according to the structure of the component to be

realised (Cui 2016). Moreover, printing of functional

inks offers new opportunities for the realisation of

novel devices and systems with special physical,

optical, or chemical properties (Sirringhaus and

Shimoda 2003; Sieber, Thelen, and Gengenbach

2020, 2021; Magdassi 2010).

Besides conventional, contact-based techniques

such as gravure-printing and screen-printing that need

printing forms for the ink transfer, also digital,

contactless processes are used in PE (Zikulnig et al.

2023). Among the digital printing techniques, piezo

inkjet is considered the most important principle. It

has already reached the necessary maturity for

industrial use, but it is limited in terms of ink viscosity

https://orcid.org/0000-0003-2811-785

and resolution (Kwon et al. 2020). To overcome these

limitations, other technologies such as aerosol jet

printing (AJP) and electrohydrodynamic jet are being

developed (Cui 2016; Kwon et al. 2020). However,

electrohydrodynamic jet as well as inkjet still face

some challenges with regard to printing on non-planar

substrates (Kwon et al. 2020; Oakley and Chahal

2018).

Aerosol jet printing (AJP) is a promising process

in the field of functional printing of new materials,

especially nanomaterial-loaded inks (Ganz et al.

2016; Gupta et al. 2016). In contrast to the inkjet

process, AJP offers higher resolution and the

possibility to print on 3D structures (Mette et al.

2007; Neotech 2021) or even to bond multiple chip

layers together, replacing wire bonding due to its

large stand-off distance of several millimetres

between nozzle and substrate (Hedges and Marin

2012).

A new principle for an Aerosol-on-Demand

(AoD) jet-printhead is being developed at our

institute (Ungerer et al. 2018). In contrast to

conventional aerosol printing systems, the atomiser

unit consisting of a capillary and a piezo actuator for

ultrasonic excitation is directly integrated into the

printhead. This eliminates all supply lines, dead

volumes in the ink supply and aerosol preparation

equipment. With an established sheath gas flow,

126

Ungerer, M., Walter, T. and Sieber, I.

Position Analysis of the Atomiser Unit of an Aerosol-on-Demand Jet-Printhead by means of Computational Fluid Dynamics.

DOI: 10.5220/0012131000003546

In Proceedings of the 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2023), pages 126-133

ISBN: 978-989-758-668-2; ISSN: 2184-2841

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

aerosol generation occurs only when needed, and

aerosol generation can be switched at any time and at

high frequency. Thus, a compact system design can

be developed that allows printing operation in all

spatial directions, broadly tunable nozzle-to-substrate

spacing, and jet-on-demand operation (Ungerer

2020).

Computational fluid dynamics (CFD) models are

used to simulate the aerosol printing process and to

design the printhead (Sieber et al. 2022; Ungerer

2022). A key issue for stable operation is the accurate

positioning of the atomiser unit in the printhead. In

this paper, fluid dynamic simulations regarding the

positioning of the atomiser unit in the printhead are

presented and the results are discussed. Assembly

rules, ensuring robust operation, can then be derived

from these simulations.

This paper is organised as follows: Section 2

presents the principle set-up of the AoD jet-printhead,

in Section 3, a model simplification which is used for

the CFD calculation of the influences of the position

variation of the atomiser unit is presented. Section 4

shows the simulation results for the individual

position tolerances axial misalignment and tilt.

Section 5 deals with the discussion of the results and

Section 6 will close the paper with conclusions.

2 SET-UP OF THE AoD

JET-PRINTHEAD

The AoD jet-printhead consists of the following

components: the atomiser unit (consisting of a

capillary and piezo actuator), where the aerosol is

generated by ultrasonic atomisation, the

antechamber, in which the flow homogenisation of

the sheath gas takes place, the mixing chamber, in

which the incoming sheath gas meets the generated

aerosol, and the nozzle, which focuses the aerosol

together with the mass flow of the sheath gas. Fig. 1

Figure 1: Schematic of the principle design.

shows the schematic of the principle design of the

inner contour of the aerosol print head.

Design for manufacturing of the AoD jet-

printhead is described in Ungerer et al. 2022, the

parameters resulting from this design are summarised

in Table 1.

Table 1: Design parameters of the fabrication process

(Ungerer et al. 2022).

Paramete

Value

Nozzle angle α

[°]

Nozzle angle α

[°]

Nozzle exit diameter d [mm]

As material for the print head, the aluminum alloy

AlMgSi1 is selected.

3 MODELLING OF THE AoD

JET-PRINTHEAD

The modelling of the AoD printhead is based on CFD,

a numerical technique for solving fluid dynamics

problems. We use Ansys Fluent version R20.1 as the

CFD tool for modelling and simulation.

For our modelling approach, we have chosen the

Reynolds-averaged Navier-Stokes (RANS) equations

(Eqs. 1, 2).

𝜕𝜌

𝜕𝑡



𝜕

𝜕𝑥





𝜌𝑢





0

(1)

𝜕

𝜕𝑡



𝜌𝑢







𝜕

𝜕𝑥



𝜌𝑢



𝑢







𝜕𝑝

𝜕𝑥





𝜕

𝜕𝑥



𝜇



𝜕𝑢



𝜕𝑥





𝜕𝑢



𝜕𝑥





𝛿



𝜕𝑢



𝜕𝑥







𝜕

𝜕𝑥





𝜌𝑢





𝑢







(2)

The continuity equation, which describes the

conservation of mass, is described by Eq. 1. ρ is the

density and u

is the mean velocity. Eq. 2 represents

the conservation of momentum, where p is the static

pressure and the symbol δ

denotes the Kronecker-

Delta. To account for turbulence, we use the k-

𝜔

𝑆𝑆𝑇

(shear stress transport) model, a compressible

turbulence model, where k denotes the kinetic energy

of the turbulence and ω the specific dissipation rate.

The calculation of the particle (droplet) tracks follows

the Euler-Lagrange approach, where the liquid phase

is treated as a continuum by solving the RANS

equations, while the dispersed phase is solved by

tracking a large number of particles through the

calculated flow field of the continuous phase. A more

detailed discussion of the equations used in our

approach can be found in (Sieber et al. 2022 and

Position Analysis of the Atomiser Unit of an Aerosol-on-Demand Jet-Printhead by means of Computational Fluid Dynamics

127

Ungerer et al. 2022). In addition, the interested reader

is referred to Wilcox (2006) and Menter (1994) for

detailed information on the calculation of these

parameters.

Using the RANS equation is generally favourable

in terms of computational effort and time, and is thus

very suitable for the calculation of complex turbulent

flows (Ansys 2021). A wide range of engineering

applications can be modelled based on the RANS

equations.

Fig. 2 shows the meshed geometry model of the

printhead. The mesh was optimised using a mesh

independence study resulting in 2.1∙10



elements.

The meshing of the printhead (left part in Fig. 2) is

performed with hexagonal elements. The density of

the mesh is controlled in a way that at the inflation

layers, forming the mesh near the walls, the element

size was 80 µm and in the region between the

capillary and the nozzle exit, an element size of

33 µm is achieved to obtain improved resolution in

the atomisation region. The free space (right part in

Fig. 2) is finely meshed in its centre to obtain a high

resolution of the free jet. Outwardly, the meshing is

done with larger elements. This mainly controls the

number of elements in order to limit simulation time.

Figure 2: Meshed geometry model of the printhead.

3.1 Modelling of the Atomiser Unit

Modelling the ink, the Euler-Lagrange model is used

which involves a particle-related consideration of the

discrete phase.

The ink itself is modelled as distilled water so that

the discrete phase consists of atomised droplets.

Replacing the functional ink with distilled water in

the model is permissible because aerodynamic

focusing does not depend on the dynamic viscosity of

the ink or the particle content in the ink. The

generated aerosol is modelled in Fluent using a cone

model (see Fig. 3), which means the generated

aerosol is described by its origin, the cone axis, the

cone angle, radius, diameter of droplets, diameter

distribution, exit velocity of the droplets, and aerosol

mass flow.

Figure 3: Ansys Fluent cone model (Ansys 2021).

The parameters used for modelling the aerosol source

are depicted in Tab. 2.

Table 2: Simulation parameters of the aerosol.

Paramete

Value

origin

cone axis

cone angle

radius

max. diameter of droplets

max. exit velocity

max. aerosol mass flow

[mm]

[°]

[µm]

[m/s]

[kg/s]

(17.5/0/0)

(1,0,0)

1.21 ⋅10

-5

3.2 Simplification of the CFD-Model

In the following position analysis, the influence of the

capillary position on the aerosol jet is investigated. To

set a certain alignment value of the capillary, the

position of the (physical) capillary in the geometry

model must be changed each time. In a next step, the

meshing has to be adapted to the new geometry. In

order to reduce this high modelling effort, we analyse

in preliminary investigations whether it is mandatory

to model the capillary in the geometry model. The

assumption is that the geometry modelling of the

capillary can be omitted, since it lies upstream with

respect to the flow of sheath gas and aerosol. If this

simplified CFD model can be used for the positioning

calculations, the alignment investigation is simplified

to the adjustment of the parameters of the cone model

and the recalculation of the mesh in the changed area.

To analyse whether this simplification is justified,

we performed simulations of the velocity distribution

of the discrete phase (droplet jet) and the jet diameter

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

128

in the free space at different distances from the nozzle

exit. In each case, these simulations were performed

with and without the geometric modelling of the

capillary.

Fig. 4 shows the velocity distribution of the

droplet tracks in a representation in which the

computational mesh is also shown: top of Fig. 4

shows the droplet tracks with modelled capillary, in

the lower representation the capillary is not modelled.

The velocity range as well as the velocity distribution

over the streamlines are in good agreement between

both models. Also, the focusing of the streamlines

matches well.

Figure 4: Velocity distribution of droplet tracks with

modelled capillary (top) and without modelling the

capillary (bottom).

Fig. 5 shows the contour plots of the flow field,

also top with the modelled capillary and bottom

without. In the contour plots a good qualitative

agreement between the flow fields with and without

capillary can also be observed. The velocity range of

the flow fields are also in good agreement.

A quantitative representation of the droplet

velocity is shown in Tab. 3 at two distances to the

nozzle exit: 1 mm and 23 mm. Again, the results are

depicted for the modelled capillary and without

modelling the capillary. In both distances to the

nozzle exit the velocity values correspond very well.

Figure 5: Contour plots of the flow field with modelled

capillary (top) and without (bottom).

Table 3: Velocities of the discrete phase at 1 mm and 23

mm distance to nozzle with and without modelled capillary.

Distance to

nozzle exit

1 mm

Distance to

nozzle exit

23 mm

With capillary 4,97 m/s 1,52 m/s

Without capillary 4,97 m/s 1,52 m/s

To determine the jet diameters, planes

perpendicular to the propagation direction of the jet

are placed in the model at defined distances from the

nozzle exit. At this positions the concentration of the

discrete phase (droplets in the example) is

determined. This procedure is excellent for gaining an

impression of the jet width at these positions.

However, since a different meshing was chosen for

the two models with and without capillary (due to the

different geometric model) and the evaluation takes

place at the nodes of the elements, a direct transfer of

the individual concentrations in both plots may differ.

However, this does not affect the general statement

about the jet widths.

The concentration of the droplets is determined in

planes at different distances from the nozzle outlet;

Fig. 6 and Fig. 7 show the droplet concentrations at

distances of 2 mm and 15 mm from the nozzle outlet,

respectively. Fig. 6 shows the distribution of the

droplet concentration for the geometry model with

capillary. Fig. 7 shows the corresponding for the

model without capillary.

Position Analysis of the Atomiser Unit of an Aerosol-on-Demand Jet-Printhead by means of Computational Fluid Dynamics

129

Figure 6: Droplet concentrations as a function of distance

to cone axis with capillary. 2 mm distance to nozzle exit

(top), 15 mm distance to nozzle (bottom).

Figure 7: Droplet concentrations as a function of distance

to the cone axis without capillary. 2 mm distance to nozzle

exit (top), 15 mm to nozzle distance (bottom).

Comparing Fig. 6 with Fig. 7 where the

distribution of droplet concentration is depicted in

case of the model without cavity, we find them in very

good agreement.

In summary, the model simplification by omitting

the geometric modelling of the capillary, describes

the flow behaviour of the discrete and the continuous

phase sufficiently well. Thus, the alignment

simulations can be carried out with this simplified

model.

4 POSITION ANALYSIS

In order to investigate the influence of the positioning

of the atomiser unit in the printhead, simulations of

aerosol generation and focusing are carried out for

different position variants of the atomiser unit. The

two most important alignment parameters are axial

alignment and tilting of the atomiser unit within the

printhead. In order to evaluate the functionality of the

AoD jet-printhead as a function of the positioning of

the atomiser unit, the most important criterion is that

there is no contact of the aerosol with the inner wall

of the nozzle. Such wall contact would not only result

in contamination of the inner wall, but could also lead

to clogging of the nozzle outlet and consequent

collapse of the printing process, or to subsequent

dripping of the ink running down the inner wall and

consequent destruction of the printed image. Another

criterion is that a comparable jet width is achieved to

ensure a defined print image.

The influences of these two alignments are

discussed in the following two sections.

4.1 Axial Alignment of the Atomiser

Unit

To model the axial origin displacement of the aerosol,

the calculation mesh must be adapted. This is done by

shifting a reference plane in the geometry model and

a subsequent, automatic remeshing. By adjusting the

mesh via the geometry change using the reference

plane, a fine mesh in the aerosol origin is ensured.

Furthermore, it is ensured that the mesh in the nozzle

interior is always generated identically in the core, so

that a comparison can be made in the front nozzle

interior independent of the mesh. Likewise, the entire

mesh in the free space is independent of the aerosol

origin and always identical.

Positions at 2 mm intervals in the range [9.5 mm,

23.5 mm] are examined. The position of the piezo

actuator serves as reference (see Fig. 1). For all

positions inside the defined range no wall contact was

observed, hence the most important criterion for

successful printing is fulfilled.

Figure 8 shows the velocity distributions of the

droplet tracks for the two extreme positions (9.5 mm

and 23.5 mm) and the position 15.5 mm.

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

130

Figure 8: Velocity distribution of droplet tracks for different

axial alignments: 9.5 mm, 15.5 mm and 23.5 mm (from top

to bottom).

An examination of the velocity distributions of

the droplet tracks for the different axial positions of

the atomiser unit yields comparable velocity values

and also droplet curves. Of particular interest are the

droplet tracks in the free space: here, both the

velocities and the jet widths are independent of the

axial positioning of the atomiser unit.

Hence, the printhead system, as it is set up, is very

robust with regard to an axial positioning of the

atomiser unit.

4.2 Tilting of the Atomiser Unit

Since the tilts of the cone axis do not cause any

changes in the mesh, there is no need to modify the

computational mesh depending on the angle of

inclination of the aerosol origin.

In the description of the aerosol source (see Tab.

1), a tilting of the capillary in the atomizer unit leads

on the one hand to a change in the orientation of the

cone axis and on the other hand to a displacement of

the origin (see Fig. 9). The values of the considered

tilt angles and the corresponding offset values are

shown in Tab. 4.

Figure 9: Capillary tilt of the atomiser unit.

Table 4: Tilt angles and corresponding offset values.

Tilt [°] 0.21 0.42 0.64 0.85 1.06

Offset

[mm]

0.05 0.1 0.15 0.2 0.25

Tilt [°] 1.27 1.70 2.12 4.25 8.52

Offset

[mm]

0.3 0.4 0.5 1.0 2.0

Figure 10 shows the velocity distributions of the

droplet tracks for tilt angles of 0.21°, 1.06°, 4.25°, and

8.52°. In the sequence of simulation results from Fig.

10 a) to d), the deflection of the aerosol source and

the associated skew propagation of the droplets

within the nozzle can be clearly seen. In all the cases

shown, the inflowing sheath gas, together with the

contour of the nozzle, achieves a focusing of the

aerosol jet at the nozzle outlet. For larger angles (see

Fig. 10 c) and d)), it can be seen that the aerosol jet

does not emerge from the center of the nozzle, but has

an offset. The velocity profile of the jet in the free

space remains relatively stable as a function of the tilt,

but a slightly increased velocity magnitude is

observed for larger tilt angles (accompanied by a

larger offset of the source origin).

The simulations of all investigated tilts and their

corresponding offsets show no wall contact, which is

defined by an exit condition of the droplets. Again,

the most important criterion for successful printing is

fulfilled. However, from a tilting angle of the

capillary of 4.25° and the associated offset of 1 mm,

droplets are also found in the outermost mesh

elements close to the wall, so that possible wall

contact cannot be fully ruled out here (see Fig. 10 c)

Position Analysis of the Atomiser Unit of an Aerosol-on-Demand Jet-Printhead by means of Computational Fluid Dynamics

131

and d)). A stable focusing behavior can be assumed

for capillary tilts of less than approx. 2°.

Figure 10: Velocity distributions of the droplet tracks for

tilt angles of 0.21° (a)), 1.06° (b)), 4.25° (c)), and 8.52° (d))

and corresponding offsets.

5 RESULTS AND DISCUSSION

A key issue for stable operation of the AoD is the

accurate positioning of the atomiser unit in the

printhead. To investigate the sensitivity of the

operation in this respect, analysis of the positioning

of the atomiser unit in the printhead are conducted for

axial misalignment as well as for a tilt of the atomizer

unit. Analysis of the axial positioning of the atomiser

unit shows that operation of the printhead is very

robust with respect to axial positioning. No influence

on the droplet tracks can be observed: both the

velocity variations within the tracks and the jet widths

show no effects with respect to the axial orientation

of the aerosol source in the investigated range [9.5

mm, 23.5 mm]. Regarding the axial positioning, we

can state that the setup used is very robust.

Analysing the tilt of the atomiser unit, both the tilt

angle and the offset of the aerosol source from the

origin are considered. The simulations of the tilt

angles show no direct wall contact for an angle range

up to 8.52°. However, since the droplet tracks are

within the outermost mesh elements towards the wall

for angles larger than 4.25°, a possible wall contact

cannot be completely excluded here. Furthermore, it

can be observed that for larger tilts, the focused

aerosol jet leaves the nozzle exit not in the center, but

under an offset. From this it can be concluded that

stable focusing with regard to tilting of the atomiser

unit is achieved for angles smaller than 2°. Due to this

sensitivity of the operation with regard to tilting of the

atomizing unit, the tilt must be controlled during

assembly.

6 CONCLUSIONS

In this article, the influence of the atomiser unit

alignment of an Aerosol-on-demand jet-printhead for

functional printing is presented using CFD

simulations. Two relevant alignment parameters are

investigated in this article, namely axial alignment

and tilting of the atomiser unit. In order to simplify

the simulation procedure, it is shown in a first step

that the capillary as a physical unit does not have to

be represented in the model. This avoids the need to

change the position of the (physical) capillary in the

geometry model for each alignment value of the

capillary and subsequently to adapt the meshing to the

new geometry.

Based on this simplified model, the effects of the

atomiser unit alignment on the droplet tracks are

determined. The velocity profiles and the focusing of

the aerosol jet within the nozzle and in the free space

are evaluated.

Two conditions must be met for the reliable

function of the AoD jet-printhead:

1. generation of a stable and focused aerosol jet

2. prevention of wetting of the inner nozzle wall

by the aerosol.

SIMULTECH 2023 - 13th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

132

Under these conditions, our analysis shows that

the setup is robust with respect to the axial positioning

of the atomizer unit. In terms of inclination, we have

found that an tilt of up to 2° is tolerable, but

inclinations beyond this should be prevented by

suitable mounting methods.

The results of this work will be used to derive

rules for the assembly and installation of the atomiser

unit in the AoD jet-printhead.

ACKNOWLEDGEMENTS

The authors would like to acknowledge Achim

Wenka (IMVT, KIT) for his continuing support in the

field of computational fluid dynamics and Klaus-

Martin Reichert (IAI, KIT) for soft- and hardware

support.

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