Droplet Generation From the Nanoliter to the Femtoliter Range
Albert-Ludwigs-Universität, Freiburg im Breisgau, Germay, (July 2006)Abstract
This thesis provides a general description of micro droplet generation at low and medium Weber numbers using analytical, numerical and experimental methods in an engineering manner of contemplation. Based on the presented results guidelines are
deduced to support the designing and operating
any
type of micro droplet generator.
In the first chapter the basic differential
equations are presented which are relevant
for the droplet formation in
the micro scale. Based on
these fundamentals analytical
and numerical descriptions
of the droplet formation process will be discussed
throughout the thesis
. Important dimensionless numbers like the Reynolds, the Weber
and the Ohnesorge number are introduced to describe
the fluid flow in microdimensions and the droplet formation qualitatively. Simple
analytical expressions are
derived for fluidic components like fluidic resistance, fluidic inertance, fluidic
capacitance, an outflow model of a nozzle, an inlet resistance and junction effects like
a contraction or an expansion
of the cross section. Such compact models can be applied
to build equivalent fluidic networks for more complicated fluidic systems. In this work some of the considered droplet generators are described by such a network approach.
The main part of the work is engaged with the fundamentals of droplet formation
especially with the necessary criteria for a droplet ejection. Therefore the Weber number respectively the critical Weber number is used to derive sufficient critical parameters for the droplet formation like the
critical velocity, the critical pressure, the critical time and the critical power. These parameters are introduced using an energetic approach based on the formulations stated in the previous
chapter. These critical values
are subsequently used to describe the
sufficient boundary conditions for a successful droplet generation with a give
n setup. Moreover these critical
values can also be used to depict the influence of the design and geometrical variations or parameter variations
of the applied liquid.
Since the energetic model is
not capable to state the dynamic
behavior of a given system it is complemented by a computational fluid dynamics (CFD) study concerning the dependence of the droplet
formation process on the
actuation dynamics. The role of the critical
values is successfully validated using the
CFD model. Based on this parameter maps for successful droplet generation in different droplet generation regimes like drop-on-demand, jet-on-demand or a jet ejection with subsequent Rayleigh breakup are presented. Finally a new, unique classification of the various
droplet generation mechanisms known today is proposed.
This classification is base
d on the underlying fluid dynamic working principle rather
than on obvious design elements of the system or historical reasons.
As a prominent example of a droplet
generator a bubble jet printhead design
provided by Olivetti I-Jet was studied intensively. This work was carried out within an
European project supported by the Federal Ministry
of Education and Research Abstract
VIII (BMBF), Germany (grant no. 16SV1607) within the EURIMUS program (IDEAL EM
42) applying the previously explained numerical and experimental methods. For a better understanding of the working principle the design and manufacturing of a bubble jet printhead and the characteristic values are presented. A fully three-dimensional
CFD simulation model was set up to simulate
the ejection process, the capillary filling and the thermal behavior of the printhead. Furthermore, the influence of specific design parameters and the opt
imization potential are explained in detail. The three-dimensional simulation model of the thermal inkjet printhead developed in this work provides a valuable approach to optimize the printhead
regarding droplet volume, droplet velocity, droplet quality and print frequency including 3D sensitive aspects.
The correctness of the used pressure
boundary condition and the simulation model in
the three-dimensional case was verified
by comparing simulations
with gravimetrical
and stroboscopic results. Thus, for the first
time a fully 3D simulation of a bubble jet
could be presented and validated. For the optimization or the design of a new printhead a variety of model parameters was investigated to study effects on, for example, geometry and ink properties.
The detailed description
of the bubble jet printhead
is complemented by the
examination of seven alternative droplet generators in a more general manner to verify the analytical approach and the criteria to predict the conditions for droplet formation
derived in chapter 3. The single droplet generators
are studied with respect to dosage
technology, experimental results, theoretical description or numerical models.
Conclusively the agreement with the considerations presented in chapter 3 is verified.
The results presented in this chapter are
partially based on work by other persons and are cited where appropriate to complete this thesis. The obtained findings confirm the analytic model approach in general. The derived critical parameters for droplet ejection are in good agreement for most of the systems. The critical parameters provide a sufficient condition to predict droplet breakup in general.
In one special case (TopSpot
dispenser) droplet breakup is even observed below the critical parameters. This observation is explained by the fact, that the necessary condition for droplet breakup
in fact is different from the conditions given by the critical parameters of the model.
To complete the thesis, guidelines for th
e systematic design of
droplet generators
are provided based on the presented results.
Because the quest for a suitable droplet
generator strongly depends on the main requirements and specifications of the system, it is distinguished therein between important main requirements along which the guidelines are developed. After the definition of these main requirements and the
presentation of general design rules, specific design rules are recommended for typical
applications. Using these recommendations an appropriate
droplet generator can be
designed from scratch or an existing
droplet generator can be optimized.
