Microfluidic capillary flows: modelling & simulation
Background
Liquids that are influenced by dynamic interfacial effects,
i.e. by the physics occurring at their (often free) boundaries, are ubiquitous
throughout industry and nature. Such phenomena become particularly
relevant in the emerging fields of nano- and microfluidics, where a high
surface-to-volume ratio results in interfacial forces becoming the dominant
mechanism controlling a liquid's flow characteristics. For example, in microfluidics, one of the most important emerging technologies are '3D-Printers',
which are used for rapid prototyping/fabrication and have a huge advantage over
traditional methods in the manufacture of custom-made products; as is the norm
in biomedical applications (see Figure 1).
Many flows of technological importance with dynamic interfacial effects involve
the behaviour of liquid drops which are known to exhibit complex, yet
aesthetic, behaviour, such as that seen in the 'coalescence cascade' phenomenon
observed when a liquid drop is deposited onto a bath of the same liquid (see Figures 2 and 3). Experimental analysis of such phenomena are complex due
to the small spatio-temporal scales of interest and, consequently, a
mathematical model which accounts for the aforementioned events is highly
sought after to enable the parameter space of interest to be mapped and, where
appropriate, to identify bifurcations in the flow regime.
Techniques and Challenges
The development of a robust framework for the description of the aforementioned
technologically-relevant phenomena requires a collaborative approach, requiring
a close interaction between mathematical modelling, computational simulation
and theory-driven experimental analysis to ensure success. Our research
in OCCAM is concerned with the first two of these challenges, whilst many
experimental aspects are being conducted in the laboratory of Professor Sigurdur Thoroddsen in
KAUST, who is acknowledged as a world-leader in ultra high-speed imaging of
free surface flows, see, for example, images of the aforementioned coalescence
cascade, from his recent review article [3].
The flows of interest are complex unsteady free-boundary problems under the
influence of the forces of dynamic capillarity, inertia and viscosity. Consequently, to simulate practically important situations we have developed a
computational platform [4,5], which is the first to incorporate the
interface formation model. Until these recent developments, this
mathematically complex model, which describes flows where interfaces are formed
(e.g. wetting) or destroyed (e.g. coalescence) [6], has only been
applied to the small region of parameter space where asymptotic progress is
possible, despite much interest in the theory, [7].
Results
Our initial interest, driven by a collaboration with Kodak European Research, was in the dynamics of microdrops ejected from inkjet printers. One of our typical simulations, published in [8], shows the influence of the substrate's wettability on the drop's dynamics, which causes the drop to rebound of the hydrophobic substrate, whilst a comparison with experimental images from [9] can be seen in Figure 3. Furthermore, novel methods of flow control have been developed by patterning the substrate with areas of high and low wettability.
A natural extension of our work is to consider situations in which the
aforementioned phenomena form the microscale component of a macroscopic
process. An example is the propagation of wetting fronts through porous media,
where it is the collective influence of a number of 'pore-scale' wetting events
which govern the dynamics of the process. This has been considered in
[10] where the main 'modes' of pore-scale motion have been identified and allow
us to explain previously indescribable 'anomalous' experimental results
[11]. Recently, we have considered the impact of liquid drops which both
spread over and seep into the surface of a porous substrate [12].
Current Research
The Initial Stages of Coalescence & Wetting
Recent experimental results on the coalescence of liquid drops, have clearly highlighted the inability of conventional approaches to even qualitatively describe the early-time behaviour of this class of flows [13]. Using our computational code, we have studied these flows and provided a quantitative comparison between both the predictions of the conventional theory and the interface formation model with experimental results [14]. Current work is concerned with studying the global dynamics of the drop coalescence phenomenon, where a comparison with the optical experiments in Professor Sigurdur Thoroddsen's seminal paper [15] is possible.
Spreading Over & Into Porous Substrates
In collaboration with Dr Jeremy Marston at KAUST, we have been studying the dynamics of liquid drops which interact with powder substrates, with applications, in particular, in the pharmaceuticals industry. In a recent KAUST-OCCAM publication [16], we have characterised the influence of a powder bed's moisture content on a drop which spreads on top of it, showing that an optimal regime exists. Currently, a newly developed theory for spreading over porous substrates is being compared to experiments conducted for a range of different liquid and solid properties. Of particular interest is the analysis of bifurcations in the flow regime which occur, for example, as the wetting front moves ahead of the contact line at which the drop's free surface meets the solid.
References
[1] Bocquet & Charlaix 10
[2] Reshaping the future of sinus surgery
[3] Thoroddsen, Etoh & Takehara 08
[4] Sprittles & Shihmurzaev 12
[5] Sprittles & Shihmurzaev 12
[6] Shikhmurzaev 08. Capillary Flows with Forming Interfaces
[7] Blake 06
[8] Sprittles & Shikhmurzaev 12
[9] Dong, Carr, Bucknall & Morris 07
[10] Shikhmurzaev & Sprittles 12
[11] Shikhmurzaev & Sprittles 12
[12] Shikhmurzaev & Sprittles 13
[13] Paulsen, Burton & Nagel 11
[14] Sprittles & Shikhmurzaev 12