AIMS Conference (5-9 July 2018, Taipei, Taiwan)

On July 5/9, I took part to the 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications in Taipei.
This conference aims at fostering and enhancing interactions among mathematicians and scientist in general. It has featured 135 special sessions with a broad range of topics. Keynote lectures were given by famous mathematicians (A. Buffa, V. Calvez, S. Peng, J. Ball, just to cite a few).

AIMS Conference schedule at a glance

I was in particular interested to two special sessions devoted to kinetic theory: "Models and Numerical Methods in Kinetic Theory" (where I was invited to give a talk) and "Kinetic and Related Equations: Collisions, Mean Field, Organized Motion".
Although kinetic equations have been traditionally applied to rarefied gas dynamics and plasma physics, these special sessions have confirmed an emerging trend in kinetic theory, namely the use of its theoretical framework to study topics in fields which are apparently far from fluid dynamics like the emergence of organized collective behaviour in vehicular traffic, crowds, swarms, social systems and biology. This wide range of new applications and the benefits that these studies can potentially bring to the society has significantly revived the interest in kinetic theory.
A detailed description of sessions along with the abstracts of presented talk can be found at the conference's website (

Overall, I was pleased to partecipate to the conference. The only negative aspect was that typhoon Maria stroke Taipei the day I had to flight back home. As a consequence, my flight was delayed and I was forced to spend almost two days segregated in hotel!

Musical Boiling

Boiling is an important feature in many engineering processes, such as in the steam cycle in many power plants. It is also a highly multiscale phenomenon, with boiling bubbles nucleating on nanoscale features of solid substrates and growing to sizes of the order of mm. Researchers at Massachusetts Institute of Technology (MIT) have demonstrated the drastic effects that alterations at the nanoscale can have on boiling nucleation with the use of surfactants. By applying a voltage to certain parts of a substrate, the surfactants effectively render the substrate hydrophobic and can rapidly induce boiling at very specific regions of the substrate.

The rate at which boiling can be switched on or off is also particularly impressive, although as we all know the ultimate test for how fast scientists can control a process is by syncing it up with classical music… MIT calls this piece “Ode to Bubbles”, enjoy!

Cho, H. J. et al. Turning bubbles on and off during boiling using charged surfactants. Nat. Commun. 6:8599 doi: 10.1038/ncomms9599 (2015)

OpenFOAM's I/O Problem (and solution)

Much of the MNF group's research output has been based around our solvers (mdFoam+ and dsmcFoam+) which are written in the OpenFOAM software framework. OpenFOAM is well known and well acknowedged as a very flexible and stable environment to develop new solvers, however it has a bit of a reputation for scaling badly on big super computers, leaving people to assume it should only be used when your problem can be tackled by a stand-alone workstation or using only a few nodes on your favourite big HPC system. This blog post will talk about the new collated file format introduced into OpenFOAM 5.0 and how it might be the beginning of the end for this mentatility.

The question is, where has this perception come from and, more importantly, is it right? If you search for the issue of OpenFOAM scalability on HPC then you will find numerous articles and topics, what is interesting though is how few are a) looking at massive scalability (most consider running on a few CPUs) b) how few recent articles there. 

The question therefore is whether OpenFOAM actually does perform badly on HPC system or is it an out of date perception. This is a hard one to answer fully as OpenFOAM has been around for a good few decades and has a number of different solvers to consider. In theory, each should parallelise as well as the others as they are all built on top of same basic libraries, however of course some algorithms work better in parallel than others and some of the solvers may not have receieved the same attention as others. Generally speaking though the methods used in OpenFOAM are sound, it employs typical static domain-decomposed non-blocking MPI in most of its solvers and allows well-known decomposition libraries such as Scotch to be used to minimise communication overhead. Undoubtedly this could all be optimised better if it were to receieve lots of attention from the HPC community but are there any other problems blocking this?

The MNF group runs many of its simulations on the UK's national HPC service Archer, run by the EPCC, a Cray XC30 machine. At the moment they provide access to OpenFOAM 4 on their system. Arguably OpenFOAM has a bad reputation for use on this system but the same problems are repeated on many systems, especially those that use a Lustre parallel file system and that is the way that OpenFOAM creates and deals with its files.

For every MPI process created, a new folder is also created and a set of files. In cases where lots of output is created during a simulation this can easily mean there are thousands of files per processor created on disk, Archer provides a hard limit per user on the number of files that can be created in their storage and also that they can have open in memory at any one time, parallel runs using OpenFOAM quickly exceed this and can have a major impact on the parallel file system for other users if the limits wern't there, as a result of this OpenFOAM has developed a bad reputation. It is worth noting that this approach is an entirely valid, if outdated, way of dealing with I/O when using MPI.

The good news is that, as of OpenFOAM 5.0, this has been changed and now there is a new way of writing files to disk known as the collated file format. This is a simple idea, rather than each MPI process creating its own folder, there is now just one set of files written by the master process and all other processes transfer data back via MPI. If you get hold of the latest development version via the OpenFOAM-dev repository then this has been further developed so you can mark individual MPI processes as "master node" writers to spread the load and reduce communication overhead as then processes only need to talk to each other within the same node. Therefore, if you were running on 48 nodes of Archer then you would have 1152 MPI processes with 24 on each node, so you would have 48 sets of files instead of 1152. This is really quite significant as if you assume there are 1000 files per set by the end of a simulation then you have 48,000 rather than 1,152,000!

We have done some basic testing and have found using the new file format to be about 50% faster on Archer using the flow past a motorbike tutorial case with simpleFoam and 48 nodes. 

Of course the really exciting thing about this development is that the HPC community can now really get stuck in to the challenge of properly benchmarking OpenFOAM over many more MPI ranks than it has previousely attempted as cases now scale, this will therefore hopefully lead to rapid development of the underlying MPI approach and only serve to increase performance of OpenFOAM across all of its solvers, including the MNF group codes!

Thermal fluctuations in nanoscale fluid interfaces

My current research focuses on the hydrodynamics fluctuations in nano-jets. The earliest research (Moseler M., Sci. 2000) found new double-cone rupture profiles due to thermal fluctuations (molecule motions), which the Navier-Stokes models failed to predict. Our research shows that these fluctuations not only affect the final rupture profiles but also change the wavelengths of perturbations. 

Moreover, I have found that thermal fluctuation effect widely exists in the nanofluids, especially those with the interfaces. So I summarized some previous research in the figure above and listed the literature (links) below.

(1)Nanojet flows:  
[1.1] Moseler M.,  2000
[1.2] Egger J., 2002
[1.3] Hennequin Y., 2006
[1.4] Kang W., 2007
[1.5] Petit J., 2012
(2)Drop coalescence
[2.1] Dirk G. A., 2004
(3)Fluid mixture
[3.1] Kadau k., 2007
(4) Moving contact lines
[4.1] Perrin H., 2016
[4.2] Belardinelli D., 2016
[4.3] Davidovitch B., 2005
(5) Bubble
[5.1]  Gallo M., 2018
(6) Thin film
[6.1] Grun G., 2005
[6.2] Fetzer R., 2007
[6.3] Diez J. A., 2016

Although the phenomena above is distinct, mathematical models were derived from the same equations, Landau and Lifshitz Navier-Stokes equations (LLNS). What's more, particle methods (MD or DSMC) can be employed to support the new physical models as numerical experiments.
Therefore, there are lots of opportunities for us to employ both math models and simulations to study this interesting topic. 

SWEP Workshop, Brighton

On May 17/18 Rohit and I gave invited talks at the inaugural Surface Wettability Effects on Phase Change Phenomena (SWEP) workshop in Brighton.  This was organised by Joel De Coninck, our first Visiting Scientist of the Programme, and Marco Marengo who are both experts in this field - their hope is that this workshop will become a yearly fixture.  They opened the workshop by reminding the audience of the incredible effects that wettability can have: adding just one layer of molecules to the top of a surface can completely change the shape of mm-sized drops that sit on top of them, which is the equivalent in scale of ants being able to change the shape of mountains (apologies for the poor quality photo)!

Rohit and I gave the last and first talks, respectively, with Rohit impressing the audience with his work on acoustofluidics whilst I spoke about 3 canonical problems involving kinetic effects in interfacial flows, including work with Mykyta (drop impact), Anirudh (drop evaporation) and Duncan.

There were many interesting presentations on a wide range of phase change phenomena.  I particularly enjoyed Carlo Antonini's talk "License to Freeze" which reviewed methods for controlling ice formation on surfaces (including an inverse Leidenfrost effect, where evaporation occurs from the underlying substrate rather than the impacting drop drop, which we could potentially simulate) and Daniel Attinger's talk on "What is the Optimum Wettability of a Pool Boiling Heater?", which carefully explained the experimental and theoretical challenges of understanding the subtle interplay between wettability, phase change and heat transfer driven by bubble formation at a (complex) solid surface.

All in all the workshop was very enjoyable and the level of scientific discussion was high (i.e. Rohit and I got grilled!) - I would recommend it to our group members in future years.

Polymer Flooding for Enhanced Oil Recovery

Only upto 40% of the original oil in place could be extracted from the oil reservoir using water flooding, the so-called primary recovery method . A large portion of oil is left behind as immobile ganglia. The enhanced oil recovery (EOR) techniques, the secondary recovery methods, are hence needed to extract the remaining oil. Polymer flooding is one such technique. In this EOR techniques, the injected water is supplemented with the long chain polymers which makes the injected water an visco-elastic fluid with a tunable viscosity. The primary purpose of adding polymer is to increase the viscosity of the flood water so that he mobility of injected water becomes less then that of oil which maximize the sweep efficiency, creating a smooth flood font without viscous fingering. This EOR technique has been successfully used to effectively recover the remaining oil from the reservoir, up to 30% of the original oil in place. 

The Weissenberg Effect

Take a look at this video on the Weissenberg effect.

When stress is applied to a fluid, a certain amount of strain, or deformation, is observed. In particular, for a Newtonian fluid, viscous stresses that arise from the flow are linearly proportional to the local rate of deformation over time. It is determined from this that for Newtonian fluids (such as water and oil), the viscosity of the fluid does not depend on the applied stress. So when a rotational stress is applied (as in the video) at the bottom of a Newtonian fluid, below an air-liquid interface, the resulting flow is dominated by inertial and gravity-effects which causes the fluid to flow down toward the source of the stress and radially outward. For pseudoplastics (such as grease), a type of Non-Newtonian fluid where the viscosity decreases as the applied stress increases, applying the same rotational stress will decrease viscosity near the source, which causes inertia and gravity to no longer dominate the flow, causing the fluid to flow upward and bulge at the air interface.

A fun instance of this effect is known as 'rod-climbing'. Rotating a rod inserted into a pseudoplastic causes the polymer chains that make up the fluid to congregate around the regions of highest stress and orient themselves in the direction of shearing, meaning that chains closer to the rod (where stress is highest) are stretched less than those chains further away, and so occupy 'lower states of energy'. The chains' desire to reach these regions of low energy creates an inward normal force and so the fluid goes in the only direction is can - UP THE ROD.

British Applied Mathematics Colloquium 2018, St Andrews

This week I attended the BAMC in St Andrews. I have given a talk as part of the “Multiscale  Analysis of Porous Media” mini-symposium. I spoke about modelling and upscaling multiphase flow in porous media and the session also included talks on upscaling the poro-elastic properties of soil, the growth of potatoes and using image-based modelling to investigate plant-fertiliser interaction.

There are a wide range of topics were presented and discussed at BAMC, which has combined with the UK Magnetohydrodynamics Meeting this year. In my own work I am modelling phenomena at the millimetre and micrometre scale, but I have had the opportunity to attend interesting talks that aim to model much larger scales, such as the formation of the Milky Way and waves in oceans. Mathematical biology was also a popular topic. There were presentations and posters on the more familiar topics of drop impacts and optimisation.

I have attended talks on the history of mathematics and have learnt that 19th Century mathematicians could be really mean to each other! Even going as far as writing whole books to explain just how wrong they thought the other person was. Luckily, most of the attendees here did not share this attitude and were friendly.

Collapsing Bubbles and Microjets

A spherical bubble becomes unstable when it is subject to forces such as gravity, or when it is in proximity of surfaces such as walls or free-surfaces. The presence of such surfaces alters the surrounding pressure field, causing the bubble to lose its original sphericity, fold on itself and collapse. As the bubble collapses, some interesting and noteworthy flow phenomena take place. The detailed high-speed visualisations in the following video reveal some of these complex dynamics for a bubble collapsing close to a free surface. 

In this case, it is the proximity of the free surface that causes the violent collapse. Once the laser-generated bubble grows to its maximum size, the collapse stage starts as the bubble begins to lose its sphericity. The upper part of the bubble accelerates downwards and becomes pierced by a liquid microjet. The jet itself tends to be difficult to observe visually, but its location can be identified by the protrusion it leaves when pushing part of the bubbles gaseous contents downwards.

When the jet impacts on the opposite bubble wall, a set of shock waves are emitted. In this case, the jet is so wide that it touches the interface not at a single point but in a ring, thus making the shock wave emission mechanism even more complex. Following jet impact, the bubble is separated into two parts, as the vapour cavity swept along by the jet becomes detached from the main toroidal bubble. Upon collapse of the main bubble, a stronger second set of shock waves is emitted which is reflected by the free surface causing excitation of nearby small bubbles.

More details here:

Why does superfluid helium creep up surfaces?

Helium, which turns into liquid at about 4.2 Kelvin, can be held in a container like a beaker due to gravity. But when it is cooled further to below approximately 2 Kelvin, it creeps up the surface of the beaker and leak. At this temperature, liquid helium is called as superfluid due to its odd properties. For example, the liquid's viscosity becomes nearly zero. Because of that, the fluid can flow very easily even as a result of the smallest pressure. On one hand, a thin liquid helium film will appear as the liquid wet the surface of the beaker. On the other hand, liquid helium has smaller dielectric permittivity than any other medium (except vapour), which results in a negative Hamaker constant and a repulsive van der Waals force across the film. This will act to thicken the film and make the liquid helium flow from the bottom of the beaker to its surface and thus leak. 

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Recent Publications

R Pillai, JD Berry, DJE Harvie, MR Davidson (2017) Electrophoretically mediated partial coalescence of a charged microdropChemical Engineering Science, 169: 273-283. (access here)

JF Xie, BY Cao (2017) Fast nanofluidics by travelling surface wavesMicrofluidics and Nanofluidics, 21: 111 (access here)

AP Gaylard, A Kabanovs, J Jilesen, K Kirwan, DA Lockerby (2017) Simulation of rear surface contamination for a simple bluff bodyJournal of Wind Engineering and Industrial Aerodynamics, 165: 13-22. (full paper here)