The erratic behaviour of drops revealed
by Arno Schrauwers
A numerical look at
When you mix two diff erent liquids, two things can happen. They either mix down to the molecular level (like water and alcohol), or they don’t (like oil and water), and instead
form minute droplets that coexist. If such a mixture is left alone, the lighter of the two liquids will eventually fl oat to the top, and the heavier liquid will sink to the bottom. During the fi nal stages of the separation process, at the interface of the two layers there is a short but intense bustle of merging droplets, as seen here in a mixture of naptha and water.
mayonnaise
By adding emulsifi ers, a dispersion of oil drops in water can be stabilised to create an emulsion, as in low-fat margarine, mayonnaise, and ointment. Emulsifi ers (e.g. soap or lecithin) have molecules that attract water on one side (bipolar or hydrophilic), and oil on the other (apolar or hydrophobic). As a result, these molecules prefer to move to the interface between the two liquids, where they can prevent the merging of adjoining droplets of the same type.
Dr. René Delfos, researcher at the Laboratory for Aero- and Hydrodynamics of the Mechanical Engineering subfaculty, uses a long swizzle stick to stir a measuring glass containing a little water and lots of colourless oil.
When he stirs the water layer at the bottom, oil droplets form in the water. When he stops stirring, large oil drops soon form, and after twenty seconds or so the oil has completely separated from the water and floats to the top. When he stirs the oil layer, water droplets form in the oil, and after several minutes the measuring beaker still looks as if it is made of frosted glass. The liquids are the same, and so is the container, but the results are completely different. This is to do with the concentration of the droplets: the probability of the relatively small number of water droplets finding each other in a sea of oil is low, so they have less chance of merging, unlike the oil droplets in water of the first experiment. In scientific terms we are looking at a multiphase liquid-liquid system. Welcome to the strange world of emulsions and dispersions.
Delfos: “Mayonnaise is one of the many emulsions made by the food industry. Industrially prepared mayonnaise will not break up easily, because the industry uses special techniques in a colloidal mill to create very small droplets that are kept stable by means of emulsifiers, usually natural ingredients. These molecules have one end that attracts water, and one end that attracts oil. A well-known example is lecithin. Their action is often supported by the presence of proteins. The best mayonnaise is of course home-made, simply because you cannot beat the drops of oil quite as small into in the aqueous vinegar and egg yolk phase. On the other hand, a home-made emulsion may separate within a day.”
Five years ago, Romanian physicist Florin Ovidiu Iancu started work at the Physical Chemistry & Molecular Thermodynamics section within the Computational Group of Prof. Dr Simon de Leeuw at the tud Applied Sciences faculty. His assignment was to get to the bottom of the processes that play a role in emulsions: how drops merge, separate, and collide. The research was
Emulsions play an important part in our daily lives, although we tend to be unaware of the fact. We take much of our food in emulsified form, and crude oil extraction often involves a constant battle between two non-mixing (and therefore often emulsifying) liquids, water and oil. The coming and going of such an emulsion is a delicate performance of drops that merge, divide, and collide in a hostile environment — depending on what that environment is doing at the time.
Romanian physicist Florin Ovidiu Iancu has made an in-depth study of the behaviour of drops, and at the Applied Physics department of TU Delft he has developed a mathematical model that reveals their erratic behaviour. The mathematical model is now being tested and validated at the Delft section for Fluid Dynamics, and will be put to use within the FOM projects Mesoscopics and macroscopics of drop coalescence and Liquid-liquid dispersions in combination with turbulence.
The knowledge can then be used to increase the yield of oil extraction, create lower fat margarines, or improve printing inks.
The column of liquid contains one part water to three parts oil. If a strong turbulence is induced in the water layer, a dispersion of oil drops in water is formed. The drops are packed so tightly together that they will almost immediately merge in massive quantities, rapidly increasing in diameter. Within a few seconds the entire emulsion separates to form two distinct layers.
co-supervised by Dr Chris Lowe, presently at the University of Amsterdam. In all that time, Ovidiu Iancu, Odi to his colleagues and friends, hardly ever set foot inside a laboratory. Iancu’s primary weapon was a Dell Beowulf computer with its (at present) 122 processors operating in parallel. Iancu’s knowledge comes mostly from silicon, in other words, mathematical models.
Simulation Emulsions come in many different forms. Ointment often is an emulsion, but so are low-fat margarine, sauces, and printing ink. Typical of an emulsion is that one of the two liquids is mixed through the other liquid in many minute droplets. Normally, as the tests shown by Delfos demonstrate, an emulsion will separate after some time, but emulsifiers can be used to prevent the droplets merging again. This is known as a stabilised emulsion.
A factory-made salad dressing has been stabilised so effectively that even after many months outside a fridge (low temperatures delay the process) there is no sign of separation. For non-food applications, soap-like products often act as emulsifiers.
“There are many different types of mathematical model to simulate the behaviour of liquids”, De Leeuw explains, “but these models do not apply to emulsions, in which two non-mixing liquids live together. The merging process of drops in particular is where the standard hydrodynamic models fall short. Back in 1992 another model called Dissipative Particle Dynamics (dpd) was developed at the Shell Laboratory at Rijswijk to study fluid behaviour. In the Shell model the liquid is represented as a large number of small spheres that interact and are subjected to a number of different forces such as friction and a random force.”
The model can be used to compute what the individual spheres do when subjected to various forces and to each other’s presence. It does not work with only a few spheres (it would yield a far from realistic result), but it does work for millions of spheres at a time. However, when you use millions of spheres, in theory the number of interactions becomes the square of all those millions, which would render the model useless, since even the fastest and most powerful parallel computer would be unable to cope.
De Leeuw: “Fortunately, the forces acting on the particles have only a short range, which means that the number of interactions is about the same as the number of particles.”
But even so, a single processor, however powerful, will not get you very far. Therefore Iancu did his simulation runs on the Dell Beowulf cluster that lives in the basement of the building of the department of Applied Physics. In order to compute the (imaginary) basin containing the liquids, the volume is first divided into smaller volumes, each of which is then fed to a different processor. A separate algorithm keeps track of the interactions between the partial volumes, and the parallel processing ultimately yields a full-colour simulation. For his production runs Iancu used up to 40 processors at a time. His dpd code
The fl ow in a cyclone is turbulent. Rather than running straight up, the paths of the separate oil drops in a turbulent mixture (these were calculated using a supercomputer) are erratic due to the fact that the drops are constantly being thrown about. Consequently, the drops will often collide with each other, which may result in their merging, producing larger drops. However, if the turbulence is too strong, the process may be reversed as the drops are broken up.
Using gravity to separate an emulsion may be cheap, but it is also slow. At the fl uid dynamics section of the faculty of Mechanical Engineering at Delft University, an alternative has been developed in the form of a hydrocyclone which contains no moving parts and which can greatly speed up the separation of large quantities of oil drops from water. In the fl ow, which rotates very fast, the centrifugal forces can reach over 1000 g. Thanks to this development, separating equipment can be made smaller and less expensive.
The oil industry sees a lot of oil-water mixtures, since large quantities of water can be released from the earth during the production of oil or natural gas. A secondary problem of the water fl owing with the oil is the corrosion damage it causes to
the inside of pipelines. (Photograph www.ddbstock.com)
If the drops of an oil-water emulsion are not made small enough during the production process, as is often the case with home-made mayonnaise, the product will start to separate in due time.
Odi Iancu has written a program that can be used to describe the behaviour of small clusters of molecules. It distinguishes between the interaction of molecules of the same type (water/water or oil /oil) and that of molecules of diff erent types (water/oil). By assuming a suffi ciently large number of clusters he was able to simulate the merging and breaking up of drops in great detail. This is a simulation of a water drop sinking through an oil layer to strike a water layer.
This time the top layer, containing the oil, is made turbulent. The result is a dispersion of a relatively lower concentration of water drops in the oil layer. Without much merging, the water drops individually sink to the bottom. The process is much slower; even after several minutes a mist of the smallest water drops remains, which takes thirty minutes to subside.
A water drop sinking through an oil layer and pushing aside the intervening oil fi lm. A computer simulation by Odi Iancu (right) compared with experimental data obtained by Dipl.Ing. Ulrich Miessner at the Mechanical Engineering department (above).
program has also been tested on the sgi altix 3700 and on the sgi Origin 3800 at the sara national computing centre in Amsterdam, and proved to be reliable for up to several hundreds of processors. However, before he got to the stage where he would be ready to look at the results, Iancu had to work out a few things on his own, and inevitably, in some cases he got it horribly wrong.
“The first simulations,” Iancu says, “yielded very unsatisfactory results. They were useless. For example, the behaviour of a drop of water sinking through another liquid, say oil, was affected by the size of the container. Also, the effect of the collision of the drop and the interface of the heaviest liquid, in other words the same type of liquid as the drop, should not be affected by the height of the column of the underlying liquid if you include it in the simulation. It took me quite a bit of time to find the right parameters. All in all, the first set of simulations looked far from good.”
Film Of course, simulations are a far cry from the real thing if the mathematical model is wrong. In fact, such a mathematical model is a sublimation of the knowledge obtained through experiments. If you build the wrong model, you get pure nonsense. Then why go to all the trouble of constructing a mathematical model at all?
De Leeuw: “These days, you can find out a lot from experiments, but not everything, far from it. One thing you cannot demonstrate in an experiment, but which becomes very clear from Odi’s model, is what happens when a drop hits the interface between the two liquids. The drop and the heaviest layer, which contains the same liquid as the drop, do not merge immediately. Initially, a thin layer of the lighter liquid comes down with the drop, separating it from the heavy liquid. The simulation clearly shows how the drop punches a dent in the surface of the liquid, how after a while a hole develops in the separating film, and how later still the drop merges with its own liquid layer.
When you build a model like this, you can use all kinds techniques to test whether the model tallies with the real world so you do not have to go into the lab to carry out all sorts of experiments. We left the experiments to the very end, and then we used mixtures of propanol and oil.”
Iancu: “We looked at three aspects. The first was the breaking up of drops under the influence of simple shearing flows. The second was the merging of drops at a liquid-liquid interface with the heavier fluidbelow the interface, and the third was collisions between drops. Unilever has used this technique many times to look at the way drops break up, but nobody had ever looked at the way drops merge. Our system also works for surfactants such as different types of soap.”
Iancu obtained proof of the soundness of his model from the United States. He runs a short movie showing the laboratory experiments of American researcher, Professor Ellen K. Longmire of the University of Minnesota.
The pictures are the spitting image of his colourful simulations of colliding and,
Iancu’s research was carried out using a Beowulf Cluster. This parallel computer containing 122 processors is located in the basement of the Faculty of Applied Physics, and is also used for simulations of acoustics, thermodynamics, hydrodynamics, neutron scattering, materials science, and biotechnology.
Merging after a head-on collision between two drops. The kinetic energy of the colliding drops is suffi cient to break though the thin oil fi lm separating them.
In a collision similar to that shown on the fi gure above, but now at lower velocity, the kinetic energy is insuffi cient to cause merging, and the drops bounce off each other. Since the drops do not hit each other head on, but slightly to one side, they also start to rotate about the same axis.
If the relative velocity of the colliding drops is very high, the drops merge, but the remaining energy is so high that the newly formed drop breaks up again, usually forming as well smaller, satellite drops.
If a spherical drop fi nds itself in a simple shearing fl ow, it soon loses its original shape to become an ellipsoid. If the fl ow is strong enough, the drop continues to be stretched until ‘waists’ form where the drop eventually breaks apart. Compare the images on the left, which were photographed by Dr. Charles R. Marks, with the ones on the right, which were calculated by Odi Iancu’s computer program.
Iancu’s simulation shows how several ‘waists’ form if an even larger drop is stretched into a very long strand. A whole series of drops is formed, often accompanied by satellite drops.
(Source: Charles R. Marks, “Drop Breakup in Sudden Onset Strong Flows”, Ph.D. Dissertation, University or Maryland, College Park, MD 20742 USA, December 1998).
ultimately, merging drops he demonstrated a few moments earlier. “The similarity is striking”, De Leeuw says without any pretence at modesty. “As it is, we were recently able to validate Odi’s results using research data from
the University of Utrecht, where confocal microscopy was used to look at the way drops merge and break up. This kind of model will be very useful in the oil industry, where water is used to pump up oil. There are lots of very good hydrodynamic models, but they have to be fed with the right parameters such as viscosity, surface tension, cohesion, polarity, and type of rock. This model is very handy, and it can also be used for all sorts of other applications in which emulsions play a role. A printer manufacturer for example could use it to determine the correct properties of a printing ink.”
So is the model finished?
Iancu smiles at what must be a naive question: “You can use it to obtain accurate predictions about the behaviour of emulsions, but when is anything ever finished in science?”
Delfos: “It is not just about applications; we also want to understand how things work, and that is why our two research groups had a joint project financed by fom, the fundamental research institute in physics in the Netherlands. The present work is co-financed by Unilever R&D Colworth, England. They have a sound interest in the physics of interfaces and emulsions.
In addition to Odi at the faculty of Applied Physics, we had Dr Prakash Vedula at the faculty of Mechanical Engineering. He was a postdoctoral researcher from India, who had previously worked in the usa for 5 years. He incorporated Odi’s results in a model for turbulent-flow emulsions.”
Sadly, that part of the project never really got off the ground because Vedula’s wife was refused a residence permit. Vedula now works as a researcher at the University of Illinois at Urbana Champaign.
For more information, please contact Prof. Dr Simon de Leeuw, phone +31 (0) 15 278 5037, e-mail s.w.deleeuw@tnw.tudelft.nl, or Dr Ovidiu Iancu, e-mail ovidiu@barium.hpac.tudelft.nl,
or Dr René Delfos, phone +31 (0) 15 278 2963, e-mail r.delfos@wbmt.tudelft.nl.
When the water drop at the interface with the water has reached a state of rest, a terminal phase appears to form in which a very thin oil fi lm remains between the water drop and the underlying water. In the presence of emulsifi ers the fi lm remains stable, but without emulsifi ers, as shown here, within seconds a hole will appear in the oil fi lm. Through the hole the fi nal merging takes place within a few microseconds. The time required for the hole to form appears to be the result of a stochastic process. Rather than being at the centre of the fi lm, the location of the hole always is somewhere near the edge, a phenomenon analogue to that of air bubbles merging in water.
A large drop of oil rises so fast that it becomes dimensionally unstable, allowing a long trail of oil to spill from its lower end.
