Mass Transfer and Spontaneous Emulsification in Ternary Mixtures

University Degree in Industrial Technologies 2018-2019

Bachelor Thesis Mass Transfer and Spontaneous Emulsification in Ternary Mixtures

Miguel Zürcher Guinea

Oscar R. Enríquez Paz y Puente 23rd of September 2019

This work is licensed under Creative Commons Attribution – Non Commercial – Non Derivatives

SUMMARY

The combination of miscible and immiscible liquids in ternary mixtures can cause a va- riety of interesting physical phenomena. A common example of these three component mixtures is found when having anise oil based liquors found in most countries around the Mediterranean. Raki, from Turkey, Pastis from France, or Ouzo in Greece all seem to magically turn into a milky white colour when adding water. The addition of water makes alcohol mix with it, causing the oil, immiscible in water, to supersaturate and nucleate. This spontaneous emulsification of oil in water makes the light scatter causing its white colour. This is called the Ouzo effect after the traditional Greek drink. Although humans have interacted with the Ouzo effect for centuries, it was not until 2003 when the physics behind were studied in depth by Vitale and Katz. Since then more scientists have taken on this topic, especially as numerous applications of the Ouzo effect in industry have arisen, mainly in the biotechnology and nano-technology fields. However, today there is still a great lack of knowledge on the mechanisms that play a role in the Ouzo effect. Studies of drops in Ouzo systems have proven to involve a large amount of complex flows and interfacial phenomena as well as the spontaneous emulsification of oil inside the drop. Gradients in concentration and surface tension cause Marangoni stresses making the drop shake, and diffusion processes to take place. The mass transfer, buoyancy flows, capillary forces, and the interface dynamics together with the Ouzo effect make a very interesting system to be explored. This project summarises the known physics involved behind the Ouzo effect and multi- component drops, as well as their multiple applications in modern day industry. It continues the work on studying the fate of water drops in different compositions of oil/alcohol mixtures. The densities of ethanol/water mixtures are known and are documented in numerous papers. However densities of anethole and ethanol have never been quantified. The densities of different anethole/ethanol compositions have been measured. These values have then been fitted to the Jouyban-Acree model. This model extrapolates our experimental measurement to be able to estimate very precisely the density of any composition of our mixture. An experiment was designed and setup up to explore different aspects of dissolving multi- component drops. Through this experiment we could observe different phenomena previously mentioned, especially the rate at which diffusion took place. The experiment was analysed through digital image processing, and different geometrical magnitudes of the drop were tracked such as the surface are or the volume. The bond number was also tracked by means of the pendant drop fitting technique. These results were compared between both compositions and with estimated theoretical values.

iii Keywords: Ouzo, Marangoni, Drop, Anethole, Ethanol, Water, Pendant, Bond.

DEDICATION

Firstly, I would like to thank my mentor for this project Oscar Enríquez, for putting forward this idea for my project. I am very grateful to have had him guiding me throughout the whole project and helping me in everything he could. Secondly, I would like to thank Jose and Nacho, for making the countless hours in the lab together fun and for lending me a hand when needed. I would also like to thank the laboratory technicians, and the rest of the professors in the fluids department, for gladly responding to any doubts I may have had. Lastly, I would like to thank all my friends and family for their support and encourage- ment in everything I set out to do.

CONTENTS

1. INTRODUCTION...... 1 2. STATE OF THE ART...... 2 2.1. Small Scale Physics...... 2 2.2. The Ouzo Effect...... 5 2.3. Ouzo Drops...... 11 2.4. Applications...... 14 3. ANETHOLE-ETHANOL DENSITY CHARACTERISATION...... 16 3.1. Realisation of the Experiment...... 16 3.2. Results and Conclusions...... 18 3.3. Future Ideas...... 20 4. PENDANT DROP EXPERIMENT...... 21 4.1. Realisation of the Experiment...... 21 4.2. Recording of the Experiment...... 22 4.3. Analysis of the experiment (image processing with MATLAB)...... 23 4.3.1. Geometry of the Drop...... 25 4.3.2. Bond Number of the drop...... 27 4.4. Results and Conclusions...... 32 4.5. Future Ideas...... 37 5. CONCLUSIONS...... 38 BIBLIOGRAPHY...... 39 APPENDICES...... 41 A. TABLES OF THE JOUYBAN-ACREE MODELS...... B. EXTRA GRAPHS OBTAINED FROM THE PENDANT DROP EXPERIMENT.

vii

LIST OF FIGURES

2.1 Tears of wine caused by the Marangoni effect...... 3 2.2 The different mechanisms that can cause emulsion degradation...... 4 2.3 Otswald ripening mechanism...... 5 2.4 The Ouzo effect. 1-2 Ouzo with no added water. 3-4 Emulsification of the drink after the addition of water...... 6 2.5 Ternary Diagram of the "ouzo mixture"...... 7 2.6 Droplet diameter as a function of excess oil for different compositions...8 2.7 Droplet diameters at 25oC and 50oC...... 9 2.8 Plot of the volume of the dispersion in a function of time at different concentration of anethol for (a) 5%-95% ethanol/water mixture and (b) 30%-70% ethanol/water mixture...... 10 2.9 Estimated surface tension of the drops as a function of ethanol concentration. Of ethanol/water mixtures of 5%-95% (Squares), 10%-90% (Cir- cles), 20%-80% (Triangle pointing upwards), 30%-70% (Triangle pointing downwards)...... 10 2.10 Plot of drop Radius as a function of time (Black dots, left axis) and the scattering intensity (white dots, right axis)...... 11 2.11 The four stages of an evaporating Ouzo drop on a hydrophobic surface.. 12 2.12 The different flows in a dissolving /water ethanol drop in anethole..... 13 2.13 Frame from the award winning video "The shaky life of a water drop in an anise oil-rich environment"...... 14

3.1 Krüss Force Tensiometer-K20...... 17 3.2 Set for determining density of liquids...... 17 3.3 Experimental and Jouyban-Acree Model values for anethole/ethanol binary mixtures at 24oC...... 19 3.4 Densities of Ethanol/Anethole and Ethanol/Water mixtures for different concentration of Ethanol...... 20

4.1 Experiment setup. Close up of the pendant drop on the right...... 21 4.2 Experiment setup...... 22

ix 4.3 Ultrasonic cleaner (right), Tray two hold the objects to be cleaned (left). 23 4.4 Original image. Dotted lines refer to the limits of the capillary. The rectangle represents the area which the software will crop to work on... 24 4.5 Subtraction of the background (middle) from the original image (left), to make most of the background black in the new image (right)...... 24 4.6 Results of the segmentation process steps 2-7...... 25 4.7 The detected contour of this frame...... 26 4.8 How a disc of a row in the drop would look like. The width of the disc is not to scale in this image...... 26 4.9 Geometrical variables involved in the calculation of the Bond number... 28 4.10 Schematic of the pendant drop tensiometry process...... 29 4.11 Flow diagran of the fitting process for frame k...... 30 4.12 Result of the fitting Bond Process...... 31

4.13 Example of how a circle is fitted to the apex of the drop toknow R0.... 32 4.14 Frame from an experiment with 4:1 in composition...... 33 4.15 Results of the volume growth of the 4 experiments analyse in 4:1 mixture until detachment...... 33 4.16 Results of the volume growth of the 4 experiments analyse in 3:1 mixture until detachment...... 34 4.17 Results of the volume growth of the drop in both compositions until detachment...... 35 4.18 Bond numbers as the drop grows...... 36 4.19 Bond numbers of both compositions 3:1 and 4:1...... 36 4.20 Experimental setup of synthetic Schlieren...... 37

B.1 Evolution of the drop surface area, since the moment the capillary is inserted in the 4:1 Anethole/Ethanol mixture...... B.2 Evolution of the drop surface area, since the moment the capillary is inserted in the 3:1 Anethole/Ethanol mixture...... B.3 Evolution of the drop volume, since the moment the capillary is inserted in the 4:1 Anethole/Ethanol mixture...... B.4 Evolution of the drop volume, since the moment the capillary is inserted in the 3:1 Anethole/Ethanol mixture......

x B.5 Evolution of the drop volume, since the moment the drop reaches Vo in the 4:1 Anethole/Ethanol mixture...... B.6 Evolution of the drop volume, since the moment the drop reaches Vo in the 3:1 Anethole/Ethanol mixture...... B.7 Evolution of the drop’s Bond number in the 4:1 Anethole/Ethanol mixture. B.8 Evolution of the drop’s Bond number in the 3:1 Anethole/Ethanol mixture.

LIST OF TABLES

3.1 Experimental values obtained for different Anethole/Ethanol compositions. 19

4.1 Experimental and estimated values for V¯ at detachment...... 35 4.2 Experimental and estimated values for Bo at detachment...... 36

xiii

1. INTRODUCTION

There is a big lack of knowledge with regards to the spontaneous emulsification and mass transfer in ternary mixtures. Certain ternary mixtures, such as water/alcohol/oil, undergo multi-diffusion processes that lead to spontaneous emulsification. When these mixtures are brought to a smaller scale some physical phenomena are magnified. Although there are endless studies on pure or binary drops, the behaviour of multi-component drops, is a topic that still has many uncertainties. The understanding on how the compositions of ternary mixtures and ambient conditions influence the mass transfer and other phenomena would be a big step closer tobeingable to properly use ternary mixtures in the numerous possible applications for them that are arising especially in the nano-technology and biotechnology fields. The mentor of this project Oscar R. Enríquez had already carried out some work studying the evolution of drops in three component systems when he put forward this project for me. His experiment consisted in placing a drop of water in an anethole/ethanol mixtures. In his experiments when placing the drop inside, bulk liquid started diffusing into the drop where spontaneous emulsification took place. The drop continuously grew until it detached from the surface and floated, throughout the whole experiment the drop was continuously oscillating. This work is explained more in detail in 2.3. Different aspects of the behaviour of the drop to be studied form his work are:

1. Characterisation the flow rate into the drop fffor di erent compositions.

2. Determination of the composition of the drop inside the mixture.

3. Characterisation of the oscillations of the shaking drop for different compositions.

4. Determination of the interfacial surface tension for different initial compositions.

5. Characterisation of the flow inside the drop.

The priority of this project is to tackle problems 1,2 and 3. To accomplish this an experiment had to be designed and setup that correctly shows how different initial compositions of anethole and ethanol affect the behaviour of water drops in the system in these specific points. This project’s objective is to try and solve another piece of the puzzle on the spontaneous emulsification and mass transfer in oil/water/alcohol mixtures. Hopefully my work will be able to be used by another person, or myself in the future, who wants to further the knowledge on multi-component systems. Ideally one day we will have full control on the behaviour of these mixtures and we will be able to apply this knowledge to accomplish break-through advancements in many different industries.

1 2. STATE OF THE ART

2.1. Small Scale Physics

The study of droplets takes place in a very small scale, the droplets studied will have a maximum volume of the order of a couple dozen millilitres. It is for this reason that different phenomena that are highly influential in large scale fluid dynamics such asthe hydrostatic pressure, inertia or other mass forces become irrelevant in this study. Other physical phenomena gain relevance due to the size of the droplets. These phenomena include surface tension, diffusion, emulsification, or nucleation. They will be briefly explained as they will be frequently mentioned throughout this study. [1]

Surface Tension

A liquid is a state of matter in which, although the molecules are disordered, they have an attraction between one another. The molecules that are found on the surface do not benefit from the same cohesive forces as interior molecules.[2] These unequal forces acting upon the molecules on the interface cause them to be pulled towards the bulk liquid. This creates a tension on the surface, making it contract to the smallest size possible compatible with the mass of the liquid. [3] To increase the interface between a liquid with another liquid or a gas an external energy is required to counterpose the intermolecular forces. In order to increase an area A by an amount δA an external work of σδA would have to be provided. This amount of energy per unit area required σ is what is known as surface tension. It is therefore measured in J/m2 [4] By doing some simple dimensional analysis we can see that J/m2 can also be expressed as N/m. Surface tension can also be defined as the force exerted by the liquid onthe plane of the surface per unit length. [3] For drops of a greater size the gravitational forces on the mass overcome the interfacial tension. However in drops with a diameter below a specific length, known as the capillary length, the surface tension dominates overthe gravitational forces causing the drop to have a spherical shape. With earth’s gravity of 9.8m/s2 the capillary length is of the order of millimetres. For this reason surface tension will be a very important property throughout this study of a water drop in a mixture of anethole and ethanol.[2]

Marangoni Flows

Marangoni flows, or the marangoniff e ect are very much related with surface tension. It is caused because of a surface tension gradient, in which the capillary forces of a certain part of the liquid pull more creating a flow in its direction. Although marangoniff e ect can

2 mostly be found in small scales it is also the cause of every day phenomena such as the tears of wine. The tears of wine are caused due to the evaporation of the highly volatile alcohol found in the drink at the rim of the glass. This creates the wine of the rim to pull wine upwards, being able to defy gravity.

Fig. 2.1. Tears of wine caused by the Marangoni effect.

A surface tension gradient, and therefore Marangoni flows can be caused for several different reasons.

• Thermal marangoni flows are caused due to a gradient of temperature. Thesur- face tension of a liquid decreases with temperature. This difference in temperature causes a difference in surface tension causing a Marangoni flow in direction to the colder region.

• Surfactant marangoni flows are caused by substances that lower the surface tension of liquids, known as surfactants. Naturally when adding a surfactant a surface tension gradient will take place causing marangoni flow away from the surfactant.

• Solutal marangoni flow is caused byff adi erence of concentration of a certain mixture. A smaller concentration of a certain substance can change the surface tension in that area causing a marangoni flow. This is the case of the marangoniff e ect of the tears of wine, as the alcohol has such a small surface tension, its evaporation causes a flow towards the rim. Solutal marangoni flow will be the most presentin this project due to the uneven dissolution of alcohol in the water drop. [1]

Diffusion

Diffusion can take place from one liquid into another, it is the process by which the ran- dom movements of molecules create a flow under the influence of forces.These forces are

3 the gradients of concentration. Molecules move from areas with high concentration to areas with lower concentration, a process that occurs until there is a homogeneous distribution of both substances.[5] Diffusion can induce another phenomenon called spontaneous emulsification. The diffusion can cause supersaturation of a substance in a mixture, which will cause nucleation of the compound forming micro-droplets in the system.

Emulsion degradation

As previously mentioned the diffusion of a liquid can cause nucleation, and create an emulsion of a liquid in an other. An emulsion is the dispersion of one liquid inside another in the form of microscopic droplets. The interfacial tension existing in the large surface area of the droplets makes the emulsion thermodynamically unstable (gibbs free energy is greater than zero). However the formation of a adsorbed layer at the droplet interface makes emulsion kinetically stable (very slow rate of reactions). Emulsion tend to reduce their instability by reducing the surface area of the droplets, by increasing the average droplet diameter. Eventually emulsions degrade into phase separation, a number of different mechanisms play a role in this degradation.[6]

Fig. 2.2. The different mechanisms that can cause emulsion degradation.

4 • Creaming consists in the movement of the droplets which float or sink, because of buoyancy forces. This makes the droplets be in proximity from one another which makes possible other degradation mechanisms to take place.

• Aggregation, also known as flocculation, is the formation of clusters of droplets that spontaneously stick together. Like creaming aggregation simply accelerates other mechanisms by making the droplets closer to each other.

• Droplet Coalescence occurs when the thin layer at the drop interface thins and eventually ruptures. This leads to the formation of large droplets by the merging of smaller ones. When particle volumes increase exponentially, coalescence is the acting mechanism. [7]

• Ostwald Ripening does not require the droplets to be in proximity. The solubility of the droplets increases when decreasing the radius. This variation in solubility causes the smaller droplets to dissolve into the bulk phase. Eventually these particles will defuse and redeposit in larger drops leading to an increase in average size of the droplet emulsion. [6]

Fig. 2.3. Otswald ripening mechanism.

2.2. The Ouzo Effect

Around the Mediterranean we can find several anise beverages. Raki in Turkey, Pastis in France, Sambuca in Italy, Anís in Spain, or Ouzo in Greece are all common examples. These drinks all have in common that they are mainly composed of anise oil and alcohol. When mixing one of the previously mentioned liquors with water the drink instantly turns into a milky white opaque colour.

5 Fig. 2.4. The Ouzo effect. 1-2 Ouzo with no added water. 3-4 Emulsification of the drink after the addition of water.

The anise oil dissolved in the drink supersaturates because of diffusion of alcohol in the newly added water. The anise oil instantaneously nucleates into small micro-droplets which scatter the light giving it this colour. [7] This phenomenon was not looked at in depth until 2003 when Vitale and Katz from the John Hopkins University in Maryland analysed this occurrence and gave it the name after the traditional Greek liquor, The Ouzo Effect. Although we have encountered the Ouzo effect for many years, there are many unsolved questions regarding the mechanisms that play a role in the spontaneous formations of these oil nuclei in water. There is also a lack of knowledge in the growth and size of these droplets as well as their stability.

Ouzo Phase Diagram

Vitale and Katz, gave some insight and meaning to the phase diagram of the Ouzo effect [7]. Oil, alcohol and water can coexist in a single, transparent phase. It is beyond a certain amount of added water that the Ouzo effect starts to take place. In a three component phase diagram the binodal and spinodal curves determine the phase diagram. The binodal curve shows the points of the minima of the Gibbs free energy of the system. Above the binodal curve we can find a stable one phase region (none, or little water has been added). Under the binodal curve we can find a two phase region. Within this two phase region we can find both a metastable and an unstable regions. These two regions

6 are separated by the spinodal curve which depicts the limits of thermodynamic stability. Under the spinodal curve we can find the unstable region. When the system is brought inside the spinodal curve, large droplets will form from the solution, these large droplets will join to instantaneously form two separate phases. This process is known as spinodal decomposition. However between both curves, spinodal and binodal, we can find a two-phase metastable region. This is a state in which although the gibbs free energy is not minimized there are barriers that prevent phase separation. It is possible for the system to find itself in this region for a very long time. It is in this metastable region where the Ouzo effect takes place.

Fig. 2.5. Ternary Diagram of the "ouzo mixture".

When an excessive amount of water is added it quickly brings the beverage into the metastable region making the anise oil to become supersaturated. This supersaturation leads to nuclei to spontaneously form due to small fluctuation in the concentration of the solute molecules. The formation of these nuclei result in a depletion of solute in its prox- imities, only allowing other nuclei to form at a certain distance from existing nuclei. The spontaneous nucleation process, which takes place almost instantly (milliseconds) results in a spatially uniform dispersion of these nuclei. Ostwald ripening process then takes place very slowly. The Ostwald ripening results in the dissolution of the smaller nuclei, because its concentration is now lower than the saturation limit, and the larger nuclei con- tinue to grow as their saturation concentration has decreased. As we can see in the three phase diagram a sufficient excess of oil would lead to a “reverse ouzo effect”, where in this case it is the water that nucleates.

7 Droplet Size

The initial droplets are formed instantly, they are dispersed homogenously and are of a relatively uniform size of the order of a micrometer.[8] In 2003 Vitale and Katz [7] carried out a series of quantitative studies on dispersions of oil droplets in water by adding water to divinyl benzene (DVB)-ethanol solution. They realised that the droplet diameter of the oil droplets dispersed only depends on one pa- rameter, the excess oil-solvent ratio (The difference between the initial oil-ethanol ratio and the final oil-ethanol ratio in the aqueous phase).

Fig. 2.6. Droplet diameter as a function of excess oil for different compositions.

The size distribution has normally a standard deviation of around 40%-80% of the mean diameter. This size distribution can be reduced my mixing the components at higher temperatures before allowing it to cool down back to room temperature. This can be explained because the solubility of the oil in the aqueous phase increases with temperature. This greater solubility leaves less excess oil to form droplets than in room temperature. Cooling down is a slower process than diffusion, the concentration of oil does not increase quickly enough to nucleate and form new nuclei. Instead the oil will gradually diffuse into existing nuclei, according to Fick’s law all droplets will absorb the same amount volume of oil. Smaller drops’ diameters will therefore grow quicker, making the distribution of the droplet diameters narrower.

8 Fig. 2.7. Droplet diameters at 25oC and 50oC.

The stability of the “Ouzo effect” is affected by the size of the droplets, as well as the density difference between the droplets and the continuous phase. Small droplets and a small density difference bulk phase separation will occur in a slower rate, making the dispersion more stable. Also any homogeneity in the mixture, such as uniform distribution of the droplets, would cause the mixture to be less stable.[7]

Droplet Growth

Natalia Sitnikova, Rudolf Sprik and Gerard Wedgam, form the university of Amsterdam, carried out some more work on the Ouzo effect[9]. They studied the mechanisms and kinetics of the oil droplet formations, measured droplet sizes trans-anethol-water-ethanol solutions using dynamic light scattering spectroscopy (DLS). The first observations they made is that the spontaneous emulsification only tookplace when a quick increase in water concentration was made. Neither adding oil to an alcohol/water nor adding alcohol to an oil/alcohol mixture created a spontaneous emulsifying. They also concluded that neither interfacial tension, nor mechanical influence had any influence in emulsification,ff adi erence in temperature on the other hand could enhance spontaneous emulsification to take place. The most interesting discovery of these experiments were about the growth of the oil droplets formed in the system. The droplets undergo two distinct stages, an initial stage where the droplets grow, and a second, equilibrium stage, where the nuclei stop growing. They could see that initially the droplets grew lineally over time, this discarded other growth mechanisms such as coalescence as this mechanism makes particles grow exponentially and not linearly. They also observed through a microscope that even though the particles often collided due to the Brownian motion they never merged.

9 Interestingly, they discovered that the amount of alcohol in the initial alcohol/oil mixture had a big influence on the growth rate of the dispersed droplets. At low concentrations of ethanol in the water/ethanol mixture (below 30% ethanol) it can be seen that the rate at which the OR occurs increases with an increase in oil. For mixtures with a high amount of alcohol (over 30%) an increase in oil concentration has an opposite effect, the rate of the droplet growth decreases, sometimes even causing the droplets to shrink.

Fig. 2.8. Plot of the volume of the dispersion in a function of time at different concentration of anethol for (a) 5%-95% ethanol/water mixture and (b) 30%-70% ethanol/water mixture.

The mechanisms that are involved in the exchange of molecules between droplets and the counter intuitive decrease of the OR rate in alcohol rich mixtures is still unclear. One proposed reason is that it is the reduction of interfacial surface tension between the droplets and the surrounding solution that drives droplet growth.

Fig. 2.9. Estimated surface tension of the drops as a function of ethanol concentration. Of ethanol/water mixtures of 5%-95% (Squares), 10%-90% (Circles), 20%-80% (Triangle pointing upwards), 30%-70% (Triangle pointing downwards).

10 In this study they managed to estimate the interfacial tension of the droplets as a function of oil content of different compositions of water/ethanol liquids. We can see that the surface tension decreases for higher alcohol concentrations. This lowering in surface tension can be explained by a formation of a strong alcohol/water layer due to an absorption of the alcohol molecules to the droplet interface. This reduction of surface tension, which builds up with an increase in ethanol concentrations could reduce the OR rate.

Fig. 2.10. Plot of drop Radius as a function of time (Black dots, left axis) and the scattering intensity (white dots, right axis).

As mentioned before after a few days of growth of the droplets, the system will reach a stability regime, in this regime the average droplet size remains constant for long periods of time (up to 30 days), and then slightly decreases because of large droplets slowly sink to the bottom or floating to the surface. These slow buoyancy movements indicate avery similar density between the dispersions and the continuous phase. [9]

2.3. Ouzo Drops

The evaporation and dissolution of Ouzo droplets leads to large amount of physical phenomena which produces great scientific interest. Studying droplets are an ideal wayto further our knowledge on spontaneous emulsification and the Ouzoff e ect. The diffusion through the interface of a drop can cause the Ouzo effect, the simplicity of the flow structures of these systems makes it easier to study the hydrodynamics ofthis special phenomenon. The surface effects of the drop play also an important role as it makes it possible to manipulate the system in certain aspects, such as to concentrate the Ouzo effect in a certain region, change the flow patterns, or to influence the configurations of the oil dispersions produced.

11 Evaporating Ouzo Drop

Huanshu Tan, at the University of Twente, worked on studying the evaporation of a mul- ticomponent sessile drop on a hydrophobic surface[10], formed by oil, alcohol and water. Initially the drop was single phase and transparent, in the stable region of our Ouzo diagram. The evaporation of the much more volatile component of this drop, the alcohol, induces a supersaturation of oil and therefore triggers the Ouzo effect. The evaporation of the Ouzo drop undergoes four distinct stages:

1. The initial stage of the drop consists of a single phase spherical-cap shaped sessile drop. The three component drop is completely transparent as the components are found above the binodal curve of the diagram, in the stable one-phase region. No ouzo effect has taken place in this stage.

2. The alcohol found in the bottom of the drop, the contact surface, evaporates more easily. This evaporation leads to a lower concentration in this region which causes some oil to nucleate, a surface tension gradient is created which makes the oil dispersions spread out throughout the whole drop giving it the characteristic white colour. In this stage the drop continues to have a spherical-cap shape. The contin- uing evaporation of alcohol leads to a supersaturation of oil, this makes the micro droplets to grow, and coalesce. An oil ring is formed.

3. In the third phase of the evaporation, the alcohol has completely evaporated and the oil has coalesced on the surface or merged with the oil ring on the surface contact line. The water gradually evaporates, much slower than the alcohol. This third stage is considerably longer than the previous one. It recovers its transparency.

4. In the last stage only the non-volatile oil remains, the drop regains its spherical shape.

Fig. 2.11. The four stages of an evaporating Ouzo drop on a hydrophobic surface.

12 Dissolution of water/ethanol drop in anethole

Huanshu also studied the dissolution of a water/alcohol sessile drop in anise oil[1]. Ini- tially both the drop and the host liquid are transparent. However quickly water micro- droplets start to emulsify on in the oil. Successively oil in water emulsification appears inside the drop. A variation in concentration along the interface creates two Marangoni flows which causes the oil micro droplets to accumulate at the centre of each Marangoni flow roll in the centre of the drop. All this occurs due to the dissolution ofethanolfrom the drop. By decreasing the amount of initial ethanol in the drop the water in oil emulsification do not occur.

Fig. 2.12. The different flows in a dissolving /water ethanol drop in anethole.

He also used thermodynamic equilibrium theory and diffusion path theory to develop a one dimensional diffusion model. The model agrees with the experimental results quan- tifying that water in oil droplets are only created if the drops have an ethanol concentration of over 52%.

Dissolution of water drop in ethanol/anethole solution

My mentor of this project, Professor Oscar R. Enriquez alongside other members of the department of fluid dynamics of the University Carlos III of Madrid, carried out another experiment involving the dissolution of Ouzo drops[11]. Their work won a Milton Van

13 Dyke Award at the GFD Gallery of fluid motion. The experiment consisted in studying what happened to a sessile drop of water placed on a hydrophobic surface inside an anethole/ethanol mixture.

Fig. 2.13. Frame from the award winning video "The shaky life of a water drop in an anise oil-rich environment"

Droplets of water start to oscillate and grow shortly after the drop is placed. These oscillations can be caused due to Marangoni stresses, these stresses are induced because of the constant change of component concentration on the drop interface. This composition variation on the interface is due to the diffusion of mainly alcohol inside the drop. The diffusion also creates a gravity current downward and away from the drop. As alcohol continues to diffuse inside the drop, it deforms and grows due to buoyancy because of its lowering density as concentration of alcohol inside the drop increases. Eventually the buoyancy force on the drop makes it detach and float to the surface. After the pinch-off another cycle takes place with the remainder of the drop. However this second process is much slower as the composition of the remaining drop is more similar to the host liquid.

2.4. Applications

The special characteristics of the Ouzo effect, has a great potential in different industries. The most attractive aspects of these spontaneously formed emulsifications are that it does not require energy. This can allow companies to save a lot energy in the production processes, and therefore potentially also reduce costs. Being able to create these emulsions without having to use surfactants can also solve environmental issues within the production process. Obtaining fine dispersions of one liquid in another, is of great importance in industries which can all benefit from a further control on theff OuzoE ect. In agriculture, oils have been used for pesticides, they are both an efficient and a safe alternative to synthetic insecticides. Oil-based pesticides are commonly used for insect

14 control, but can also be used against fungi.[12]Pesticides may only require less than one percent of oil dispersed in water when applying it. For this reason the Ouzo effect has taken an important role in this industry. “Self-emulsifiable oils” are added to an excess amount of water directly before its use. These type of pesticides have been used for many years before any important investigations on self-emulsification has ever been done. A more in depth knowledge of the emulsification of the oil in water would facilitate the correct formulation of pesticides.[13] In the pharmaceutical industry the ouzo effect can also be used to improve drug deliv- ery systems. The active ingredients of drugs have to efficiently reach the damaged cells, tissues or organs. The fastest way to reach these target cells is through injection in the cir- culatory system, which solves problems such as the decrease of drug concentration when passing through the digestive system. However this therapy has two important risks. The medication must only be a liquid solution or a fine dispersion in a liquid. The medication cannot react with the blood or the blood vessel, there for the solvent must be chemically inactive, and isotonic. Using homogenous liquids is not suitable as the active ingredient may interact with any cell in the way of the blood, instead of the target cells. The most common alternative is the dispersion of therapeutic drug in an aqueous solution compatible with blood. The ouzo effect seems to be an efficient solution to this drug carrying problem for different reasons. Firstly, in contrast to an ordinary emulsion, it has no added surfactant to stabilize the emulsion. Many surfactants destroy blood cell walls. Also, the droplets sizes produced with the ouzo effect, are of the optimum size (100nm-500nm) to eliminate can- cer cells. A correct understanding of the metastable region in the Ouzo diagram would be a great step towards this biotechnological breakthrough [14]

15 3. ANETHOLE-ETHANOL DENSITY CHARACTERISATION

When working with ouzo drops, we thought it was important to know the characteristics of the different mixtures in our system. When we researched written literature of the characterisation of the density of ethanol/anethole mixtures we could not find any papers on this topic. What we could find were many papers of scientists that had characterised the properties of alcohol/ethanol mixtures as well as other binary mixtures. Many of these papers had in common that they used the Jouyban Acree Model to describe the physicochemical properties of binary mixtures.[15] Physicochemical properties of liquids such as density, viscosity or surface tension influence the mass transfer, and therefore emulsification processes in solutions. Inmost cases mixtures of liquids have slightly different properties from an ideal mixing of the properties of the components. The Jouyban-Acree Model is the most accurate model to correlate physico-chemical properties of a mixture, with few experimental data. The Jouyban-Acree model is:

x · x x · x · (x − x ) x · x · (x − x )2 lnρ = x ·lnρ + x ·lnρ + J · 1 2 + J · 1 2 1 2 + J · 1 2 1 2 (3.1) m 1 1 2 2 0 T 1 T 2 T

Being ρm the physicochemical property of the mixture. ρ1 and ρ2, are respectively the physicochemical property of substance 1 and 2 of the binary mixture. x1 and x2 refer to the mole fractions. T denotes the absolute temperature at which the measurements have been made. J1, J2, and J3 are three dimensionless coefficients that are obtained by means of a no-intercept regression of experimental data.

3.1. Realisation of the Experiment

In this experiment were mainly interested in the density of an Anethol/Ethanol mixture. To fit it to the Jouyban Acree Model we made a series of a mixtures and measured itsden- sities using "Krüss Force Tensiometer-K20", with this we were able to measure densities of liquid both easily and precisely.

16 Fig. 3.1. Krüss Force Tensiometer-K20

The sophisticated instrument, normally used to calculate the surface tension of a certain liquid, also has a set of accessories that allows us to calculate the density of our mixture.

Fig. 3.2. Set for determining density of liquids

It is based on the buoyancy force exerted on the cylindrical platinum-iridium body of mass m. Firstly the body alone is weighed giving us its weight in the atmosphere F1, then it is submerged in the liquid giving the weight of the body in the mixture F2. The apparent weight of the submerged body is the result of the real weight of the body due to gravity minus the buoyancy force which is the weight of the liquid displaced due to the submersion of the body.

F1 = Vcylinder · ρcylinder (3.2a)

17 F2 = Vcylinder · ρcylinder · g − Vcylinder · ρliquid · g (3.2b)

F2 = F1 − Vcylinder · ρliquid · g (3.2c)

F1 − F2 = Vcylinder · ρliquid · g (3.2d)

F1 − F2 ρliquid = (3.2e) Vcylinder · g

We measured the density of five different anethole/ethanol mixtures. The mixtures were made varying the amount of anethole in volume. The experiment measurements were carried out at 24oC. The mole fractions of each component were calculated as we knew the molecular weight, and density of both pure substances, MWanethole=148.2 g/mol, MWethanol

=46.07 g/mole, ρanethole =0,988 g/ml, and ρethanole =0,79 g/ml. The Kruss machine made 10 measurements in a few seconds and gave a result with a very small uncertainty, negligible for our study. In between measurements all the equipment was cleaned with acetone, and handled with gloves and tweezers. Once the measurements were made MATLAB was used to calculate the coefficients that fitted the Jouyban Acree model with the least error. Thecoefficients were found by solving the matrix equation:

⎛ x ·x x ·x ·(x −x ) x ·x ·(x −x )2 ⎞ ⎛ ⎞ e1 a1 e1 a1 e1 a1 e1 a1 e1 a1 − · − · ⎜ T T T ⎟ ⎛ ⎞ ⎜lnρm1 xe1 lnρe1 xa1 lnρa1⎟ ⎜ 2 ⎟ ⎜J0⎟ ⎜ ⎟ ⎜ xe2·xa2 xe2·xa2·(xe2−xa2) xe2·xa2·(xe2−xa2) ⎟ ⎜ ⎟ ⎜lnρ − x · lnρ − x · lnρ ⎟ ⎜ T T T ⎟ ⎜ ⎟ ⎜ m2 e2 e2 a2 a2⎟ ⎜ · · · − · · − 2 ⎟ · ⎜J1⎟ = ⎜ ⎟ (3.3) ⎜ xe3 xa3 xe3 xa3 (xe3 xa3) xe3 xa3 (xe3 xa3) ⎟ ⎜ ⎟ ⎜lnρ − x · lnρ − x · lnρ ⎟ ⎜ T T T ⎟ ⎝⎜ ⎠⎟ ⎜ m3 e3 e3 a3 a3⎟ ⎜ ⎟ J2 ⎜ ⎟ ⎝ ...... ⎠ ⎝ ... ⎠

3.2. Results and Conclusions

Five experimental densities of the anethole/ethanol mixtures were taken 80%/20%, 75%/25%, 50%/50%, 25%/75%, 0%/100%. The density of pure anethole was also used as data, it was not measured as it would have been an unnecessary waste of anise oil. These were densities measured:

18 Anethole Ethanol Density (kg/m3) 100% 0% 988 80% 20% 951 75% 25% 941 50% 50% 893 25% 75% 841 0% 100% 788

Table 3.1. Experimental values obtained for different Anethole/Ethanol compositions.

The values of the coefficient that best fitted these values of mixtures at this given temperature were J0 = 68.147, J1 = −35.992, and J2 = 21.123. This allowed us to make reasonably good approximation for any ethanol/anethole mixture used in our experiments through the Jouyban-Acree Model.

1000 Joyban Acree Values Experimental Values Data Values

950

) 3 900

850 Density (kg/m Density

800

750 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ethanol Concentration (%)

Fig. 3.3. Experimental and Jouyban-Acree Model values for anethole/ethanol binary mixtures at 24oC.

Our characterisation of the density of Anethole/Ethanol mixtures, together with the work carried out by the university of Kuwait [15] on Ethanol/Water mixtures, gives us a good understanding of the density on the two possible miscible combinations in our system. The Jouyban Acree coeficients of Ethanol/Water mixtures were calculated, and proved to be J0 = −30.808, J1 = −18.274, and J2 = 13.89.

19 1000 Anethole/Ethanol Water/Ethanol

950

) 3 900

850 Density (kg/m Density

800

750 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ethanol Concentration

Fig. 3.4. Densities of Ethanol/Anethole and Ethanol/Water mixtures for different concentration of Ethanol.

3.3. Future Ideas

It would be a great interest to carry out a work as precise as the Department of pharmaceu- tics of the university of Kuwait [15] did with ethanol/water mixtures, but with anethole and ethanol. This would consist in making many more measurements to obtain more reliable Jouyban- Acree coeficients. Measurements would be taken atdifferent temperatures. Different physicochemical parameters could be analysed such as viscosity or surface tension. More measurements were not made in this project because the conditions in the laboratory of the department of fluids were not the best for these very precise measurements, temperature could also not be controlled. Another related work that can be done on this topic is to calculate the ternary density diagram of the Ouzo components; water, anise oil, and alcohol. If this were to be successfully carried out, by knowing the density of any Ouzo drop or streamline we would immediately know its composition.

20 4. PENDANT DROP EXPERIMENT

4.1. Realisation of the Experiment

This was the main experiment of this project. It consisted in placing a syringe connected to a thin glass capillary full of water inside an Ethanol/Anethole mixture. When the syringe is placed inside the mixture, the ethanol of the bulk liquid quickly starts diffusing into the syringe and floating upwards due to its low density. This upward flow of the alcohol pushed more water out of the syringe due to its constant volume. A drop hanging from the capillary appears which keeps growing due to the ethanol rich mixture diffusing into it. Eventually the drop would fall from the capillary. During the whole experiment a downward plume of what seems to be an anethole-rich mixture is present, this can be seen because of the higher refraction index of the anise oil. This higher concentration in oil of the falling plume makes sense, as ethanol will diffuse into the water of the syringe, leaving high concentration of its previous co-solute, anise oil, around the drop. Oil in water dispersions are formed both inside the drop as well as the stream line floating up the syringe, this can be distinguished because of the characteristic milky colour of the ouzo effect.

Fig. 4.1. Experiment setup. Close up of the pendant drop on the right.

21 4.2. Recording of the Experiment

Setup

The experiments took place in the fluids department lab in the Carlos III university of Madrid. The setup of the experiment was very simple. It consisted of a light source, this allowed us to see the drop clearly, it also made the footage to consist of shades, which made easier the following segmentation to analyse the frames. In front of the light source we placed a diffuser, the diffuser was simply a sheet of tracing paper. The diffuser was essential as the light source has many small LED bulbs which was an inconvenience for the images. Just in front of the light source and diffuser we placed the syringe and the glass with the mixture. The syringe was held by an adjustable holder which made it possible to gently lower the syringe into the mixture. Facing the syringe and glass we used a Nikon camera to film the growth and eventual fall of the drop. Two focusing lenses were used in the experiment.The camera was connected to a computer which stored all footage to later be analysed. The camera settings were a shutter speed of 1/1250, an aperture of f16, and an ISO of 80. The light source was on at 30% of its maximum intensity.

Fig. 4.2. Experiment setup.

Procedure

Firstly the mixture of which the experiment was going to be done was made. Each component (Ethanol and Anethole) had its own syringe to make the initial mixtures. Mixtures were made by concentration in volume. At the end two compositions of Anethole/Ethanol were analysed 80%/20% and 75%/25%. The mixture for 2-3 glass were made, each glass

22 being of 25ml. The mixture was stored in a previously washed sealed bottled. A new 2ml syringe was used for each composition studied. It was fully filled with dexoy- genated water. Once the light source, and camera were set to their usual parameters. The test glass was filled 25ml using another syringe exclusively for the mixture of the composition used. After each experiment was carried out and filmed, the water syringe was rinsed outby filling, and emptying it of deoxygenated water about 5-6 times. Then it was filledagain. The mixture in the glass (now with very small amount of water) was mixed. And then another experiment would take place. Each glass of 25ml of mixture would be used for three drops. It could be clearly seen that the mixture was too contaminated when the same mixture was used for over four drops. Once a glass had already taken three drops a new water syringe was used and the capillary was cleaned. Three videos were made for each glass, the glass was then cleaned in an ultrasonic cleaner. Ultrasonic cleaners make use of high pressure sound waves to agitate contaminants that are adhered to surface, in our case the inner walls of our glass. Cleaning the glass took about 30 minutes. Having three glasses sped up this process. If a new Anethole/Ethanol composition was used a new syringe for the mixture was taken.

Fig. 4.3. Ultrasonic cleaner (right), Tray two hold the objects to be cleaned (left)

4.3. Analysis of the experiment (image processing with MATLAB)

Once the footage of several drops in different compositions was obtained, it is analysed with image analysis computer software, MATLAB. As in most image analysis the first step to be able to obtain any information from the video is to do image segmentation on the video. This consists in converting our frames into a binary image, where each pixel has the value of 1 (white) or 0 (black). In our case we would want the drop to be ones, and all the rest to be zeros. The MATLAB code had several different steps to obtain this desired binary image.

23 1. Initially some parameters of the video are introduced. The left and right boundaries of the capillary, as well as its tip. This information is important as it would be the upper limit of the drop for all frames throughout the video. An estimate boundary for the whole drop is also introduced to be able to crop each frames so that the program works on smaller pictures, making the code faster.

Fig. 4.4. Original image. Dotted lines refer to the limits of the capillary. The rectangle represents the area which the software will crop to work on.

2. A common technique of image processing is called Background subtraction, or Foreground detection. It consists on subtracting the background of an image, in our case the image before any drop appears, to the rest of the frames. This is very useful to detect objects in the foreground, as is the case of our drop. Theoretically by subtracting the background we would already have all the background of a [0 0 0] black colour, although it is not yet binary nor is the drop completely white. Also the background isn’t completely black as it is not exactly the same in all frames.

Fig. 4.5. Subtraction of the background (middle) from the original image (left), to make most of the background black in the new image (right).

3. To further work on the image it was important to convert the current truecolour RGB image to a grayscale intensity image. This allows us to work with a single colour channel on the image, instead of the common three colour channel RGB images. Grayscale represents each pixel depending on the amount of light, ranging

24 from black at weakest intensity (0), to white at the strongest intensity (255). The MATLAB function used was "rgb2gray()".

4. Before converting the image from grayscale to binary, "imadejust()" is used. This maps all the pixels that aren’t black (the drop) on the higher end on the intensity spectrum, making the drop much whiter.

5. At this point, we convert the image to binary. A binary image has only two possible values for each pixel, 0 or 1. Given a threshold,"im2bw" function on MATLAB converts all pixels with lower index than the threshold to zeros, and all pixels with higher value in ones.

6. Now although we have a binary image there are certain imperfections we have to fix. Holes within the drops are filled firstly using "bwmorph", and then "imfill".

7. Any other white object that may have been detected is eliminated using "bware- open". This function eliminates all objects with smaller area than a given threshold. In our case the threshold is the area of the biggest body, the drop, found by "region- props" function.

Fig. 4.6. Results of the segmentation process steps 2-7.

4.3.1. Geometry of the Drop

Once the drop is in a binary image calculating different geometrical properties is quite simple. Three main characteristics are calculated in each frame: the detected contour of the drop.the volume of the drop, and its surface area. Each frame is analysed by using a loop.

25 1. The contour of the drop is detect by a loop analysing each row of the drop from the

bottom y0 to the top y1 . In each row the coordinates of the first and last white pixel (1) are stored. These coordinates are all the points of the contour we look for.

Fig. 4.7. The detected contour of this frame.

2. To calculate the volume of the drop we divide the drop in many circular discs of one pixel of width, one for each row of the image. The diameter of each disc is the absolute value of the difference of the x coordinates of the contour (left and right boundaries).

Fig. 4.8. How a disc of a row in the drop would look like. The width of the disc is not to scale in this image.

The volume of each disc (Vd) would be that of a regular cylinder, and the volume of the whole drop would simply be the sum of all these discs. Although the volume of the disc is calculated in pixels3 by knowing the width of the capillary in mm as well as in pixels in our image we have a pixels to mm scale. This allows us to

26 convert the volume to mm3 π · D2 · 1 V = (4.1) Disc 4

∑y1 VDrop = VDisc (4.2)

y=y0 3. The surface area is calculated in the same way as the volume. Instead of calculating the volume of each disc, we calculated the surface area of each disc. The surface area of the whole drop is the sum of the areas of all the discs.

ADisc = π · D · 1 (4.3)

∑y1 ADrop = ADisc (4.4)

y=y0

Both the volume and the area are made dimensionless with respect to the volume V0 and area A0 of a drop with a diameter equal to the diameter of the capillary, 2.33mm.

4.3.2. Bond Number of the drop

Theory

A pendant drop hanging from a capillary obeys the Young-Laplace equation: ( ) 1 1 γ · + = ∆P ≡ ∆P0 − ∆ρgz (4.5) R1 R2 The Young-Laplace equation relates the Laplace pressure along the drop interface with the curvature of the drop and the interfacial surface tension. The difference in pressure can also be expressed as a function of a reference pressure P0 at the bottom of the drop and the hydrostatic pressure caused by the density of the fluids. As the pendant drop is symmetric we can use cylindrical coordinates to obtain a set of dimensionless differential equation in terms of the arc length s from the drop apex. dϕ sin ϕ = 2 − Boz¯ − (4.6a) ds¯ r¯

dr¯ = cos ϕ (4.6b) ds¯ dz¯ = sin ϕ (4.6c) ds¯ All these variables refer to different geometrical parameters of the drop profile. ϕ refers to the angle of the tangent line to the drop contour with the horizontal axis. The coordinates on the horizontal and vertical axis, are described by r and z respectively. These

27 coordinates take the drop apex as the origin. The length of the arc along the drop profile from the drop apex is s. These parameters can be more clearly seen in 4.9. All r, z, and s are made dimensionless with relation to R0 which is the radius of the circle tangent to the apex of the drop.

Fig. 4.9. Geometrical variables involved in the calculation of the Bond number.

The pendant drop technique for surface tension measurement becomes more complex as the equations 4.6 can only be solved analytically for drops which are perfect spheres. However we can observe from 4.6 that the drop profile shape depends exclusively on the Bo term. Bo, the bond number, is a dimensionless number which measures the importance of gravitational forces compared to the surface tension. ∆ρgR2 Bo ≡ 0 (4.7) γ The Bond number depends greatly in the characteristic length of the drop. In our equations

28 the characteristic length is R0, the radius at the apex. The Pendant drop tensiometry technique consists on finding the drop profileff fordi erent Bo values until the best fit to the real drop is found. The Bond number will giveusthe surface tension of the drop knowing its density. In our experiment both the difference in density ∆ρ as well as the interfacial surface tension γ are unknown. The bond number will however give us a relation between both magnitudes.[16]

Fig. 4.10. Schematic of the pendant drop tensiometry process.

Bond fitting on MATLAB

Our fitting to obtain the Bond number in MATLAB follows the following steps:

1. Firstly the contours obtained in 4.3.1, are centred by translating the drop apex to the origin of the coordinate system. The drop contour is then scaled so that the radius of the capillary from which the drop hangs is exactly one. This will be important to compare it with the different shapes we’ll generate which will also be scaled this way.

2. An arbitrary initial Bond number Bo, and a non-dimensional volume, Vo (non- dimensionalised with respect to the radius at the apex) has to be introduced to begin the guess generation in the first iteration.

3. The bond fitting starts by drawing the drop profile for this given bond number. By means of "Ode45()" the differential equation 4.6 are integrated for the given Bo. The program also calculates the volume inside the generated drop profile. The odeset event function halts the integration once the volume of the drop profile equals the volume Vo given.

4. Once we have generated our drop profile, we compare it to the real contour tosee if it is an acceptable fit. Firstly it is also scaled, so that the radius of the capillary is one.

29 5. A direct difference between both profiles can not be done as they do not havethe same set of points. For this reason using the "interp1()" MATLAB function the values of the fitted contour are interpolated on the set of real drops data points.

6. A direct subtraction of the interpolated generated drops shape and the orginal drop is made to find the residual value. By using "fminsearch()" the steps 2-7 are continuously iterating changing Bo and Vo until the residual value is lowest, or the fit is best. At this point we can say it has converged and Bo is the real bond number for that drop.

7. Once one frame has converged the next frame carries out the exact same process. However the initial estimates of the next frame is the Bo and Vo calulated in the previous frame this way it converges quicker. The bond number, as well as the fitted contours of each frame are stored in an array.

Fig. 4.11. Flow diagran of the fitting process for frame k.

30 9

4 mm

0 Bond=0.30 V=6.35 -1 -6 -4 -2 0 2 4 6 mm

Fig. 4.12. Result of the fitting Bond Process.

Bond characteristic length

As mentioned before the characteristic length of the bond number obtained by integrating its contour from the 4.6 equations is the radius of the circle on the apex. For this study it is inconvenient as we would not know if a change in the Bond number is due to a variation in the γ/∆ρ relation or if it is just due to an increase in the radius of the apex of our growing drop. For this reason we decided to use the radius of our capillary r as the characteristic length of our Bond number. To carry out this change in the characteristic length we simply had to divide it by Ro2 and multiply it by r2. The radius of our capillary is of 1.165mm. ∆ρgR2 r2 ≡ 0 · Bo 2 (4.8) γ R0

To find the value of R0 of each frame the Pratt method of circle fitting was used. This method is a robust and accurate circle fit that only requires small amount of data. Inour case the circle was fitted to the bottom 5% of the drop profile. The radius at theapexof each frame was also stored in an array.

31 Fig. 4.13. Example of how a circle is fitted to the apex of the drop toknow R0.

4.4. Results and Conclusions

The drop proved to grow in a greater rate with a higher concentration in the initial bulk mixture.This seems to be logical as there is more alcohol wanting to diffuse into the water. We could visually see how the drop quickly took the milky white colour of the Ouzo effect, meaning there was oil in water nucleation. We could also see a stream of "ouzo colour" liquid quickly ascending the needle into the syringe. This ascending substance is probably composed of mostly alcohol. A downward plume of a substance with a different light refraction index was also observed. We believe it is an anethole-rich mixture that remains outside when alcohol enters the drop. It sinks due to its higher density with respect to the mixture. Similarly to the sessile drop experiments [11] the drop was oscillating continuously, especially when the volume is small, this is because of the marangoni flows caused by the constant change in concentration on the interface.

32 Fig. 4.14. Frame from an experiment with 4:1 in composition.

As the drop gets bigger the gravity force eventually, becomes greater than the buoyancy force exerted on the drop as well as the force caused by the interfacial surface tension of the drop. Four experiments were analysed for each composition, the results proved to be very re- peatable, even between first, second or third drops in the same mixture. This madeus trust our results were reliable.

Volumes 20-80 30 1st Drop 3rd Drop 25 1st Drop 3rd Drop

0 0 20 40 60 80 100 120 140 160 180 200

Fig. 4.15. Results of the volume growth of the 4 experiments analyse in 4:1 mixture until detachment.

33 Volumes 25-75 25 1st Drop 2nd Drop 20 1st Drop 2nd Drop

0 0 20 40 60 80 100 120 140 160 180

Fig. 4.16. Results of the volume growth of the 4 experiments analyse in 3:1 mixture until detachment.

We can estimate the Fritz radius at which gravity will overcome the other forces and detachment will take place. The Fritz radius is the radius of the sphere with equivalent volume to the drop at the moment of detachment. Tthe Fritz radius is calculated in terms of the interfacial surface tension of the drop γ, the radius of the needle from which the drop is hanging r (in our case 1.165mm), the difference in densities between the drop and the bulk liquid ∆ρ, and the acceleration of gravity g = 9.81m/s2. In our case to calculate the Fritz radius two assumptions were made. Firstly, Huanshu Tan’s approximation for the interfacial surface tension was used. He estimated γ to be half of the interfacial tension of pure-water with pure anethole (24.2mN/m)[1]. The composition of the drop is also unknown in our system. We will assume most of the alcohol entering the drop floats up the capillary, therefore the drop has an estimated density of pure water, 997kg/m3. Following the fritz model an estimation of the volume of the drop at detachment Vdrop was made.

Volumes are non-dimensionalized to Vo, the volume of a sphere of radius r.

( ) 1 3γr 3 R = (4.9a) F 2∆ρg

4 V = πR3 = V (4.9b) F 3 F drop 4 V = πr3 (4.9c) o 3

V R3 3γ V¯ drop F = = 3 = 2 (4.9d) Vo r 2∆ρgr

34 The result of V¯ for a 4:1 mixture (∆ρ = 46kg/m3) is 29.6. For a 3:1 mixture (∆ρ = 56kg/m3) V¯ turned out to be 24.34. These values are close to the results experimentally obtained from MATLAB, suggesting that the assumptions made are feasible.

Average experimental detachment V¯ Estimated detachment V¯ 4:1(80%/20%) 24,27 29,6 3:1 (75%/25%) 20,695 24,34

Table 4.1. Experimental and estimated values for V¯ at detachment.

0 0 20 40 60 80 100 120 140 160 180 200

Fig. 4.17. Results of the volume growth of the drop in both compositions until detachment.

The bond number detect by our fitting process showed that the Bond number ofboth compositions was almost identical. Bond numbers were very low and remained almost constant at around 0.05, there is a very slight decrease toward the end. This indicates that the surface tension is dominating over the gravitational forces during the whole experiment. These results are consistent with the estimation of the Bond number we can make using the same assumptions used to calculate the Fritz radius. Calculating the Bond number in this manner we would obtain a value of 0.05 for a 4:1 mixture and a bond number of 0.06 on the 3:1 mixture.

35 Average Experimetal detachment Bo Estimated detachment Bo 4:1(80%/20%) 0,054 0,05 3:1 (75%/25%) 0,0665 0,06

Table 4.2. Experimental and estimated values for Bo at detachment.

Fig. 4.18. Bond numbers as the drop grows.

1.2

0.8

0.6

0.4

0.2

0 0 20 40 60 80 100 120 140 160 180 200

Fig. 4.19. Bond numbers of both compositions 3:1 and 4:1.

36 4.5. Future Ideas

From this experiment two different ideas for experiments have been generated to have a better understanding of what is going on in our system.

Particle Image Velocimetry (PIV)

A long time of this project was invested in trying to segment the downward, anethole-rich, plume that descends away from the drop. The idea behind this was to track the velocity of the plume. If the speed at which this substance falls were to be successfully measured, assuming sinking plume is exclusively due to gravitational forces, we would know the exact density of this sinking mixture, and therefore its composition. The composition of the substance diffusing into the drop would also be known from the difference between the composition of the falling plume and the composition of the bulk liquid. I was not able to segment this plume good enough to track its speed. To measure the speed of this sinking substance particle image velocimetry, or PIV, could be an efficient solution. PIV would consist in putting tracer particles in the system. These particles are so small that are assumed to not have any influence and only follow the fluid dynamics. By tracking the position of these tracker seeds we would be able to determine the flow field in our system.

Synthetic Schlieren

Synthetic Schlieren would be another effective option to discover the densities, and therefore the compositions of the different flows in our system. It consists on filming apattern placed on the background of the medium to be analysed. Variation in the refraction index in the system causes the camera to see the pattern in the background distorted. This dis- tortion can be measured and used to determine the light refraction index in the different regions of the studied medium.These refraction indexes, can be used by the Gladstone- Dale relation to determine a qualitative density field of the liquid.[17]

Fig. 4.20. Experimental setup of synthetic Schlieren.

37 5. CONCLUSIONS

At the beginning of the project we wanted to figure out three main aspects inthe dynamics of a water drop in an ethanol/anethole mixture.

1. Characterize the flow rate into the drop fffor di erent compositions.

2. Determine the composition of the ouzo drop.

3. Determine the interfacial surface tension for different initial compositions.

A majority of the time of this project was trying many different types of experiments most of which were dismissed because of a lack of repeatability. However at the end a simple experiment was designed in which only the fluid dynamics of the system act, with no need of external action on the system. The results and conclusions of this experiment are explained in 4.4. By means of digital image analysis we were able to characterise the flow into the drop for two different compositions (point 1). Despite putting a lot of thought into determining the composition of the drop, this goal was not accomplished. However I believe the two ideas put forward in this project of PIV and synthetic schlieren will be able to determine the composition of the drop (point 2). The bond number was successfully measured for two components using the pendant drop technique. This will result in knowing the interfacial surface tension of the drop as soon as the density of the drop is known (point 3). During this project another task came up when we needed to know the density of a certain anethole/ethanol mixture. Not being able to find any characterisation of the density of this mixture, The characterisation of this mixture became a new task in this project. The density of this mixture was correctly characterised for any possible composition using the Jouyban-Acree model. Conclusion of this part of the project is explained in detail in 3.2.

38 BIBLIOGRAPHY

[1] H. Tan, “Evaporation and dissolution of droplets in ternary systems”, 2018. [2] P.-G. De Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and wetting phenomena: drops, bubbles, pearls, waves. Springer Science & Business Media, 2013. [3] B. E. Poling, J. M. Prausnitz, J. P. O’connell, et al., The properties of gases and liquids. Mcgraw-hill New York, 2001, vol. 5. [4] A. C. Martınez, Mecánica de fluidos. Editorial Paraninfo, 2006. [5] H. J. V. Tyrrell and K. Harris, Diffusion in liquids: a theoretical and experimental study. Butterworth-Heinemann, 2013. [6] P. Taylor, “Ostwald ripening in emulsions”, Advances in colloid and interface science, vol. 75, no. 2, pp. 107–163, 1998. [7] S. A. Vitale and J. L. Katz, “Liquid droplet dispersions formed by homogeneous liquid- liquid nucleation:“the ouzo effect””, Langmuir, vol. 19, no. 10, pp. 4105– 4110, 2003. [8] I. Grillo, “Small-angle neutron scattering study of a world-wide known emulsion: Le pastis”, Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 225, no. 1-3, pp. 153–160, 2003. [9] N. L. Sitnikova, R. Sprik, G. Wegdam, and E. Eiser, “Spontaneously formed trans- anethol/water/alcohol emulsions: Mechanism of formation and stability”, Lang- muir, vol. 21, no. 16, pp. 7083–7089, 2005. [10] H. Tan et al., “Evaporation-triggered microdroplet nucleation and the four life phases of an evaporating ouzo drop”, Proceedings of the National Academy of Sci- ences, vol. 113, no. 31, pp. 8642–8647, 2016. [11] O. Enrıquez, D. Robles, P. Peñas, and J. Rodrıguez, “The shaky life of a water drop in an anise oil-rich environment”, Bulletin of the American Physical Society, vol. 63, 2018. [12] C. E. Bogran, S. Ludwig, B. Metz, et al., “Using oils as pesticides”, Texas FARMER Collection, 2006. [13] M. Groves and R. Mustafa, “Measurement of the ‘spontaneity’of self-emulsifiable oils”, Journal of Pharmacy and Pharmacology, vol. 26, no. 9, pp. 671–681, 1974. [14] R. Botet, “The" ouzo effect", recent developments and application to therapeutic drug carrying”, in Journal of Physics: Conference Series, IOP Publishing, vol. 352, 2012, p. 012 047. [15] I. S. Khattab, F. Bandarkar, M. A. A. Fakhree, and A. Jouyban, “Density, viscosity, and surface tension of water+ ethanol mixtures from 293 to 323k”, Korean Journal of Chemical Engineering, vol. 29, no. 6, pp. 812–817, 2012.

39 [16] J. D. Berry, M. J. Neeson, R. R. Dagastine, D. Y. Chan, and R. F. Tabor, “Measure- ment of surface and interfacial tension using pendant drop tensiometry”, Journal of colloid and interface science, vol. 454, pp. 226–237, 2015. [17] H. Richard and M. Raffel, “Principle and applications of the background oriented schlieren (bos) method”, Measurement Science and Technology, vol. 12, no. 9, p. 1576, 2001.

40 Appendices

41 A. TABLES OF THE JOUYBAN-ACREE MODELS.

2 x1 x2 x1·x2·(x1−x2) x1 x2(x1−x2) Anethole Ethanol Xa Xe Xalnρa Xelnρe J0 · T J1 T J2 T lnρm ρm 100% 0% 1,000 0,000 6,896 0,000 0,000 0,000 0,000 6,896 988,000 99% 1% 0,975 0,025 6,721 0,169 0,006 -0,003 0,002 6,894 986,756 98% 2% 0,950 0,050 6,552 0,333 0,011 -0,005 0,003 6,893 985,312 97% 3% 0,926 0,074 6,388 0,492 0,016 -0,007 0,004 6,891 983,713 96% 4% 0,903 0,097 6,228 0,646 0,020 -0,009 0,004 6,890 981,995 95% 5% 0,881 0,119 6,073 0,796 0,024 -0,010 0,004 6,888 980,186 94% 6% 0,859 0,141 5,923 0,941 0,028 -0,011 0,004 6,886 978,311 93% 7% 0,838 0,162 5,777 1,082 0,031 -0,011 0,004 6,884 976,388 92% 8% 0,817 0,183 5,635 1,220 0,034 -0,011 0,004 6,882 974,432 91% 9% 0,797 0,203 5,497 1,353 0,037 -0,012 0,004 6,880 972,455 90% 10% 0,778 0,222 5,363 1,483 0,040 -0,012 0,004 6,878 970,466 89% 11% 0,759 0,241 5,232 1,609 0,042 -0,011 0,003 6,876 968,473 88% 12% 0,740 0,260 5,105 1,733 0,044 -0,011 0,003 6,874 966,479 87% 13% 0,722 0,278 4,981 1,852 0,046 -0,011 0,003 6,872 964,490 86% 14% 0,705 0,295 4,860 1,969 0,048 -0,010 0,002 6,870 962,507 85% 15% 0,688 0,312 4,743 2,083 0,049 -0,010 0,002 6,867 960,533 84% 16% 0,671 0,329 4,628 2,194 0,051 -0,009 0,002 6,865 958,569 83% 17% 0,655 0,345 4,516 2,302 0,052 -0,008 0,002 6,863 956,614 82% 18% 0,639 0,361 4,407 2,408 0,053 -0,008 0,001 6,861 954,669 81% 19% 0,624 0,376 4,301 2,511 0,054 -0,007 0,001 6,859 952,733 80% 20% 0,609 0,391 4,197 2,611 0,055 -0,006 0,001 6,857 950,807 79% 21% 0,594 0,406 4,095 2,709 0,055 -0,005 0,001 6,855 948,888 78% 22% 0,580 0,420 3,996 2,805 0,056 -0,005 0,000 6,853 946,976 77% 23% 0,566 0,434 3,900 2,899 0,056 -0,004 0,000 6,851 945,070 76% 24% 0,552 0,448 3,805 2,990 0,057 -0,003 0,000 6,849 943,169 75% 25% 0,538 0,462 3,713 3,080 0,057 -0,002 0,000 6,847 941,272 74% 26% 0,525 0,475 3,622 3,167 0,057 -0,002 0,000 6,845 939,377 73% 27% 0,512 0,488 3,534 3,253 0,057 -0,001 0,000 6,843 937,485 72% 28% 0,500 0,500 3,447 3,336 0,057 0,000 0,000 6,841 935,592 71% 29% 0,488 0,512 3,363 3,418 0,057 0,001 0,000 6,839 933,699 70% 30% 0,476 0,524 3,280 3,498 0,057 0,001 0,000 6,837 931,805 69% 31% 0,464 0,536 3,199 3,577 0,057 0,002 0,000 6,835 929,909 68% 32% 0,452 0,548 3,120 3,654 0,057 0,003 0,000 6,833 928,010 67% 33% 0,441 0,559 3,042 3,729 0,057 0,004 0,000 6,831 926,107 66% 34% 0,430 0,570 2,966 3,802 0,056 0,004 0,000 6,829 924,200 65% 35% 0,419 0,581 2,891 3,875 0,056 0,005 0,000 6,827 922,288 64% 36% 0,409 0,591 2,818 3,945 0,055 0,005 0,001 6,825 920,371 63% 37% 0,398 0,602 2,747 4,015 0,055 0,006 0,001 6,823 918,447 62% 38% 0,388 0,612 2,676 4,082 0,054 0,006 0,001 6,821 916,518 61% 39% 0,378 0,622 2,608 4,149 0,054 0,007 0,001 6,818 914,582 60% 40% 0,368 0,632 2,540 4,214 0,053 0,007 0,001 6,816 912,640 59% 41% 0,359 0,641 2,474 4,278 0,053 0,008 0,001 6,814 910,690 58% 42% 0,349 0,651 2,409 4,341 0,052 0,008 0,001 6,812 908,734 57% 43% 0,340 0,660 2,345 4,403 0,051 0,009 0,002 6,810 906,770 56% 44% 0,331 0,669 2,283 4,463 0,051 0,009 0,002 6,808 904,799 55% 45% 0,322 0,678 2,221 4,523 0,050 0,009 0,002 6,806 902,821 54% 46% 0,313 0,687 2,161 4,581 0,049 0,010 0,002 6,803 900,836 53% 47% 0,305 0,695 2,102 4,638 0,049 0,010 0,002 6,801 898,844 52% 48% 0,296 0,704 2,044 4,695 0,048 0,010 0,002 6,799 896,844 51% 49% 0,288 0,712 1,986 4,750 0,047 0,011 0,003 6,797 894,838 50% 50% 0,280 0,720 1,930 4,804 0,046 0,011 0,003 6,794 892,826 49% 51% 0,272 0,728 1,875 4,858 0,045 0,011 0,003 6,792 890,806 48% 52% 0,264 0,736 1,821 4,910 0,045 0,011 0,003 6,790 888,781 47% 53% 0,256 0,744 1,768 4,961 0,044 0,011 0,003 6,788 886,749 46% 54% 0,249 0,751 1,716 5,012 0,043 0,011 0,003 6,785 884,712 45% 55% 0,241 0,759 1,664 5,062 0,042 0,011 0,003 6,783 882,669 44% 56% 0,234 0,766 1,614 5,111 0,041 0,012 0,004 6,781 880,621 43% 57% 0,227 0,773 1,564 5,159 0,040 0,012 0,004 6,778 878,568 42% 58% 0,220 0,780 1,515 5,206 0,039 0,012 0,004 6,776 876,510 41% 59% 0,213 0,787 1,467 5,253 0,038 0,012 0,004 6,774 874,448 40% 60% 0,206 0,794 1,419 5,299 0,037 0,012 0,004 6,771 872,382 39% 61% 0,199 0,801 1,373 5,344 0,037 0,012 0,004 6,769 870,313 38% 62% 0,192 0,808 1,327 5,388 0,036 0,012 0,004 6,766 868,239 37% 63% 0,186 0,814 1,282 5,432 0,035 0,012 0,004 6,764 866,163 36% 64% 0,179 0,821 1,237 5,475 0,034 0,011 0,004 6,762 864,084 35% 65% 0,173 0,827 1,194 5,517 0,033 0,011 0,004 6,759 862,003 34% 66% 0,167 0,833 1,151 5,559 0,032 0,011 0,004 6,757 859,920 33% 67% 0,161 0,839 1,108 5,600 0,031 0,011 0,004 6,754 857,835 32% 68% 0,155 0,845 1,066 5,640 0,030 0,011 0,004 6,752 855,748 31% 69% 0,149 0,851 1,025 5,680 0,029 0,011 0,004 6,750 853,661 30% 70% 0,143 0,857 0,985 5,719 0,028 0,011 0,004 6,747 851,573 29% 71% 0,137 0,863 0,945 5,758 0,027 0,010 0,004 6,745 849,484 28% 72% 0,131 0,869 0,906 5,796 0,026 0,010 0,004 6,742 847,396 27% 73% 0,126 0,874 0,867 5,833 0,025 0,010 0,004 6,740 845,307 26% 74% 0,120 0,880 0,829 5,870 0,024 0,010 0,004 6,737 843,219 25% 75% 0,115 0,885 0,791 5,907 0,023 0,009 0,004 6,735 841,132 24% 76% 0,109 0,891 0,754 5,942 0,022 0,009 0,004 6,732 839,046 23% 77% 0,104 0,896 0,717 5,978 0,021 0,009 0,004 6,730 836,962 22% 78% 0,099 0,901 0,681 6,013 0,020 0,009 0,004 6,727 834,879 21% 79% 0,094 0,906 0,646 6,047 0,019 0,008 0,004 6,725 832,799 20% 80% 0,089 0,911 0,611 6,081 0,019 0,008 0,004 6,722 830,720 19% 81% 0,084 0,916 0,576 6,114 0,018 0,008 0,004 6,720 828,645 18% 82% 0,079 0,921 0,542 6,147 0,017 0,007 0,004 6,717 826,572 17% 83% 0,074 0,926 0,509 6,180 0,016 0,007 0,004 6,715 824,502 16% 84% 0,069 0,931 0,475 6,212 0,015 0,007 0,003 6,712 822,435 15% 85% 0,064 0,936 0,443 6,244 0,014 0,006 0,003 6,710 820,372 14% 86% 0,060 0,940 0,410 6,275 0,013 0,006 0,003 6,707 818,313 13% 87% 0,055 0,945 0,379 6,306 0,012 0,006 0,003 6,705 816,258 12% 88% 0,050 0,950 0,347 6,336 0,011 0,005 0,003 6,702 814,207 11% 89% 0,046 0,954 0,316 6,366 0,010 0,005 0,003 6,700 812,160 10% 90% 0,041 0,959 0,286 6,396 0,009 0,004 0,002 6,697 810,119 9% 91% 0,037 0,963 0,255 6,425 0,008 0,004 0,002 6,695 808,082 8% 92% 0,033 0,967 0,225 6,454 0,007 0,004 0,002 6,692 806,050 7% 93% 0,028 0,972 0,196 6,482 0,006 0,003 0,002 6,690 804,023 6% 94% 0,024 0,976 0,167 6,510 0,005 0,003 0,002 6,687 802,002 5% 95% 0,020 0,980 0,138 6,538 0,005 0,002 0,001 6,685 799,987 4% 96% 0,016 0,984 0,110 6,566 0,004 0,002 0,001 6,682 797,977 3% 97% 0,012 0,988 0,082 6,593 0,003 0,001 0,001 6,680 795,974 2% 98% 0,008 0,992 0,054 6,620 0,002 0,001 0,001 6,677 793,976 1% 99% 0,004 0,996 0,027 6,646 0,001 0,000 0,000 6,675 791,985 0% 100% 0,000 1,000 0,000 6,672 0,000 0,000 0,000 6,672 790,000 B. EXTRA GRAPHS OBTAINED FROM THE PENDANT DROP EXPERIMENT.

Areas 20-80 9 1st Drop 8 3rd Drop 1st Drop 7 3rd Drop

0 0 20 40 60 80 100 120 140 160 180 200

Fig. B.1. Evolution of the drop surface area, since the moment the capillary is inserted in the 4:1 Anethole/Ethanol mixture.

Areas 25-75 8 1st Drop 7 2nd Drop 1st Drop 6 2nd Drop

0 0 20 40 60 80 100 120 140 160 180

Fig. B.2. Evolution of the drop surface area, since the moment the capillary is inserted in the 3:1 Anethole/Ethanol mixture. Volumes 20-80 30 1st Drop 3rd Drop 25 1st Drop 3rd Drop

0 0 20 40 60 80 100 120 140 160 180 200

Fig. B.3. Evolution of the drop volume, since the moment the capillary is inserted in the 4:1 Anet- hole/Ethanol mixture.

Volumes 25-75 25 1st Drop 2nd Drop 20 1st Drop 2nd Drop

0 0 20 40 60 80 100 120 140 160 180

Fig. B.4. Evolution of the drop volume, since the moment the capillary is inserted in the 3:1 Anet- hole/Ethanol mixture. Volumes 20-80 30 1st Drop 3rd Drop 25 1st Drop 3rd Drop

0 0 20 40 60 80 100 120 140 160 180

Fig. B.5. Evolution of the drop volume, since the moment the drop reaches Vo in the 4:1 Anet- hole/Ethanol mixture.

Volumes 25-75 25 1st Drop 2nd Drop 20 1st Drop 2nd Drop

0 0 50 100 150

Fig. B.6. Evolution of the drop volume, since the moment the drop reaches Vo in the 3:1 Anet- hole/Ethanol mixture. Bond Numbers 20-80 1.2 1st Drop 1st Drop 1 3rd Drop

0.8

0.6

0.4

0.2

0 20 40 60 80 100 120 140 160 180 200 220 Time(s)

Fig. B.7. Evolution of the drop’s Bond number in the 4:1 Anethole/Ethanol mixture.

Bond Numbers 25-75 1.2 1st Drop 2nd Drop 1 1st Drop 2nd Drop

0.8

0.6

0.4

0.2

0 0 20 40 60 80 100 120 140 160 180 Time(s)

Fig. B.8. Evolution of the drop’s Bond number in the 3:1 Anethole/Ethanol mixture.