> M.ENG RESEARCH PROJECT < 1

Superspreading Effect of Nanofluids on Solid Surfaces

Timothy Peterson supervised by Dr Sergii Veremieiev

Abstract - The impact on droplet velocity down an inclined plane of varying concentrations of Aluminium Oxide nanoparticles with a nominal diameter of 50nm on Isopropanol has been investigated. A method of extracting frames of footage from video recordings and processing them to calculate velocity of a moving droplet was developed and employed, along with apparatus and surface modification of substrates, for subsequent use to reliably capture results. The response displayed has shown velocity to increase with nanoparticle concentrations up to 2.5 wt.%, at Bond Numbers close to unity. At higher concentrations and Bond Numbers the increased viscosity and viscous dissipation induced by the particles dominate over the enhanced wetting behaviour displayed in equilibrium, slowing the droplets.

Index Terms - Droplet, Incline, Nanofluid, Surface Energy, Velocity.

I. INTRODUCTION

anofluids are any fluid that has had nanoparticles of nominal diameter <100 nm dispersed throughout them in a suspension or solution. They

comprise a rapidly changing and expanding field of research due to the enhanced and unique properties they exhibit. The dynamic effects that are available by utilising nanofluids are found in many situations, such as industrial coating processes [1] or advanced medicines, pharmaceuticals [2] and power plants [3].

Another important and increasingly prevalent driving factor behind research into nanofluids is the improved thermal conductivity they exhibit, providing superior thermal management and mass transfer capability compared to ordinary fluids [4], [5], [6].

Originally theorised by Maxwell [7] the addition of nanoparticles has been shown to have a significant effect on the wetting and thermal characteristics of fluids. A number of studies have shown that a measurable enhancement in the wetting and consequential lubricating effect of the nanoparticles up to a 1% concentration by weight is observed [8], [9]

This report is the result of an investigation into literature surrounding nanofluids and a project further investigating

the enhanced characteristics of nanofluids by experimentally analysing the impact of nanoparticle concentration on the velocity of nanofluids travelling down an inclined plane. It will briefly cover the background theory of droplet motion and analytical expressions for predicting droplet velocity as well as the fluid properties of nanofluid solutions. It will then cover the experimental method used to conduct experiments and the theory behind any novel procedures developed throughout the project, before presenting and discussing the results gathered.

II. THEORY

To fully understand the results presented by previous studies, and hence the relevance of the results this project, a good understanding of the theory is necessary.

A sessile droplet can be analysed statically and dynamically through a number of fluid properties. A droplet surrounded by a gas, on a solid surface, subject to balanced forces can be considered in static equilibrium, as shown in Figure 1a.

Where 𝜃! , is the equilibrium contact angle, which is determined by droplet size, non-homogeneity and roughness of the substrate, and the method in which the droplet was deposited onto the substrate. The three phase contact line describes the line where the solid, liquid, and gas interact.

These contact angles can show the degree of wetting the droplet is experiencing. Good wetting is considered to be when 𝜃! = 0° and when 𝜃! > 90° wetting is said to be poor.

Once in motion, the analysis is no longer static and is dynamic contact angle theory. When surface tensions upon the droplet are unbalanced, movement occurs and two individual contact lines are apparent.

On the advancing edge is the advancing contact line, and its corresponding angle 𝜃!"#, which moves towards the vapour phase and provides the upper limit of contact angle.

On the trailing edge is the receding contact line and its angle 𝜃!"#, which provides the minimum contact angle as it moves towards the liquid phase, both the advancing and receding contact angles, along with the angle of inclination are shown in Figure 1b.

N

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Figure 1: Diagrams showing contact angles for (a) Static Equilibrium and (b) Droplet motion

The difference between the two is known as contact angle hysteresis, θ!!"# , and has been shown to be proportional to the balance of forces acting upon the droplet in incline [10].

θ!!"# = θ! − θ! (1)

Previous studies have extensively looked into the cause of this. Many studies attribute the difference to surface roughness [11] [12]. Other studies attribute the hysteresis to liquid molecular size and penetration of the substrate resulting in surface swelling. [13] [14].

Moving to droplets on an incline, a significant quantity of work has been done on the shape of droplets at the onset of motion [15] [16] [17], and as they begin to move down an inclined plane [18] [19]. This work most recently was built upon by Le Grand et al [20], who investigated the aspect ratios of the droplets with reference to the Capillary Number 𝐶𝑎 and Bond Number 𝐵𝑜. These are common properties to quantify fluid behaviour. The Capillary Number, defined as,

𝐶𝑎 = 𝜇𝑈 ⁄ 𝛾 (2)

is the ratio of interfacial tension to viscous forces on the droplet. Where 𝜇 is the dynamic viscosity, 𝑈 is the drop velocity and 𝛾 is the surface tension.

The Bond Number, based on the component of gravity parallel to the plane is defined as,

𝐵𝑜! = 𝐵𝑜 𝑠𝑖𝑛𝛼 = 𝑉! ! (𝜌𝑔 𝛾) 𝑠𝑖𝑛𝛼 (3)

where the 'true' Bond Number is Bo, which is the ratio of gravitational to surface tension forces. 𝛼 is defined as the angle of inclination of the plane, 𝜌 is the density of the fluid, 𝑔 is acceleration due to gravity and 𝑉 is the volume of the droplet - which in the case of Le Grand N. et al are V = (6 ± 0.2)mm3 [20].

These parameters allow a number of properties to be quantified, Podgorski [19] worked to find definable Bond Numbers at which droplet motion down an inclined plane would transition from rounded to cornered and pearling flow as shown in Figure 2.

Figure 2: Diagrams showing droplet flow regimes, (a) Rounded droplets at low speed, (b) Cusping regime, on

border of pearling, and (c) Pearling drop releasing periodic series of droplets.

By rearranging Equation (3) an optimal droplet volume can be calculated in order to form droplets within the rounded flow regime if the maximum inclination angle, fluid density and surface tension are known. Podgorski et al [19] found that the transition Bond Number for rounded flow is relatively similar for all fluids. Experiments conducted for that paper on 47V10 Silicon Oil, which has very similar physical properties to the fluids in use for this paper, were looked at, and the data from those specific sets of experiments have been used, giving a transition of rounded - corner 𝐵𝑜 = 1.

Research into numerically predicting the terminal velocity of water droplets has been conducted by Puthenveettil, B. A., Senthilkumar, V. K. and Hopfinger, E. J. [21]. The work was based off the idea that for a given drop volume, there exists a critical slope angle at which motion onsets where gravitational forces are in balance with the local triple line pinning force.

Once motion is onset, these forces are balanced by the action of viscosity, the shear stresses arising from Stokes wedge flow and the shear stress experienced by the droplet bulk. This leads to these following equations, describing droplet motion.

𝐿 = 2𝜋𝑅! (4)

𝑉! = 𝜋𝑅!!ℎ (5)

𝑐(𝜃!) = !"#!!!!!!!!"#!!!

(6)

𝑈 = !"#$%&' ! !!!"(!"#!!" ! !"#!!")![!!(!!/!!) ! !!!!"(!!)!"(!!/!)]

(7)

where 𝑐! = 1.5 , 𝑐! = 1.57 and 𝑐! is constant of order unity. 𝑅! is the base radius of the drop, ℎ is the drop height, 𝑤 the base width and 𝜆 is the slip length, where the continuum approximation fails, typically of the order 10 nm.

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At larger Reynolds Numbers, defined as the ratio of inertial forces to viscous forces,

𝑅𝑒 = 𝜌𝑈𝑙 𝜇 (8)

where 𝑙 is the characteristic linear dimension, boundary layers will develop within the drop near the substrate and the dissipation inside these layers will dominate, which is to say that the retarding forces from bulk movement shear stress are significant and Stokes Wedge flow effects are neglected. This modifies the equation to become

𝑈 = !!!

!"#$%!" ! !!!"(!"#!!" ! !"#!!")

!!!!!!

(9)

where 𝑐! = 1.8 and 𝜈 is the kinematic viscosity, which is defined as

𝜈 = 𝜇 𝜌 (10)

The surface tension of nanofluids is addressed by Bhuiyan M.H.U et al (ICTE 2014). They conclude that the surface tension of nanofluids increases with respect to concentration of the nanoparticles and bulk density of the particles, a larger nanoparticle causing an increased change in surface tension.

However, the results themselves show that this change can be considered negligible. At the lowest end of the spectrum a 0.05 Vol.% of SiO2 in Distilled Water shows a surface tension of just under 71 mNm-1, and at the other end of the spectrum observed in this study, a 0.25 Vol.% of TiO2 in Distilled Water shows an increased surface tension of approximately 72.5 mNm-1, giving a total change of under 1.8%. Therefore, no alternative equation for surface tension was used, since the impact of nanofluids on them did not have a significant effect.

The interfacial tensions of the fluid has been shown to have a direct impact on the contact angles produced through Young's classical equation

𝛾!" − 𝛾!" − 𝛾!"𝑐𝑜𝑠(𝜃!) = 0 (11)

where 𝑙 refers to the fluid, 𝑔 the gas, and 𝑠 the solid.

A concept of surface energy is the dominating attribute we see from these equations. It is the ratios of surface tensions between the phases or the interfacial tensions. Since the experiments must be conducted within normal atmosphere, the dominating factor is the relationship between the fluid and substrate surface tensions. Following the work of Zisman (1964) [22] it was found that with the simple molecular liquids such as Isopropanol, and simple low energy surfaces, the Van der Waals forces begin to dominate. Consequently the interfacial tension between the

solid and liquid is determined irrespective of the liquid, and instead by the solid surface energy characteristic. Though the interfacial tensions between the liquid and gas phases are largely unaffected by the introduction of nanoparticles, the solid-liquid interfacial tensions do have a quantifiable change that is discussed later in the paper.

In regard to the viscosity, the Einstein equation,

!!!

− 1 = 2.5𝜙 (12)

where 𝜇 is the dynamic viscosity of the nanofluid, 𝜇! is the dynamic viscosity of the base fluid and 𝜙 is the volume fraction of solid particles within the fluid, is found to drastically under predict the viscosity [23].

Hence, an equation developed by Valery Ya. Rudyak [24] can be utilised, which accounts for the dependence of viscosity on both the base fluid and particle size. This gives the viscosity of the nanofluid as

!!!= 1 + 2.5 + 13.43𝑒!!.!"#

!!! 𝜙 + 7.35 +

38.33𝑒!!.!"#!!! 𝜙! (13)

where d0 is the characteristic size of the carrier fluid molecule and d is the nominal diameter of the nanoparticle.

All of this work has lead to the conclusions of Trokhymchuk et al [25] that the observed enhancement in wetting characteristics with the introduction of nanofluids is partially due to the solid like ordering of nanoparticles near the three phase contact line, creating a structural disjoining pressure that causes the enhanced wetting characteristics.

Additionally, the deposition of nanoparticles upon the substrate is theorised to increase the contact line velocity as the nanoparticle's sphericity enables the droplet to 'roll' over nanoparticles at the three phase contact line as observed by Sefiane et al [26], [27].

III. METHOD

A. EXPERIMENTAL SETUP

Experimental conditions and set up were focused on repeatability. Consequently, to carry out experiments accurately and consistently on an inclined substrate an experimental rig was devised, as pictured in Figure 3. The XYZ directions are of a standard Cartesian space to provide a sense of orientation.

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Figure 3: Experimental set up of equipment, (a) top down view, (b) side view - as if from camera

A 210 mm x 210 mm glass plate was suspended within a plastic shell by a pair of metal clips, on top of which a 75 mm x 25 mm glass slide was affixed. The underside of the glass plate was covered in black card to reduce glare. This holder was attached to a stand that raised it from the ground by 250 mm, a pivot screw at the point of attachment allowed the inclination angle 𝛼 to be altered within ±0.5°. To ensure repeatability, an inclinometer was used to measure and verify the angle at which the plate was set. Experiments were conducted within a 'clean' laboratory space. Effort was made to minimise external airflow and any dust in the air. Temperature and humidity were monitored in the lab and found to average 21°C and 49% humidity.

Following on from Equation (3), the optimal droplet size at an inclination of 15° was 35 µL. A microliter pipette was used to measure this out, and, in practice, it was found that droplets up to volumes of 40 µL were viable without transitioning too far into the pearling regime. For conducting the experiments at a higher 30° inclination, the same droplet volume was used. Although this forces a higher Bo and pushes it into the cornered regime, the droplets were found to still be able to be processed by the code discussed later and did not leave any distinct 'pearls' behind.

B. VISUALISATION AND IMAGE PROCESSING:

A Digital USB Microscope was set up level with the substrate at 200 mm away from the substrate in the horizontal plane. In order to properly capture images of the droplet profile a polarising filter was placed in front of the

lens and a black background behind the droplets. Due to the time delays incurred between sending the command to the microscope to capture an image, save it and then capture another, taking individual images of the droplet as it moved down the plane was unachievable. Consequently, video footage was taken through the microscope, and the resulting footage split into its constituent frames, with each frame having a timestamp generated by setting the frame rate of the camera to 30fps and calculating the timestamp from the frame number. The program performed a number of steps on the resultant images in order to calculate the velocity of the droplets and the alignment of the camera with the horizon. Firstly, the image was re sized and run through an RGB - Grayscale conversion. The image was then run through Sobel edge detection and Hough transformed to identify the horizon, the droplet being analysed, and calculate its velocity.

The Sobel transform breaks the image down into edges by assigning value to the intensity of each pixel and analysing the gradient of the pixels to determine where an edge lies. The Hough transform then looks at all these edges and attempts to fit a parametric representation of them, defined by: r = x*cos(θ) + y*sin(θ) for a line, or x2 + y2 = r2 when looking for a circle. If the identified shapes are within user specified parameters of circle radius and line length. The coordinates of each correctly identified shape are stored in an array, which is used to calculate the rate of movement of any detected circles [28], [29]. The results of these processes on a frame of footage are shown in Figure 4 & 5.

Figure 4: Results of the Sobel Edge Detection Transform. The detected 'edges' are displayed as white lines.

Figure 5: Plot of the r, θ values generated from a Linear Hough Transform on a frame of footage of a deposited

droplet in motion.

> M.ENG and B.ENG RESEARCH AND INDUSTRIAL PROJECTS < 5 [30], [31], [32], [33].

TABLE I. SPECIFICATIONS OF FLUIDS USED

Solution Solvent Solute Diameter

Solute Concentration (by % wt)

Surface Tension (mN/m)

Dynamic Viscosity (mPa.s)

A Isopropanol - - 21.40 2.04

B Isopropanol <50nm 1% 21.40 2.07

C Isopropanol <50nm 2.5% 21.40 2.12

D Isopropanol <50nm 5% 21.40 2.21

E 50% Isopropanol & 50% UHQ water

<50nm 2.5% 24.78 3.00

This procedure is reliant on the concept that if the droplet is sufficiently poorly wetted, then with a black background, and the images fed through a polarising filter that was placed over the lens of the digital microscope, to limit any reflections from the equipment, help control the light levels in the experiment and increase the contrast of the captured images. The refraction of light through the fluid and its reflection in the glass plate is significant enough to register as a circle in the program and therefore be used to calculate droplet velocity.

Experimental practice showed that depending on program parameters such as how low the change in gradient required for identifying an edge, multiple circles could be detected. However, it was found that the droplet would always be located at the right hand side of the image, with any circles on the left often being artefacts from the light source or the pipette moving out the frame.

Consequently, the code was designed to access the array of circles detected and calculate velocity using the rightmost set of coordinates. Frames such as those in Figure 6, were checked after each experiment to ensure that the droplet was being calculated with the appropriate set of coordinates.

The altering light conditions in the lab were adjusted for by altering the sensitivity of the circle-detecting algorithm and carefully choosing which video frames from the captured footage would be fed through to calculate velocity.

The results of the linear Hough Transform were used to calculate the longest line visible in the image and comparing it to the alignment of the camera and plate to detect any offset in the experimental set up. The results of performing both the linear and circular Hough transforms are shown in Figure 6. The same image that was used in Figures 4 & 5 has been used.

C. FLUID AND SUBSTRATE PREPARATION

The chosen nanofluid was an Isopropanol and Aluminium Oxide mixture, with nominal particle size < 50nm and a rated density of 0.79 g/cm3 at 25°C. [34]. The density of isopropanol on its own is 0.785 g/cm3. Therefore, for these experiments the density of the solutions used was assumed 0.79 g/cm3 since any variations in density would be negligible. Fluid properties are detailed in Table I.

Surface alteration was required to overcome the low surface tension of the isopropanol-based fluid and provide greater contact angles by altering the fluid-solid and solid-gas interfaces in Young's Equation (10). This both eases the image analysis by increasing the height of the deposited droplet and provides better results as a key factor for movement is differing advancing and receding contact angles - something that is not possible with extremely well wetted fluids. To achieve the sufficiently low surface energy needed to produce high contact angles on glass, a self-assembled monolayer of perfluorosilane was created. The introduction of CH3/CF3 groups has been shown by Zisman (1964) [22] to dramatically reduce surface energy of solids. The surface modification was performed on the 75 mm x 25 mm glass slides discussed previously.

Figure 6: A fully analysed and process frame of video footage displaying the droplet on the left and the detected horizon on the right. Note - The wavy line on the right is the metal clip holding

the substrate.

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A. Preparation of slides:

The use of clean glass slides is crucial to obtain reproducible results. The procedure followed was:

1. Glass slide dried at 100°C for 60 minutes in the oven 2. Sonication 3 × 15 minutes in sonication bath. 3. Wash in running hot water for 10 minutes. 4. UHQ (Ultra High-Quality) water rinse 5 minutes, held

with clean tweezers. 5. Slides are blow dried with N2 gas. 6. Slides are bathed in chlorosulfuric acid for 120 minutes. 7. Repeat steps 3-5 8. Slides are further dried at 100°C 60 minutes in the oven. B. Silanisation of glass slides: 1. Slides are placed in a vacuum chamber with the silane,

and left for 60 minutes. 2. Slides are rinsed in UHQ water for 2 minutes. 3. Slides are blow dried with N2 gas 4. Slides are further dried at 37-45°C overnight.

Slides were observed with UHQ water and isopropanol to produce high, symmetrical contact angles. Care was taken with the slides to handle with latex gloves at all times and carefully cleaned to reduce degradation of the silane monolayer. A pictorial representation of the surface chemistry is shown in Figure 7.

Experiments were conducted with Isopropanol, Isopropanol-Aluminium Oxide Nanofluid and a Water-Isopropanol-Aluminium Oxide mixture. The properties of these fluids are shown in Table I. They were synthesised by mixing the 20 wt.% Isopropanol-Aluminium Oxide nanofluid with technical grade Isopropanol to dilute it to the desired concentrations.

IV. RESULTS AND DISCUSSION

Experiments were conducted with the fluids detailed in Table I. at inclinations of 15° and 30° degrees to the horizontal, to investigate the effect of nanoparticle concentration on the velocity of the droplets sliding down the inclined plane. The results of these experiments are presented and discussed here. The results presented have been selected because of their interesting features and insight into the underlying mechanisms behind the behaviour exhibited.

A. DROPLET VELOCITY

Results are first presented for the average Capillary Number, which serves as a non-dimensional velocity, of 40 µL droplets sliding down both the 15° and 30° inclined glass slides, against the varying concentrations of aluminium oxide nanoparticles within the isopropanol suspension that were tested as detailed in Table I. The same droplet volume was used for both the 15° and 30° inclines, giving them Bond Number's 1.089 and 2.105 respectively. For the 15° incline this was within the rounded flow regime as calculated, however, on the 30° this pushed it into pearling. This was done in order to compare the behaviour of a droplet on the 15° incline, where viscous and gravitational forces are balanced, against the 30° where gravitational forces dominate, hence producing the higher Bo. The results of these experiments are shown in Figure 8. For each concentration, three experimental results were collected, and their average calculated. Both the results and their averages are plotted.

Figure 8: Plot of the average Capillary Number of recorded experiments and the analytical predicted behaviour from

Equation (7) against particle concentration.

Figure 8 also shows the predicted change in velocity based off the analytical equations for an ordinary fluid presented in Equation (7), the analytical response form Equation (9) was also calculated, however, it was found to show results that disagreed with experimental results by an order of magnitude. By altering constant c5, and setting it to equal 0.035, Equation (9) was found to produce results that are more reasonable. However, analysis of the equation shows that it is dominated by the static volume of the head of the droplet, and neglects the effects of viscosity and geometric profiles to an extent, leading to a relatively unchanging predicted velocity.

The predicted behaviour that is plotted shows that theoretically velocity should increase as nanoparticle concentration is increased, due to the reduced equilibrium contact angle dominating the equation. The increasing

Figure 7: Silanisation of glass

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viscosity, which according to Equation (7) should slow the droplets, has a negligible effect on the theoretical analysis.

The data shows that for the 15° inclination, the velocity of the droplets increases with nanoparticle concentration, up to a saturation point around 2.3-2.5 wt.%, wherein it starts to reduce the terminal velocity of the droplets, drawing even to the velocities of base isopropanol at approximately 4 wt.% concentration and continuing to reduce the terminal velocity past that to lower than base velocities. In contrast, the data from experiments at a 30° inclination show a dramatic drop off in terminal velocity at the introduction of nanoparticles, and a subsequent more gradual decrease in terminal velocity as the wt.% is further increased.

B. DROPLET GEOMETRY

The shape of the droplets is potentially an indicator as to why the velocity varies with nanoparticle concentration as it does. Hence, presented next are the contact angles and geometric profiles of the droplets both in motion and measured on a flat plane. The images used for this analysis are taken from the Image Analysis code discussed in section III. Images were selected from the available frames based on how developed the flow had become. This meant that the droplets had to be clear of the pipette and the side profile had to maintain a relatively consistent shape from that point onwards, hence allowing the assumption that forces within the droplet are balanced. The side profiles of the droplets are presented in Figures 9 and 10.

The advancing and receding contact angles for all these droplets and the equilibrium contact angles for when the droplets were deposited on a level plane were measured. The data showed that the increasing nanofluid concentration marginally lowered the equilibrium contact angle, as expected. The enhanced wetting characteristics, changing the equilibrium contact angle from a value of θ! = 33 for the Isopropanol on its own, and θ! = 28 for the highest concentration, 5 wt.% solution.

The variations in receding and advancing contact angles are shown in Figure 11, measured from captured frames of the droplets in motion, the same frames as the ones used in the side profiles displayed in Figures 9 and 10 were used for consistency. It is clear that as the concentration of nanoparticles increases, the advancing contact angle decreases linearly for both the 15° inclination and the 30°, where as the receding contact angle is relatively unchanged with the introduction of nanoparticles.

Comparing the measured contact angle data to the side profiles shown in Figures 8 & 9, it can be seen that the consistent receding contact angle comes from the fact that

Figure 9: Side profiles of droplets in motion on a 15° inclination.

Figure 10: Side profiles of droplets in motion on a 30° inclination.

Figure 11: Variation of advancing and receding contact angles with nanoparticle

concentration

Figure 12: Variation of Tail Length with measured Capillary Number. Base Isopropanol

data points are outlined with red.

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the developed tail of the droplet in motion forms a consistent contact angle with the substrate regardless of nanoparticle concentration and inclination of slope. What can be noted is that the length of the tail does dramatically change. Figures 8 & 9 shows the growth of the tail measured from the termination of the tail of the droplet to the point where fluid thickness reached a value of approximately 3x the thickness of the end. Tail length versus the Capillary Number of the droplets shows an almost linear relationship between the two, as shown by Figure 12.

C. MULTIPLE FLUID MIXTURES

The addition of water into the isopropanol nanofluid was experimented with in an investigation to see whether the significantly higher surface energy of water would dominate the mixture and cause different trends. A 50/50 [by weight] mixture of UHQ water and 2.5 wt.% nanofluid was deposited on the treated glass substrate at a 15° incline. It was found that the water did have an effect, though not as dominating as hypothesised. Initial tests with pure water found that the interfacial tensions were high enough that the droplets did not slide with the original 40 μL volume, as they did not pass the critical Bo for sliding. When mixed in a 50/50 solution by weight with 2.5 wt.% Isopropanol - Aluminium Oxide, sliding did occur. The recorded images show negligible difference between the geometry of the 2.5 wt.% nanofluid and the 50/50 UHQ water and 2.5 wt.% nanofluid aside from a marginally longer tail. The calculated velocities and Capillary Numbers show a decrease of approximately 11% from an average velocity across runs of 89 mm s-1 to 79 mm s-1.

D. DISCUSSION OF RESULTS

The results gathered show a strong correlation between the length of the tail running behind the droplets as they traverse the slides, and their overall velocity. Furthermore it is apparent that with the introduction of nanoparticles into the fluid, the behaviour no longer follows that which is analytically predicted. The 15° inclination tests, where the gravitational and viscous elements of the Bond Number were roughly in balance, showed an increase in velocity up to a concentration of 2.5 wt.% before declining, where as on the 30° inclination, where gravitational forces dominate the droplet an increase in nanoparticle concentration showed a drop in droplet velocity. Although the work by K.Sefiane et al [27] found that advancing contact line increased with the increasing particle concentration before decreasing again once it reached a saturation point around 1 wt.%. These experiments found a continual reduction in advancing contact line. However, this is partially attributable to the small values of contact angle being measured, due to the high degree of wetting exhibited by isopropanol, increasing

the percentage error in measurements. Additionally, experiments were conducted with the fluids detailed in Table I., which only included concentrations greater than 1 wt.%, hence overlooking the area where theoretically an increasing advancing contact angle could have been seen.

If the fluids were to be considered as classical Non-Newtonian fluids, then the increasing viscosity of the fluids from the introduction of the nanoparticles should cause the advancing contact line at the front of the droplet, to slow as well, which would correspond to a lower overall velocity. This behaviour is seen in the 30° incline, where gravitational forces are dominant and hence the effects of the nanoparticle lubrication and potential surface modification form the deposition of particles are minimised. Therefore, as particle concentration increases, the increased viscosity and change in the droplets' geometric profiles, as the higher viscosity causes a greater proportion of the deposited fluid to shift towards the advancing edge of the droplet. Leaves a shorter tail, and heightens the viscous dissipation taking place on the leading edge due to the discussed greater quantity of fluid and as a result higher proportion of nanoparticles, slowing the droplet, as shown by P.G. de Gennes [35] and Dussan and Davis [36].

For the experiments with the 15° incline, the mechanisms previously discussed are still occurring, however, the initial increase clearly shows that other mechanisms are dominating the movement of the droplet. Wasan et al [9] demonstrated how structural disjoining pressure induced by the ordering of nanoparticles on the on the advancing edge of the droplet can enhance the spreading of fluids, an effect that dominates over Van der Waals forces and impacts over a larger proportion of the droplet profile. Although this theory was developed for fluids in equilibrium, K.Sefiane at al [27] demonstrated its applicability in dynamic movement and it is believed that it is a factor in the increased velocity exhibited. Additionally, the deposition of nanoparticles on the surface is a viable mechanism. A reduction in drag on the solid liquid boundary has an obvious impact on fluid velocity. Hence, the deposition of nanoparticles on the surface as the advancing contact line progresses down the plane is providing a reduction in friction as the fluid 'rolls' over the particles.

Beyond the saturation point for the 15° incline, the droplet velocity although reducing, remains higher than the base isopropanol to concentrations up to 4 wt.% hypothetically. This indicates that the lubricating effect created by the nanoparticles dominates the change in viscosity and consequential increase in viscous dissipation ablating the kinetic energy of the droplets, up to a saturation point. At which point, a reduction in velocity to speeds slower than

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the base isopropanol is contributed to by the increased quantity of nanoparticles depositing in a thicker, more uneven layer, reducing the drop in friction they provide. Furthermore, at the higher particle concentrations the enhanced wetting also tends to dominate, as the contact angle hysteresis reduces, a factor that previous studies [27] have shown is important in fluid spreading velocity.

Experiments with a 50/50 UHQ water and 2.5 wt.% nanofluid mixture yielded data that indicated the water did not dominate the surface energy of the fluid as much as expected, as indicated by the relatively unchanged contact angles. However, a slightly lower velocity was observed with this mixture, which can be attributed to the higher viscosity of the Water-Isopropanol mixture, hence indicating that the viscous dissipation within the droplets is a dominating factor.

V. CONCLUSIONS

The unusual dynamic behaviour of nanofluids has been experimentally demonstrated. The observed behaviour leads to an increased droplet velocity for Bond Numbers close to or less than unity for particle concentrations by weight of up to 2.5 wt.%. For higher concentrations a decrease was observed, though overall velocity still tended to be higher than the base fluid for concentrations as great as 4 wt.%.

For droplets with higher values of Bo a steady decrease in velocity was observed as nanoparticle concentration increased. The initial introduction of nanoparticles to the base fluid caused a steep drop in velocity and then a more gradual decrease as concentration was increased past 1 wt.%.

Fluid behaviour is attributed to increased viscous dissipation encouraged by the nanoparticles. A shift in droplet geometry due to the enhanced wetting characteristics nanoparticles caused the bulk of the fluid in the droplet to move towards the advancing edge of the droplets in motion. This increased the rate of viscous dissipation on the leading edge that led to a reduction in droplet velocity.

Increases in droplet velocity are attributed to a structural disjoining pressure induced by the ordering of nanoparticles at the three phase contact line. Combined with nanoparticle deposition on the solid surface must reduce friction, and, therefore increase the velocity at which the three phase contact line may advance.

ACKNOWLEDGMENT

T. A. Peterson would like to thank Dr Sergii Veremieiev for his support and guidance, Dr Chris Pearson for all his help and assistance working with nanofluids and Aixa Pineiro-Romero for her help creating a self assembled monolayer.

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