Advanced methods for droplet capture in water recovery systems and agricultural sprays

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Advanced Methods for Droplet Capture in Water

Recovery Systems and Agricultural Sprays

by

Maher Damak

Ing6nieur de 1'Ecole Polytechnique Ecole Polytechnique, France, 2013

M.S. Mechanical Engineering

Massachusetts Institute of Technology, 2015

SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING IN

PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING

AT THE

MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2018

Signature redacted

A uth or ... ...

Department of Mechanical Engineering May 15, 2018

Certified by ...

S ignature redacted

Khpa K. Varanasi Associate Professor of Mechanical Engineering

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Advanced Methods for Droplets Capture in Water Recovery Systems and Agricultural Sprays

by

Maher Damak

Submitted to the Department of Mechanical Engineering on May 15, 2018 in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy in Mechanical Engineering

Abstract

Water scarcity is one of the important challenges of our century. In this thesis, we investigate advanced methods to mitigate it in two ways: water recovery from fog and reducing chemicals runoff in agriculture.

In the first part, we review current fog collector design and identify droplet deviation around the wires of mesh collectors as the main bottleneck in water collection. We introduce an electrostatic force to overcome aerodynamic drag around the collector, using space-charge injection into the fog droplets and an electric field that drives them to the collector. We quantitatively model the collection and show that it scales from a one-wire system to a mesh. We demonstrate increases of up to 50X in collection efficiency, and show that various geometries and designs can be used. In particular, we propose the usage of this method to capture water from industrial condensation plumes. We model these plumes by taking into account the mixing dynamics between vapor and air and the heat transfer dynamics for droplet growth. Based on this model, we provide design

guidelines for effective plume collectors.

In the second part, we aim to enhance the retention of droplets on hydrophobic surfaces to reduce bouncing losses when pesticides are sprayed. We review current methods to retain impacting droplets and identify their limitations. We introduce simultaneous spraying of oppositely charged polyelectrolytes as a new method to enhance retention. We show that in a drop-on-drop impact with polyelectrolytes, a precipitation reaction occurs and surface defects are formed in-situ. These defects pin the retracting droplet and

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number increases. We demonstrate that, for low enough viscosities, oil impregnates the surface under the droplet during impact and generates a suction force that prevents bouncing. We then provide the optimal parameters for which the retention can be enhanced, to guide the preparation of effective agricultural sprays.

Thesis Supervisor: Kripa K. Varanasi

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Acknowledgments

First and foremost, I would like to thank my PhD advisor, Professor Kripa Varanasi, who made this thesis possible. His passion for research was contagious and he has been my biggest source of inspiration for this work. He taught me how to select impactful research topics, ask the right research questions and effectively communicate my results through papers and conference talks. Our meetings were great opportunities for exchange of ideas and scientific debate, and it has been overall a great pleasure to work with him and learn from him.

I also thank Professor Ahmed Ghoniem and Professor Paulo Lozano for serving on my

doctoral committee and for their insights and feedback.

I was also lucky to be surrounded by an exceptional team during my time at MIT. It has

been a great pleasure to get to know and to work with the Varanasi group members. I would like to especially thank Dan, whose insights and feedback have on many occasions steered my research in the right direction, as well as Jolet, Susmita, Nasim, Arindam and all other former postdocs. I also thank the current and former graduate students for all our research discussions as well as the fun we had outside of the lab: Sami, Karim, Henri-Louis, Leonid, Divya, Brian, Adam, Srinivas, Taylor, Ingrid, Sam, Vishnu and all the others. I also thank Srimayi who worked with me as a UROP, and our successive lab administrators Lauren and Rob.

This work would not have been possible without the support of the Tata Center for Technology and Design at MIT. In addition to financial support, the Tata Center has allowed me to learn about design for the developing world through both classes and field

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all the professors I took classes with, the staff of the Martin Trust Center for Entrepreneurship and the DeltaV 2017 cohort, the staff of the LMP and Edgerton machine shops, the MakerWorks volunteers and the MechE administrators, especially Leslie Regan.

To my family, who has been an inexhaustible source of support of encouragement for the past 28 years, thank you. My parents, Mounir and Samia Damak, and my brother Mehdi are the reason I am here today. They have always been there for me and have always pushed me to use my potential to its fullest. Our weekly Skype calls have been a staple of my time in Cambridge and I am grateful we got to see each other and travel together in the US, Europe and Tunisia over the past four years.

I finally thank all of my friends. I have met incredible people in the past few years both at

MIT and in the Boston area, and they are the main reason I can say that Cambridge has become the third city that I can call home. I also thank my old friends who have also been a great source of support from around the world.

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List of figures

Figure 1-1. Photograph of a typical fog collection system.5 _... . ... . . . . ₂₂ Figure 1-2. Causes of spraying inefficiency. (a) Water droplets on a lotus leaf. The leaf

is superhydrophobic and impacting or deposited droplets bounce and roll away, leading to very low retentions.2 4 _{(b) Wind drift of pesticides from an agricultural field}

to a nearby road. ... .. ... ... ... ... . . 25

Figure 2-1. Trajectories of fog droplets around a cylinder with and without the

application of corona discharge. (a-b) Schematic of air streamlines and droplet

trajectories and photograph of droplet trajectories in the absence of an electric field. The inset shows the velocities of the wind w and the particle u and the drag force acting on the droplet. The bright ring is the edge of the cylinder. (c-d) Schematic of air streamlines, electric field lines and droplet trajectories and photograph under corona discharge. Droplets closely follow the electric field lines in this case. The inset shows the additional electric force acting on a droplet. The cylinders in (b) and (d) have a diam eter of 1.88m m ... 34 Figure 2-2. Mechanism of droplet collection on a cylindrical wire. (a) Schematic of

simplified experimental setup and droplet trajectories. (b) Schematic of the acceleration phase undergone by droplets. The electric field, the initial and terminal velocities, as well as the forces acting on a droplet are shown. (c) Added velocity as a function of V2. A linear fit of the data (R2 = 0.94) gives a slope 0.006 m.s'.kVW . The gray area is where the voltage is not high enough to induce corona discharge. The error bars reflect the standard deviation over four measurements. (d) Schematic of the cross-section of the collection phase near the cylinder. Streamlines, field lines and trajectories of the droplets are shown. (e) Nondimensional collection area as a function of V2 _{for four different wind speeds. The gray area is where there is no}

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Figure 2-5. Dependence of the deposition efficiency on the electrical number. The data corresponds to five values of the wind speed and five values of the voltage. The colors represent different wind speeds (Red 0.55m/s, Blue 0.6m/s, Green lm/s, Orange 1.65m/s, Purple 3.3m/s). The solid line is a linear fit (R 2=0.92), with a slope o f 0 .2 6 ... 4 4 Figure 2-6. Mechanism of droplet collection on two parallel cylindrical wires. (a) Schematic of droplet trajectories with two distant wires. The collection area of each single wire AsW and the distance D are shown. (b) Schematic of droplet trajectories in a two-wire system with spacing saturation. The parameters Ai, A,,, and D are shown. The green arrows show the single wire areas of collection A,,. (c) Photograph of the droplet trajectories for two distant wires. The wire diameters are 1.88mm. The distance between them is 10mm. The applied voltage is 10kV. (d) Photograph of the droplet trajectories in a spacing saturation case. The wire diameters are 1.88mm. The distance between them is 6mm. The applied voltage is 14kV. (e) AinAo/D* as a function of Ke for three different wire distances. The gray region covers theoretically inaccessible values. The vertical dashed lines represent the predicted spacing saturation values for D *=1.7 and D *=4.2... 46 Figure 2-7. Nondimensional collection area for two wires as a function of Ke for

three different wire distances. Closed symbols represent Ai" and open symbols

represent Aout. Aout has a linear behavior with a slope close to that of a single wire. Collection is not lim ited on the outer side. ... 48 Figure 2-8. Fog collection on meshes. (a) Snapshots of meshes at different time intervals of fog exposure. In the first row, a 15kV voltage was applied, while there was no electric field in the second row. Red dye was added to the dispersed fog for visualization purposes. (b) Photographs showing the collection mesh and the storage beaker for collected water after 30 minutes of exposure. The case with high voltage resulted in the collection of 30mL of water, while only three droplets were collected without electric field. Complete video of collection in Supplementary movie 4. (c) Mass of the collected water as a function of Ke for different meshes. The vertical dashed lines represent the predicted onset of spacing saturation from the two-wire

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model for meshes I to 3. (d) Deposition efficiency of the five meshes as a function of Ke. The colors represent different meshes according to the color code of (c). ... 50 Figure 2-9. Lab-scale setup of plume collector. With the electric field off, shown on left, the plume can pass through it unaffected. However, when the field is switched on, as shown on the right, the plume vanishes almost instantaneously, and the water begins to collect on the device. The water shown above is directed into the beaker b elo w th e m e sh . ... 5 3

Figure 3-1. Plume formation in cooling towers. (a) Photograph of a plume forming at a cooling tower of the MIT COGEN Power Plant on 5-6-2016. Ambient conditions were 10 C and 80%RH. (b) Saturation curve of water with different mixing scenarios:

Mixing along CA may cause plume formation while mixing along CD remains in the subsaturated regim e. ... 56

Figure 3-2. Schematic and photograph of experimental setup... 58

Figure 3-3. Photograph of a plume generated in our experimental setup. V0,=2.6m/s

an d T 0 ,= 7 2 iC ... 5 9

Figure 3-4. Schematic of a mixing plume and definition of model parameters. ... 61 Figure 3-5. Regime map for plume formation. Regime map outlining the limiting cases

discussed in the model as a function of two nondimensional numbers, and the location of experimental and cooling tower conditions in the chart... 68

Figure 3-6. Maximum droplet diameter as a function of maximum liquid water

content for various exhaust velocities and temperatures... 70

Figure 3-7. Plume droplet diameter as a function of height. Flow rate is 10cfh. Solid lines are model predictions and symbols are experimental data points... 71 Figure 3-8. Experimental concentration of plume droplets as a function of model sc a lin g ... 7 2

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Figure 4-2. Effect of high molecular weight polymers on droplet impacts. In case (a) a

typical water drop bounces off the surface while in case (b) polymer additives in the drop provide a high extensional viscosity, which dissipates the energy needed to propel the drop off the surface. 107... 82 Figure 4-3. Simultaneous spraying of opposite polyelectrolytes. (a) Schematic of

experimental setup for simultaneous spraying of opposite polyelectrolytes. (b) Expected behavior for the impact of a droplet with one polyelectrolyte polarity on a droplet with an oppositely charged polyelectrolyte. The coalesced drop sticks to the surface. (c) Snapshots of simultaneous spraying on a superhydrophobic surface. Sprays with very low droplet density were used to enhance visualization and slow down the process. In the first row, the two sprayers are spraying water and the surface remains dry. Almost all droplets bounce off. Some small droplets are deposited but they are cleared as soon as another droplet hits them. In the second row, opposite polyelectrolytes are sprayed. Individual droplets hitting the surface still bounce off. After 120ms of spraying, the first event of a droplet of one polyelectrolyte hitting a droplet containing the opposite polyelectrolyte happens. The coalesced drop sticks to the surface. Subsequent drops that hit this droplet also coalesce on it. Similar events happen all over the surface. Many droplets can be seen on the surface after 3 seconds o f sp ray in g . ... 8 6

Figure 4-4. Surface tension of polyelectrolyte solutions. Experimentally measured values of surface tension of the solutions that were used in experiments throughout the paper. All surface tensions of used solutions remained between 63 and 73mN/m. The changes in surface tension did not seem to be attributed to the polyelectrolytes but rather to the addition of NaOH and HCl to the solutions. ... 88

Figure 4-5. Impact of positive and negative polyelectrolyte droplets on a superhydrophobic surface. Both LPEI and PAA droplets bounce off the surface.

The presence of a single polyelectrolyte does not seem to influence the impact b eh av io r...8 9

Figure 4-6. Possible droplet interactions in simultaneous spraying of opposite polyelectrolytes. The first column contains schematics of the five possible scenarios.The next columns are snapshots of individual drop impacts for each of the

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previous scenarios. The rightmost column contains SEM images of the surface after the impacts. The images were taken at a tilt angle of 30'. Only the last two cases result in arresting the droplet and leaving a residue on the surface. (a) A 2 mm droplet of LPEI is deposited on the superhydrophobic surface and another LPEI droplet impacts it vertically. Snapshots of the impact show a similar behavior to typical single droplet impacts: Upon coalescence the merged droplet expands then retracts and eventually bounces off the surface. The process lasts around 20ms, which is comparable to the contact time of single impinging droplets of similar radius. The

SEM image shows the features of the surface, uncovered, as they were before the

impact. (b) The PAA on PAA impact exhibits a similar behavior and results in an unspoiled surface as well. (c) LPEI and PAA solutions are premixed, forming a bulk precipitate. The impact of a droplet of this mixture on a superhydrophobic surface results in bouncing, with no satellite droplet left behind. SEM images show that nothing is deposited on the surface. The precipitates seem to remain in the bulk and not act as a pinning site on the surface. (d) When a PAA drop impacts an LPEI drop, after a similar expansion phase, the retraction phase ends with an arrested droplet. The SEM image shows the deposition of a residue on the surface, formed by the precipitation of the opposite polyelectrolytes when the two droplets merged on the surface. (e) LPEI on PAA is similar and leads to the droplet sticking on the surface. 91 Figure 4-7. Impact of a water droplet containing 3pm silica particles on a

superhydrophobic surface. The droplet bounces off in a similar fashion to a pure

water droplet. No silica particles are left on the surface... 92

Figure 4-8. Defects formation and drop-on-drop impact dynamics. (a) Schematic of the formation of precipitates in the liquid and the role of surface precipitates in pinning the receding contact line of a droplet. (b) Top view snapshots of drop-on-drop impacts. Water droplets exhibit an axisymmetric uniform retraction, while, for

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contact length as a function of time for four scenarios. All droplets expand, reach a maximum diameter then retract. Bouncing occurs in three cases where the spreading coefficient goes to zero, while sticking occurs in the case with the highest polyelectrolyte concentration C. (e) Restitution coefficient as a function of the impact Weber number for water. The Weber number was varied by changing the droplet size and the impact velocity. In all drop-on-drop experiments, both drops had the same siz e . ... 9 4 Figure 4-9. Precipitate formation upon coalescence of two droplets. (a) Schematics and snapshots of the mixing of two polyelectrolyte droplets and the precipitate formation in air. (b) Schematic of experiments and snapshots of droplet mixing on a hydrophobized glass surface. The images were treated for better visualization. The snapshots corresponding to the precipitate formation time T are indicated in (a) and

(b). (c) Experimental precipitation time variation with polyelectrolyte concentration (d) log-log graph of the precipitation time (in ms) as a function of the volume of the

droplets (in mm3). The fitting lines have a slope of -1/2. ... 100

Figure 4-10. Bouncing-Sticking transition in a two-drop impact. The data points are experimental outcomes of impacts at different concentrations, radii and impact velocities. The figure axes are the work of pinning and the kinetic energy of the droplet. The dashed line roughly indicates the transition between bouncing and sticking and corresponds to Pi-0.1. Below the dashed line, pinning forces are larger than inertia and pinning of the droplet is expected, while bouncing is expected above. The inset illustrates the defect size, and the region around the contact line that is acted upon by pinning forces at a certain tim e... 102 Figure 4-11. Water and opposite polyelectrolytes spraying on a superhydrophobic surface. (a) Photographs of a 2x2" superhydrophobic surface after spraying fixed volumes of water and polyelectrolytes (LPEI and PAA). A fluorescent dye was added to allow visualization. (b) Coverage of the surface by the liquid in the same experiments. (c) Retained volume of liquid on the same surface after spraying water, LPEI + PAA and Chitosan + Alginate. (d) Retained volume of Chitosan + Alginate o n a L otu s leaf ... 104

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Figure 4-12. Retention and coverage after spraying water on a superhydrophilic

surface. The surface was silicon nanograss, with a contact angle close to 0'. The

values of retained volume (left axis) and surface coverage (right axis) are slightly larger than those for polyelectrolyte spraying on superhydrophobic surfaces. ... 105 Figure 4-13. Water (left) and polyelectrolyte (chitosan/alginate, right) sprays on

various plant surfaces. (a) Grape leaves. (b) Strawberry leaves. (c) Orange leaves. (d ) O ran g e fru its... 10 7

Figure 4-14. Effect of pH on precipitate formation with and without the addition of

0.15M NaCl. (a) Average coverage of the surface as a function of pH. (b) Average

turbidity of the polyelectrolyte mixture as a function of pH. Polyelectrolytes are Chitosan and Alginate with a concentration of 10mM. (c) Literature results of zeta potential of Chitosan and Alginate as a function of pH, for various ionic strengths. (P am in et. al. 151)... 111

Figure 4-15. Effect of NaCl concentration on precipitate formation. (a) Average coverage of the surface as a function of NaCl concentration. (b) Average turbidity of the polyelectrolyte mixture as a function of NaCl concentration. Polyelectrolytes are Chitosan and Alginate with a concentration of 10mM and at pH 5... 112 Figure 4-16. Effect of polyelectrolyte concentration on precipitate formation with

and without the addition of 0.15M NaCl. (a) Average coverage of the surface as a

function of polyelectrolyte concentration. (b) Average turbidity of the polyelectrolyte mixture as a function of polyelectrolyte concentration. Polyelectrolytes are Chitosan an d A lg in ate at p H 5 ... 113

Figure 4-17. Turbidity as a function of coverage for various polyelectrolyte solutions

in a log-log plot. Data points are from experiments at various pH, NaCl

concentrations, polyelectrolyte concentrations. Experiments were performed with two polyelectrolyte pairs: Chitosan/Alginate and LPEI/PAA. Solid line has a slope 1 and

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The droplets coalesce and expand until they reach a maximum diameter Dmax corresponding to a thickness h, then retract and bounce off. (c-d) Snapshots of the high-speed video of drop-on-drop impacts. (c) corresponds to the inertial-capillary

regime ( Di = Ds = 2.3mm , V = 1.1ms-1, t = 8.9.10-4Pa. s (water) ), while (d) corresponds to the viscous regime ( Di = Ds = 3.4mm , V = 1.23ms-1, p =

0 .3 4 P a. s). ... . . . 12 0

Figure 5-2. Expansion dynamics of drop-on-drop impacts. (a) Snapshots of the high-speed video of the impact of small water droplet on a bigger one (first row:

Di = 2.3mm , Ds = 3.5mm , V = 1.6ms-1, Supplementary movie 3) and vice-versa (second row: Di = 3.8mm , Ds = 2.0mm , V = 0.98ms-1, Supplementary movie 4). Both impacts are in the inertial-capillary regime. (b) Comparison of predicted (solid line) droplet thickness at maximum expansion and experimentally measured (symbols) thicknesses for various drop size ratios, velocities and viscosities. (c) Comparison of predicted and experimentally measured maximum diameter for the sam e d ata ... 12 3

Figure 5-3. Maximum expansion diameter results for drop-on-drop impacts. The x-axis is the Impact parameter P and the y-x-axis is the product of the normalized maximum diameter by the Reynolds number to the power 1/5. Two distinct regimes are observed. In the inertial-capillary regime (P < 1, solid line), DmaxDt varies as the Wel/4 and does not depend on viscosity. In the viscous regime (P < 1, dashed

line), DmaxDt varies as the Re1/5. The shown data are our results for size ratios of 1 and 2 as well as single drop data from literature. All data collapse on a single master cu rv e ... 12 6

Figure 5-4. Retraction results for drop-on-drop impacts. (a) The x-axis is the Ohnesorge number and the y-axis is the product of the retraction rate by the inertial-capillary timescale. Two distinct regimes are observed. In the inertial-inertial-capillary regime Eri is constant and does not depend on impact velocity, viscosity and size ratio. In the viscous regime Oh > 0.5, the retraction rate scales as the inverse of the

viscous-capillary timescale. (b) Snapshots of a drop-on-drop impact of water droplets

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drop impact (Di = 2.85mm,V = 0.98ms-1). The contact line moves exactly the same as the last case in the retraction phase. (d) Snapshots of a drop-on-drop impact

of water droplets of the same size (Di = Ds = 2.3mm , V = 0.71ms-1)... 129 Figure 6-2. Water and oil-in-water emulsion droplet impacts on superhydrophobic surfaces. (a) Schematic of experimental setup. (b) Snapshots of high-speed videos of emulsion and water droplets impacting on a surface. At We=50 both droplets bounce. At We-87, water bounces while the emulsion sticks. At We=95, both droplets splash and bounce. (c) Schematic of mechanism. When emulsion droplets impact, oil impregnates the texture on the surface under the droplet, so that the droplet retracts on a surface infused w ith oil. ... 137

Figure 6-3. Oil impregnation of surfaces during emulsion impacts. (a) Microscope images of surface after impacts of emulsion droplets at various concentrations on inclined superhydrophobic surfaces. (b) Snapshots of high-speed bottom-view videos of the spreading phase of a 20% hexadecane-in-water emulsion droplet impact on a transparent superhydrophobic surface (We=60). The focus of the lens is on the interfacial plane between the droplet and the surface. (c) Experimental measurements of normalized deposit diameter as a function of the Weber number for various concentrations of hexadecane-in-water emulsions. (d) Oil coverage of the surface after impact. Symbols are experimental measurements and solid line is model prediction. The inset is a schematic of the change in shape of droplets when they im pregnate the surface...139 Figure 6-5. Restitution coefficient and bouncing-sticking-bouncing transitions. (a)

Restitution coefficient of water droplets impacting superhydrophobic surfaces as a function of the Weber number. (b) Top view image of a droplet impact before the onset of splashing (We=26). (c) Top view image of a droplet impact after the onset of splashing (We=53). (d) Experimental results of emulsion impacts with various

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solid lines are estimates of the suction force for emulsion concentrations of 20% and

5% resp ectiv ely ... 14 5

Figure 6-7. Snapshots of water droplet impacts on liquid-infused surfaces (LIS). (a

-c) 1.5 cSt Silicone oil impregnating a microtextured surface with square pillars (width 10 tm, pitch 10[im, height 20pm). (d - f) 10 cSt Silicone oil impregnating a

microtextured surface with square pillars (width 10pQm, pitch 50pm, height 1 pm). (g

- i) 100 cSt Silicone oil impregnating a microtextured surface with square pillars (width l0tm, pitch 50pm, height 10pm). (a) We=38. (b) We=92. (c) We=130. (d) We=30. (e) We=90. (f) We=140. (g) We=30. (h) We=90. (i) We=140. ... 149 Figure 6-8. Impregnation of surfaces by impacting emulsion droplets and effect on

bouncing/sticking transition. (a) Schematic of impregnation dynamics of a single oil

droplet in water. (b) Snapshots of top view high-speed video of a 1 OcSt Silicone oil in water emulsion impacting on a surface at We=27. (c) Snapshots of top view high-speed video of a 1OOOcSt Silicone oil in water emulsion impacting on a surface at We=24. (d) Snapshots of top view microscope video of a 10OOcSt Silicone oil in water emulsion impacting on a surface at We=50. Images show oil droplets impregnating the surface and spreading dynamics. (e) Graph of oil droplet spreading diameter as a function of time for two selected droplets. Solid lines have a slope of

1/10 and indicate a t1/10 dependency. (f) Experimental impact outcomes of

oil-in-water emulsions of various viscosities on superhydrophobic surfaces and of oil-in-water droplets on liquid-infused surfaces (LIS) with lubricating oils of various viscosities. The lower solid line shows the limit at below which suction forces do not overcome the droplet inertia and where bouncing is expected to always occur for emulsions. The higher solid line shows the viscosity limit above which oil droplets in the emulsion do not have time to impregnate the surface during the contact time and the surface during the retraction phase diverges from an LIS-like surface. ... 152

Figure 6-9. Macroscopic spraying of emulsion on non-wetting surfaces. (a) Snapshots of high-speed video of water and emulsion (8% hexadecane in water) sprays on superhydrophobic surfaces. Spray droplets are on the order of 1mm in radius. All water droplets bounce while emulsion drops stick and accumulate on the surface. (b) Graphs of retained volume of spayed liquid on superhydrophobic surface after

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spraying fixed amounts of water and 20% hexadecane emulsions. Dashed lines are linear fits. The slope of the red dashed line corresponding to the emulsion case is 10 times larger than the slope of the water line. (c) Photograph of hosta leaf after spraying the left side with water and the right side with a 20% hexadecane emulsion. The left side remains largely dry while a film of liquid covers the right side... 154

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List of tables

Table 2-1. Characteristics of meshes... 36

Table 4-1. Molar weight, concentration, pH and zeta potential of the polyelectrolyte solutions used in the experiments... 85

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1. Introduction

Freshwater plays a critical role in many aspects of our lives -residential use, agriculture, manufacturing, energy production - and demand for freshwater will continue to rise as populations increase.' According to studies by the UN and the US State Department, we are on the path to an extreme freshwater shortage by 2030. Today already, although access to clean water is considered as a human right, there are still over 1.1 billion people who lack access to safe drinking water worldwide according to the World Water Council', and this number is expected to increase, as water resources get more and more polluted and scarce due to global warming. Water scarcity causes serious economical and social issues in the regions where it occurs. One promising solution to provide clean water to some regions is fog harvesting. Fog harvesting is particularly appropriate in remote, drought-prone areas where rainwater harvesting is impossible and where water transportation is prohibitively expensive. It can also be useful in regions where water is currently available, but where non-renewable groundwater is heavily used. Collecting water from fog can then mitigate the depletion of groundwater reserves.2 _{If dense fog}

occurs on a regular basis in such areas, then fog collection may be an economically viable solution to meet the needs in water of local populations. Areas prone to large fog formation are usually close to oceans where fog clouds form over the water and are then transported by the wind, but there are also some inland areas where climatic conditions make it possible for a dense fog to form.

Fog collectors have been successfully implemented in 17 countries, generally to provide water to poor communities, even if it has also been implemented in some developed countries such as Spain. A photograph of a typical system is shown in Fig. 1-1. The technology used is simple and sustainable and the water provided could be used in various applications: In addition to drinking water for humans and animals, the collected

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1 4

Figure 1-1. Photograph of a typical fog collection system.

Although fog-harvesting systems have been designed for centuries, and even with the improvements of the last decades, their efficiency remains dramatically low, around 2% for the systems used in practice. Typical values in actual systems range from 1 to 10 L/m2_{/day. Although many studies have focused on optimizing the collector shape and}

material, one main bottleneck, which is the deviation of fog droplets around collectors, severely limits their collection efficiency in practice. One objective of this thesis is thus to overcome this bottleneck and design highly efficient fog collectors.

In addition to natural fog, fog plumes also occur in several industrial processes, in particular power plant cooling towers. In evaporative cooling towers, hot water is evaporated to cool down the cycle and the generated vapor-saturated air is rejected from the outlet. Upon mixing with the ambient colder air, this vapor-saturated air cools down, which can lead to re-condensation of small droplets that are similar to droplets of natural fog. Plumes are a transient phenomenon: droplets condense due to temporary supersaturation conditions, but as more mixing occurs with sub-saturated air, droplets

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evaporate again and the plume dissipates.6 _{However, during their persistence time,}

plumes can pose visibility issues when they are produced in the vicinity of roads or airports. Limiting their size in these areas is important.7

The amount of water consumed in cooling towers is significant. Coal plants consume an average of 2100L/MWh, which is equivalent to 3,000 gallons per minute for a 250MW power plant.8'9 On a national level, the US's largest water withdrawal source is power plants, which account for 139 billion gallons of freshwater per day, which amounts to

50% of total US freshwater withdrawalsI and the 2014 DOE report The Water-Energy

Nexus: Challenges and Opportunities stressed the "urgency to address the water-energy nexus in an integrated and proactive way".0

For these reasons, applying fog collection methods to extract water from these industrial plumes can be beneficial." It can be part of the solution to the world water crisis by reducing the net water consumption of one of the biggest freshwater consumers (cooling towers), and it can serve as a plume abatement system to offset visibility problems. To be able to capture these plumes, it is necessary to understand their physical properties to make adapted collectors. So another objective of this thesis is the modeling of the formation and dynamics of water plumes.

Apart from collecting water from non-conventional sources such as fog and plumes, another important approach to mitigate the water crisis is the conservation of conventional freshwater sources such as rivers, lakes and groundwater. One of the main dangers for these water bodies is contamination by pesticides and other agricultural chemicals. A study found that pesticides could be detected 90% of the time in agricultural streams, 50% in shallow wells and 33% in major deep aquifers across the US.2

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found that 98% of insecticides and 95% of herbicides end up in the soil, water, air or on other species than those that were targeted. 13-15 This contributes to soil, water and air

pollution. It is also a risk for local ecosystems. For example, significant honeybee losses have been attributed to pesticides.16 There are two main reasons for the extremely low efficiency of pesticide application. First, many plants are hydrophobic and droplets of water-based solutions that are sprayed on them bounce or roll off their surface and end up

in the soil, where it they pollute the soil and contaminate groundwater.'7 _{Second, since}

agricultural chemicals are delivered in sprays of fine droplets, they are sensitive to wind drift that may take pesticides away from the fields, leading to pollution and contamination of other areas. Adverse health effects of pesticides have been shown, and people who are exposed to them may suffer from severe nervous diseases, reproductive problems and cancer.'s-22 These health effects are more prevalent in developing countries, where less precautions are taken when handling and spraying pesticides. In particular, most farmers use handheld sprayers, and do not wear personal protective equipment while spraying. This is partly due to the lack of resources, but mostly to the lack of awareness of the dangers of pesticides. A study found that up to 25 million persons in the developing world suffer pesticide poisoning every year, from which 3 million experience severe poisoning. 22

Due to all these adverse effects of pesticides, there is an increasing pressure to reduce their use.'7 _{Therefore, the challenge is to eliminate the sources of deposition}

inefficiencies in sprays. One of the most important inefficiencies is due to the hydrophobicity of certain plants, which leads to the bouncing or rolling of impacting droplets from the spray (Figure 1-2a). Such hydrophobic plants are common, and they usually get this property from the presence of waxes and hairs on the surface of their leaves.23 _{For these plants, most of the sprayed liquid ends up in the soil and does not}

benefit the plant. The goal is then to increase the efficiency of the pesticide spraying process by making the pesticide droplets stick to the plant and to ensure a better coverage of the surface of the leaves. Several parameters influence the outcome of droplet impacts on surfaces such as the liquid's surface tension and viscosity and the size of the droplets., with small droplets sticking better.

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a

b

Figure 1-2. Causes of spraying inefficiency. (a) Water droplets on a lotus leaf. The leaf is superhydrophobic and impacting or deposited droplets bounce and roll away, leading to very low retentions.24 _{(b) Wind drift of pesticides from an agricultural field to a nearby}

road.

Another important problem in pesticide spraying is the drift of pesticide droplets due to the wind. These droplets are generally on the order of 100 microns and, thus, can be easily carried over large distances by the wind.26,27 Such a case is shown in Figure 1-2b. Contrary to the retention problem, wind drift is aggravated by a decrease in droplet size. Thus, when growers choose their spray droplet size, they face a tradeoff between mitigating these two problems.

A third problem is the rapid evaporation of pesticide droplets, when their size is very

small. This evaporation may occur in the air and upon deposition, limiting the amount of pesticide actually absorbed by the plant.28

The final aim of this thesis will be to present two novel methods that can largely enhance the retention of different types of sprays on hydrophobic plants and may also mitigate drift and evaporation losses.

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1.1 Outline of thesis

The first part of this thesis focuses on methods for water recovery from fog and plumes. Fog collection can be a sustainable solution to address water scarcity in many regions around the world. Most of proposed collectors are meshes that rely on inertial collision for droplet capture. However, these designs are inherently limited by aerodynamics, as most fog droplets closely follow air streamlines and pass through the openings of the mesh. Most recent studies have focused on modifying the surface properties of the mesh, which do not address the aerodynamic limitation. In Chapter 2, we propose a new approach where we introduce electrical forces that can overcome the aerodynamic drag force. Using an ion emitter, we introduce a space charge into the fog and thereby impart a net charge to the incoming fog droplets, and direct them toward a collector with an imposed electric field. This approach results in non-standard droplet trajectories that are able to curve backwards into the collector, thereby dramatically increasing the collection efficiency by capturing traditionally inaccessible droplets. We experimentally measure the collection efficiency on single wires, two-wire systems and meshes and propose a physical model to quantify it. We show that the physics can be captured by a single non-dimensional number Ke, which is the ratio of the electrical force to the drag force on a droplet. We identify the regimes of optimal collection and provide insights into designing effective fog harvesting systems. Our approach results in collection efficiencies 50 times higher than traditional collectors, paving the way for fog harvesting to become a scalable and reliable freshwater source. We then expand this approach to the collection of water from plumes in industrial processes, in particular cooling towers.

Cooling towers use water evaporation for cooling in power generation and other industrial applications. The emitted vapor can condense at the outlet of the cooling tower and form a fog plume, causing visibility problems for nearby roads and airports. In Chapter 3, we design and build a model cooling tower prototype and use it to measure the characteristics of the generated plume, such as shape and spatial droplet size distribution. We use literature models to study the dynamics of the mixing of the saturated air leaving the tower with the ambient air. We also model the condensation heat transfer dynamics

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and compare its timescale to the mixing timescale. Based on this ratio, we model the kinematics of plume formation in the vicinity of cooling towers as a function of ambient conditions and investigate the role of aerosols in plume formation. We identify two critical non-dimensional numbers that lead to a regime map of expected fog formation as a function of ambient and exhaust parameters. This map can be helpful in deciding the location of power plants and the need for a plume abatement system, as well as in designing plume collection systems.

In Chapter 4, we start the second part of this thesis and focus on the retention of agricultural sprays on plant surfaces. Bouncing of sprayed pesticide droplets from leaves is a major source of soil and groundwater pollution and pesticide overuse. In Chapter 4, we describe a method to increase droplet deposition through the in-situ formation of hydrophilic surface defects during drop impact. Defects are created by simultaneously spraying oppositely charged polyelectrolytes that induce a surface precipitation reaction when two droplets come into contact. Using high-speed imaging, we study the coupled dynamics of drop impacts and surface precipitate formation, and we build a physical model to estimate the energy dissipation by the defects and predict the transition from bouncing to sticking. The model provides insights into designing effective agricultural sprays, and using our approach, we show large macroscopic enhancements in spray retention and surface coverage for different surfaces. We finally show how the chemical properties of the solution affect precipitate formation, and present guidelines on

optimizing the spray solution.

In Chapter 5, we further study the impacts of liquid droplets on other stationary droplets on a surface, that are not only the main mechanism in the polyelectrolytes approach, but also ubiquitous in numerous applications such as agricultural sprays on dew covered

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effective diameter, velocity and Weber number that allow the accurate prediction of the maximum diameter in drop-on-drop. We use our model to predict the transition to the viscous regime and rationalize the maximum diameter in this case with an energy balance. We finally show that the retraction phase is a no-memory phenomenon and only depends on the volume of the coalesced droplet. We identify capillary and viscous regimes for the retraction and accurately model the retraction rate in each regime. Our approach provides a framework to characterize the dynamics of multiple drop impacts.

In Chapter 6, we investigate the use of oil-in-water emulsion sprays for pesticide delivery. We experimentally study the impact of emulsion droplets on non-wetting surfaces and we observe an unusual behavior where droplets bounce at low Weber numbers, stick at moderate Weber numbers and bounce at high Weber numbers. We also observe that some of the oil from the droplet impregnates the surface texture during the impact. We experimentally and theoretically quantify the coverage of the surface with oil as a function of the emulsion parameters and show that only oil droplets that are immediately adjacent to the surface during the impact can be adsorbed. We then show that because of the impregnated oil, the droplet retracts on a pseudo liquid impregnated surface. The oil on the surface exerts a suction force that we quantify and compare to inertia to determine the regimes where the droplet can stick. The bouncing-sticking-bouncing transition is rationalized by showing that at the onset of splashing, there is a sharp drop in restitution coefficient and thereby vertical inertia due to the ejection of droplets sideways. This effect allows inertia to be overcome by the suction force in a certain range of Weber number after the onset of splashing. We finally show that viscosity plays two conflicting roles: while it increases the dissipation in the lubricating

film, it also increases the timescale of impregnation, making high viscosity oils

non-effective at the timescale of a droplet impact. Using our models, we make a two-dimensional design map that can guide the choice of droplet size, velocity and oil viscosity to enhance the retention of sprays.

Finally, in Chapter 7, we summarize our findings in the two main areas of fog collection and retention of sprays, outlining the original methods presented in the thesis as well as

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the main physical forces in play in each phenomenon. We then briefly discuss the avenues for future works and the potential for improvement of our approaches.

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2. Electrostatically-driven fog collection using space charge

injection

2.1 Introduction

There are over 1.1 billion people who lack access to safe drinking water worldwide, according to the World Water Council 1. This number is expected to increase as water resources are getting increasingly polluted, and global warming is leading to severe water scarcity. Many remote drought-prone coastal areas have little or no rain and prohibitivcly expensive water transportation costs, but have dense fog occurring on a regular basis.2 9

Fog harvesting is a promising solution to provide clean water in these regions. Fog collection can also be useful to prevent the depletion of water reserves in regions where

2

non-renewable groundwater is heavily used for irrigation and industrial processes . Areas prone to dense fog formation are usually close to oceans where fog clouds form over the water and are then transported by the wind 3. Fog is composed of tiny droplets of diameters ranging from 1 to 40pm with a typical diameter of 10pm. Various artificial fog-harvesting systems have been designed, some of which mimic natural fog collection mechanisms in animals and plants 30-37, and small-scale fog collectors have been successfully implemented in several countries 4,38,39

The most common design for fog collectors is a large woven mesh that stands perpendicular to the fog-laden wind, held by a frame 4,40-42. The wind blows the fog

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The main mechanisms that limit the efficiency of mesh-based fog collectors are the slow shedding rate of collected droplets and the aerodynamic deviation of fog droplets. If captured droplets cannot shed easily by gravity and remain on the mesh they can decrease the efficiency by two mechanisms. The mesh openings can be clogged by water, making the mesh impervious to air flow, thus locally acting as a "plate". Re-entrainment of the droplets due to wind drag also occurs before these droplets are collected. Improving the shedding rate has recently received significant attention, and researchers have studied fog-harvesting animals and plants for inspiration and developed coatings to improve the shedding rates =4. Significant improvements in shedding rates have been reported 42

However, the overall fog collection efficiency of these meshes remained low, around

10% in laboratory setups, suggesting that the main limitation is not the shedding rate 42

The main limitation is the aerodynamic deviation of fog droplets, which can occur on two scales: on the scale of the mesh (aerodynamic efficiency 71a) and of individual mesh wires (deposition efficiency 17d). The overall collection efficiency is 77 = 7ald. The mesh, of size W, will deviate the flow in a region of size W around it, thereby diminishing the number of fog droplets directed toward it. The actual number of droplets directed toward the mesh wires divided by the total number of droplets that were directed toward the collector far upstream is defined as the aerodynamic efficiency 40. This efficiency depends on the shading coefficient (SC) of the mesh, which is the ratio of the projected area of the mesh wires to the total area of the mesh. A high SC would lead to an impermeable plate-like situation where the air streamlines are greatly deviated, while a small SC would cause most of the droplets to pass through the mesh openings. Hence, both extremes lead to low efficiencies and it has been shown that a SC around 55% leads to a maximum aerodynamic efficiency 4142

A more significant bottleneck in the fog collection process is the deviation of the droplets

around the individual wires of the mesh. The deposition efficiency 17d is defined as the ratio of captured droplets to those initially directed towards the wire. The flow through the mesh wires can be modeled as a flow past a cylinder, which has been extensively

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studied 43. Far from the cylinder the air streamlines are parallel and the trajectories of fog droplets follow them closely. Close to the cylinder, in a region of characteristic size Re, the radius of the cylinder, the air streamlines start deviating and the flow separates, as schematically shown in Fig. 2-la. In this region, fog droplets are only subject to drag forces exerted by the air. The ability of droplets to follow streamlines is characterized by the Stokes number, which is the ratio of the droplet inertia to the drag force 43. The

Stokes number is also defined as the ratio of the response time of the droplet to the

characteristic time of the flow. St - partice - Inertia _ 2R Pw U, where Rd is the radius

Tf low Drag 9_7gRc

of the droplet, p, the density of water, U the air speed and rlg the viscosity of air. For low Stokes number, the droplet trajectories will follow the air streamlines very closely, and because streamlines are deviated, few droplets will be collected. An example presented in Fig. 2-lb shows the air streamlines and droplet trajectories around a cylindrical wire for St=0. 05. For high Stokes number, the drag forces will not affect the trajectories, and the droplets that are directed towards the cylinder will continue along their trajectories and collide with the cylinder. Based on such collisions, an empirical

formula has been established for the deposition efficiency: 77d = S 42. However, large

St+-2

Stokes numbers require very fine meshes, which are difficult to fabricate and lack structural integrity. Hence low deposition efficiencies remain a significant challenge in fog collection.

In this chapter, we propose to overcome the fundamental aerodynamic limitation of streamline deviation around the collector wires by introducing an additional electric force that will overcome the aerodynamic drag force and propel the fog droplets towards the collector. Active control of droplets with electromagnetic and other fields has recently received significant attention 44.46 Here, we developed a new approach to enhance fog

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lines and deposit on both sides of the collector wire. We demonstrate this concept experimentally in Fig. 2-1d, which shows that droplets are collected all over the wire and that some droplets that were not initially directed towards the wire are also captured. Intuitively, this suggests that the deposition efficiency, which was previously defined as the fraction of droplets directed towards the wire that are collected, can become greater than one, as we will quantitatively show in this paper. The physics of the collection on a single wire will be generalized to a system of two wires and to the more general case of a mesh.

a

Air streamlines F b Droplet trctory C Emnitter-Electrode Ai streamlines Electric fild lines

Droplet trajectory F

d

Figure 2-1. Trajectories of fog droplets around a cylinder with and without the

application of corona discharge. (a-b) Schematic of air streamlines and droplet

trajectories and photograph of droplet trajectories in the absence of an electric field. The inset shows the velocities of the wind iO and the particle il and the drag force acting on the droplet. The bright ring is the edge of the cylinder. (c-d) Schematic of air streamlines, electric field lines and droplet trajectories and photograph under corona discharge. Droplets closely follow the electric field lines in this case. The inset shows the additional electric force acting on a droplet. The cylinders in (b) and (d) have a diameter of 1.88mm.

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2.2 Methods and materials

Experimental set-up and procedure

Samples were placed 4cm away from the outlet, perpendicularly to the axis, of two concentric cylinders (6.3cm, 5cm inner diameters) from which a uniform stream of fog was coming. Fog consisted in a cloud of air-suspended water droplets of radius 3.5vam, generated using an ultrasonic humidifier (Air-O-Swiss AOS 7146) delivering a volume rate of up to 0.1 L/hour. Fog was generated directly into the smaller cylinder through an orifice. At the inlet of the larger cylinder, a speed-tunable fan (Thermaltake Mobile Fan II External USB Cooling Fan) was placed to create the airflow that would convect the fog towards the collection area. A honeycomb flow straightener (Saxon Computers 120mm Honeycomb Airflow Straightener) was placed after the fan to ensure that the wind velocity is uniform through the area of the cylinder, thus reproducing real-fog conditions. The outlet velocity was measured with an anemometer (Testo 405 Hot Wire Thermo-Anemometer) and was spatially uniform within a 15% interval. Corona discharge was produced by placing a sharp metallic needle inside the cylinders, its tip coinciding with the outlet of the smaller cylinder. The needle was connected to a high-voltage generator (Spellman SL600) delivering voltages from 0 to -25kV. Corona discharge was observed to start at a voltage around -7.6kV. In all experiments, the collector was connected to the ground, setting its voltage at OV. All experiments were performed in ambient temperature

and humidity conditions.

Wires and meshes

In single and two-wire experiments, cylindrical needles, made of stainless steel, of length 4cm, and of diameter 1.88mm were used as collectors.

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Mesh Wire diameter Opening size D* Open area (in) (in) Mesh 1 0.063 0.062 1.98 25% Mesh 2 0.063 0.104 2.65 39% Mesh 3 0.063 0.187 3.97 56% Mesh 4 0.063 0.270 5.29 66% Mesh 5 0.063 0.437 7.94 76%

Table 2-1. Characteristics of meshes

2.3 Collection on a single cylindrical wire

The setup developed in this study is shown schematically in Fig. 2-2a. A sharp electrode that serves as an ion emitter, is placed at a distance L from the horizontal cylindrical wire of radius Re, which serves as a collector. The distance L is much larger than Re, which is in turn much larger than the radius Rd of the fog droplets. The collector is electrically grounded (V=O), while a high voltage V is applied to the emitter electrode, thus establishing an electric field between them. When V is above a critical value V, 5, corona discharge occurs, the air surrounding the emitter is ionized and a plasma region is formed. Electrons are accelerated and have enough energy to ionize the air atoms when they collide with them. A chain reaction occurs with every collision creating additional electrons and ions. After a collision, electrons and ions are pulled in opposite directions

by the electric field, preventing recombination. At a certain distance from the emitter, the

electric field can no longer provide enough energy to the electrons to sustain the reaction. In this region, ions travel freely in the air towards the opposite electrode, collide with fog droplets and are captured by them. Thus the droplets acquire a net charge q of the same

polarity as V47,52,53

As L>>R,, apart from small regions around the emitter and the collector, the electric field lines are essentially parallel and horizontal in the central region and the electric field E

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V

can be estimated as -. We assume in the following analysis that the electric field is not

disrupted by the presence of the fog, and we neglect inter-droplet interactions.

In the central region, fog droplets are accelerated, because of the electric field (Fig. 2-2b). The droplets enter the region with the wind velocity Uo. Since they acquired a net charge from the corona discharge, an electric force F = qE accelerates them. As their velocity increases, they are subject to a drag force Fd from the surrounding air. When F = Fd, the droplet reaches a terminal velocity Uf.

The equation of motion for the droplet in this phase can be written as

di _{-- )}

--m j = 6T7g Ra (9 - U) + qE [1]

Where U' is the droplet's velocity, m is the droplet's mass and W is the air velocity.

To determine whether the droplet will reach its terminal velocity during the acceleration

phase, we compare the experimentally measured droplet time of flight Ty - to the

acceleration timescale Ta = 6 m = R 2 w. Here, Ta << T (one to two orders of

7lfgRd 9 ng

magnitude smaller). Thus, the droplets should reach their terminal velocity, which can be obtained by balancing drag and electric forces.

Uf = U0 + 6 qE

7T7llgRd

In the case of a weak electric force, the terminal velocity will be close to the initial velocity, whereas in the case of a high electric force, the terminal velocity will be

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21rRd _3E0V 54,55

dielectrophoresis, whose magnitude ~ 0 v is around six orders smaller than that

of drag force and hence no added velocity is observed. Upon the onset of corona discharge, droplets are charged and the added velocity is experimentally measured to be proportional to V2. The explanation for this proportionality is that the electric field is

proportional to V, and the charge on the droplets is also proportional to V, which makes the electric force qE grow as V2.

a

L

U A

----.---V -_-_-_ --

_---Dropiprrajectory

b

Acceleration phase

d

Collection phase

E

0 Uf

2R -2RJ- - 4-

-4-qE

Fdrag

qE

Air streamline

Air streamlines Electric field lines Droplet trajectory

1.6

e

*Wind speed:O0.6m/s 1.4 . 4 5 W ndns Windspeed: 1.65m/s * 4 Winds : 3.3m/s 1.2- * C03.5-E 1 ₂₃ 0 0 008 - 2.5 Z 2-0.6 - / z. 0.4 -0.2 . 000 0 50 100 150 200 250 50 100 150 200 250 300 V2 _(kV2₎ V2 (kV2)

Figure 2-2. Mechanism of droplet collection on a cylindrical wire. (a) Schematic of simplified experimental setup and droplet trajectories. (b) Schematic of the acceleration

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phase undergone by droplets. The electric field, the initial and terminal velocities, as well as the forces acting on a droplet are shown. (c) Added velocity as a function of V2_{. A} linear fit of the data (R2 ₌_{0.94) gives a slope 0.006 m.s'.kV}2_{. The gray area is where}

the voltage is not high enough to induce corona discharge. The error bars reflect the standard deviation over four measurements. (d) Schematic of the cross-section of the collection phase near the cylinder. Streamlines, field lines and trajectories of the droplets are shown. (e) Nondimensional collection area as a function of V2 _{for four different wind}

speeds. The gray area is where there is no corona discharge.

As droplets are conductive, the charge is localized at the surface and the surface charge per unit area can be estimated as a-E0E, using the normal boundary condition for

electric fields across an interface.

Droplets can gain charge when the ions attach to them but they cannot lose charge to the air (insulator), so the final charge of a droplet will be determined by the value of the electric field it encounters in its trajectory. We can then estimate the surface charge

density as a~E -, and more precise calculations give a = 3Eo

-explanation uses Warburg law.

A more detailed