The Role of Liquid Properties on Lifetime of Levitated Droplets

Subscriber access provided by CORNELL UNIVERSITY LIBRARY

Article

The role of liquid properties on lifetime of levitated droplets Ashkan Davanlou Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02750 • Publication Date (Web): 31 Aug 2016 Downloaded from http://pubs.acs.org on September 1, 2016

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

The role of liquid properties on lifetime of levitated droplets Ashkan Davanlou Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, USA

ABSTRACT: It is known that the temperature difference between a droplet and a liquid surface can extend the levitation time of that droplet by providing a thin air film between the surface and the droplet. But the effect of fluid properties, liquid surface velocity, and air film thickness on the lifetime of droplets is still not well understood. Also there is inconsistency in the literature about the role of vapor pressure in non-coalescence. Here we test a variety of liquids including silicone oil, fluorinert and water to understand the effect of surface tension, density ratio, viscosity and heat capacity on droplet lifetime. Droplets with larger heat capacity and vapor pressure like water remain floating for a longer time compared to oils. Similarly, higher surface velocity which is seen in low viscous liquids helps the air to replenish into the interstices beneath droplet and delay the drainage process. We also discuss the air film variation with temperature and propose a correlation for the minimum thickness required to balance the droplet weight. 1. INTRODUCTION The impact of droplets with liquid substrates is a recurring phenomenon in nature with application in combustion processes, spray painting and meteorology.1-5 Based on the physicochemical properties of the involved liquids and impact velocity of the droplet, the impingement of a drop on a liquid surface may lead to floatation, full or partial coalescence, jetting, bouncing, and splashing. In partial coalescence, the capillary waves reach to the peak of the drop before being damped and help the surface tension forces on the side of drop to overcome the vertical forces. As a result, the pinch-off occurs and a daughter droplet forms.6,7 The produced droplet undergoes a coalescence cascade while it shrinks in size. The generated daughter droplet bounces up and down at the air/liquid interface until it comes to rest momentarily; a procedure that repeats several times. Typically, partial coalescence occurs if both droplet and reservoir are of an identical fluid or if they are from different fluids but immiscible. On the other hand, full coalescence occurs when both fluids are of the same type or different but miscible and the kinetic energy of the impact is low enough.8 Non-coalescence is another possible outcome of droplet impact with a liquid surface that is first observed by Osborne Reynolds in 1881.9 In this condition, the liquid surface deforms because of gravity and surface tension effects, however, two masses are not in real contact and there is an air gap between them. The air flow into this gap creates an overpressure which helps balancing the weight of the droplet

1 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 21

and avoids coalescence.10 The air gap between two media shrinks gradually if there is no external stimuli. Finally, as it reaches to critical values of O (nm), the droplet coalesces with the liquid surface.11 The rupture of the air layer can be attributed to large van der Walls attraction force created when interfaces become sufficiently close. In absence of external perturbation, the transition from levitation to submersion occurs so quickly that one can hardly notice the droplet levitation at the interface. Typically, this is reported as lifetime of a droplet, i.e. the time during which a droplet freely floats at the air/liquid interface while a layer of air cushion separates the droplet from the liquid layer beneath it. It can also be called the residence time of a droplet at the air/liquid interface. Yet, to prolong the droplet lifetime, the use of hydraulic jump,

12

vertical vibration of liquid surface,

11

electric or magnetic field13,14, and applying

chemicals (surfactants)15 has been reported. Jones and Wilson16 revisited the film drainage problem in droplet coalescence. In their study, the induced circulation inside the droplet and the pool speeds up drainage while constriction in the film thickness at its periphery tends to slow it down. Sreenivas et al. 12 investigated the levitation of a drop over film flow. They conjectured that only a thin liquid film can support large drops. Later, Monti and Dell’Aversana17 exploited the temperature difference to avoid coalescence between two neighboring droplets with focus on applications in microgravity environment. Savino et al. 10 demonstrated that thermocapillary effect promotes the air to flow into the interstice under droplet and maintain the pressure buildup that supports the droplet. More recently, Phan18 showed that by adding a surfactant to an oil surface, the floating water droplet will find an acute contact angle which is kinetically more stable and immune to strong disturbances. Alizadeh et al. 19 investigated the effect of substrate elasticity on droplet impact and found that wetting increases when substrate elasticity decreases. Steady and transient instabilities are reviewed in experiments employing both large and small aspect ratio geometries of different symmetries in free surface flows driven by thermocapillarity.20,21 Kim and colleagues22 focused on swirling flow patterns generated by spontaneous Marangoni mixing of two liquids which have different surface tension using particle image velocimetry (PIV). As mentioned earlier, non-coalescence is time-restricted. Due to the bearing action air is dragged into the interstices between the droplet and the liquid bath. The created pressure buildup supports the droplet weight also known as hydrodynamic lubrication. Drainage of air film which separates and lubricates the liquid surfaces eventually leads to coalescence of two liquids. So far, high-speed imaging, laser interferometry and X-ray phase contrast imaging have been implemented to visualize the film rupture and measure its thickness.23,24 Tran et al. 25 discovered that the rupture position is governed by liquid viscosity as well as the impact velocity. The thickness profile at different vertical positions is measured through color interferometry, and it confirmed that due to air drainage the air gap becomes thinner with time. In another effort, Couder and colleagues11 measured the local thickness of an air film using interference fringes for an oscillating system. Complementary analysis based on lubrication theory is employed to 2 ACS Paragon Plus Environment

Page 3 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

explain this phenomenon. The use of high-speed interferometry to monitor the thickness evolution of the air layer during the entire bubble entrapment process is reported.26 In this study, we experimentally and theoretically investigate the parameters affecting the levitation time of a droplet on a liquid surface due to thermal gradient. A variety of fluids including fluorinert oil, water and silicone oil are used to better understand how the density, surface tension and viscosity of involved fluids affect the lifetime of a droplet. In this context, we study three cases; (a) droplet and substrate are identical liquids, (b) droplet is lighter than the pool, (c) droplet is heavier than the pool. Additionally, other parameters such as vapor pressure and heat capacity of droplet are studied to have a full picture of the underlying physics. Based on the lubrication theory, we find the minimum air gap thickness required to balance the droplet’s weight. Our findings show that existence of a thicker air gap between the droplet and the liquid pool does not necessary lead to a longer lifetime. The results of this study is of interest to many practical applications such as demulsification process, spray painting and samples manipulation in droplet-based microfluidics. 2. ANALYTICAL FRAMEWORK The entrapment and drainage of air in the interstice between liquids is due to the relative motion of the fluid interfaces as a result of surface tension gradient in that region. This surface tension gradient is either generated due to a chemical mismatch at the shared boundary or an applied thermal gradient between two media. The assumption that drainage and replenish of air within the thin gap is able to sustain the droplet weight explains the formation of pressure buildup.24 Here using the lubrication theory, we explain the generation of pressure buildup. Also that the pressure buildup in the air gap is due to the moving interfaces, which prevents fluid surfaces to come in direct contact with each other. 27 The equation of continuity for an incompressible fluid in Cartesian coordinates is V =

+

+

=0

(1)

Similarly, the momentum equation in rectangular Cartesian coordinates (x1, x2, x3)

+ V. ∇ = − + ∇ +

(2)

for i=1, 2, 3. Here t is time, is the viscosity, v = (vx1, vx2, vx3) is the velocity field vector and g = (gx1, gx2, gx3) is the gravitational acceleration vector. We assume that the body forces and inertia are negligible, fluid is Newtonian, and has a constant density, and viscosity and pressure are both constant through film. The governing equations (eq1 and 2) can be combined under the assumptions of lubrication theory (stated 3 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 21

earlier) to yield a single equation to compute the pressure inside the film which is also knows as Reynolds equation. In addition, we consider the lubricating film is constrained between two solid surfaces. Letting the z-axis to be in the direction of the film thickness h(x, y), while the span of the liquid layer on the xy plane is much larger than its thickness. The fluid motion can in xy plane is in form of (U,V). The momentum equations under introduced assumptions become

= ( )

(3)

= ( )

(4)

In lubrication theory viscous term scales are dominant, thus the appropriate pressure scale can be written

+ , where * + is the average of film thickness for a flow in a narrowing gap at inlet as ~ !"# $%#& '( /* and outlet, Usurf is the surface velocity, µair is the air viscosity and Lc is the characteristic length scale. Here we simplify the general Reynolds equation by considering only tangential motion such that .

.

,- = $- + /- and that only the surface at z = 0 moves (i.e. $ 0- = 1% , $ 02+ = 0). Therefore, the general Reynolds equation reduces to . 4 . 4 3 6 + 3 5 6 5

.

.

= 6$ + 6/

(5)

For an infinitely wide bearing, we can assume the flow is one dimensional. In other words, the side (y) leakage is negligible. Now, the momentum equation in the flow direction can be written as: 8

+

9 9

=0

(6)

By integrating eq. 6, the velocity profile will be :

;

+ ) + 1% (1 − ) 1 = 5 3 6 (< − - ( + )< = >- 1
3 °C was deployed. Phan et al. demonstrated that water droplets up to certain volume can float on oil surface because of interfacial tensions and buoyancy forces.35 Herein we introduce another mechanism to stabilize heavier drops using temperature difference. It is also seen that density plays a major role in 9 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 21

levitation of heavier droplets. Due to the larger weight, pressure buildup needs to be increased to balance the extra weight. If not, under similar conditions, the lifetime of a certain droplet would be shorter. It is noteworthy to mention that temperature difference was not as effective factor in high viscous fluids as in low viscous fluids. For instance, the levitation time of silicone oil droplets with a viscosity of 50100 cSt only increased 3s for a temperature difference of 30 ˚C. This observation is in agreement with Monti and Savino36, who stated that for droplet viscous than 100 cSt, the non-coalescence behavior was not detected because the high viscosity of drop caused reduction of surface speed and less air motion in the interstitial space.

Figure 5. Measured temperature difference (Tp-Td ) between pool and droplet for different combination of fluids, the first fluid represents the droplet and the second represents the pool. Droplet temperature rise will eventually lead to rupture of the air film. The results are compared with Savino et al.10

Fig. 5 shows that as long as there is a minimum temperature difference between the droplet and the pool, the droplet remains floating at the pool surface. The water droplet reaches to the steady state temperature faster than the other two fluids. At the same time, the steady temperature is higher than what is numerically expected. This unusual behavior can be ascribed to evaporation of water droplet. Without considering the partial evaporation, the steady temperature will be lower for all fluids.10 Fig. 5 also shows that both oil droplets tend to reach to steady temperature faster and consequently they coalesce after a short time whereas the water droplet stands indefinitely over the pool.


Page 11 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Here, an order of magnitude analysis is established to correlate the magnitude of film thickness at equilibrium condition to temperature difference. For this purpose, we simplify the problem using two main assumptions; 1) the Marangoni effect inside the droplet is negligible, 2) the levitated droplet has a perfect spherical shape. To avoid coalescence of a levitated droplet with the pool, the total pressure over the contact area between the droplet and liquid surface, S, must be equal to the weight of the droplet: ∆FY = /

(12)

where ρd is the density of the droplet, g is the gravity acceleration, V is the volume of the droplet, and ∆p is the pressure increase that is defined based on the lubrication theory concept37: ∆F =

ZR [ ] \9

(13)

m is the Marangoni velocity which defined as10: ^ = _` (a − a )/

(14)

b is the thickness of the air film, R is the radius of the droplet, µa is the viscosity of the air and µp is the viscosity of the pool. The contact area is: Y = bc]

(15)

where f is the portion of droplet affected by pressure buildup, here we assume f= ¼. The film thickness can be formulated as: @ f Z

d = e:h S gT ZR (a − a ) i

(16)

j

Figure 6 shows how the film thickness changes as the temperature between the pool liquid and the droplet (Tp – Td) increases. The film thickness grows as (Tp – Td) increases. The increase of film thickness prolong the levitation time of a droplet. The increase in film thickness for water droplets floating on FC43 pool is much faster than silicone oil. From eq. 16 it can be inferred that temperature difference, surface tension gradient, density of the droplet and viscosity of the pool are determining parameters in the air gap thickness. Typically, a viscous carrier fluid has lower surface mobility and therefore requires longer time for replenishing the air film. Similarly, a large dependence of surface tension on temperature (σT) translates in greater surface velocity vectors and pulling more air into the intervening layer of two liquid masses. Fig. 6 also suggests that the FC-43 droplet on a water pool has the thickest air gap compared to the other two combinations. However, eq 16 does not account for the evaporation effect. Moreover, the low


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 21

specific heat of oils leads to sudden reduction of the temperature difference and consequently the film rupture. In other words, the rate at which the air gap changes is the highest for FC-43 (see Fig. 5).

Figure 6. Theoretical relationship between film thickness and temperature difference (Tp – Td) for all three cases.

Apart from thermocapillary, vapor pressure is also introduced as a dominant factor in droplet levitation. For example, Hickman et al.

38

and Weilert et al.

39

discussed the potential effect of evaporation as a

precursor in coalescence inhibition. On the contrary, we know that the rise of temperature of the pool will increase the vapor pressure, thus the amount of the vapor around the interface. So it is expected that the generated vapor molecules squeeze out the air film and expedite the rupture.40 Dell’Aversana and coworkers41 looked into this topic. They commented that coalescence can occur for low enough gas pressures. Moreover, the critical pressure for coalescence tends to decrease with increase of ∆T.41,42 In other words, at low ambient pressures, temperature difference could provide sufficient gas for lubricating the fluid interstices. Thus, it is safe to assume that in this work, temperature difference is more effective than evaporation in levitation of droplets at the liquid interface. Particularly that the chosen liquids are not volatile and have relatively low vapor pressure compared to alcohols.43 whereas for volatile liquids the effect of vapor pressure is more pronounced in inhibiting the coalescence. 5. CONCLUSION In summary, we demonstrated how the liquid properties affect the lifetime of droplets floating at the liquid interface. While temperature difference between the liquid pool and the droplet is vital for noncoalescence, not all floating droplets have the same lifetime. We found that a pool with less viscosity and higher surface tension gradient promotes a thicker air film underneath the droplet as it drags more air into 12 ACS Paragon Plus Environment

Page 13 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

the intervening layer of two liquid masses. Our results also indicated that a larger air film does not necessary translate into longer lifetime. Instead, the rate at which the film thickness changes is a determining factor. Moreover, since liquid droplets with low specific heat tend to reach to thermal equilibrium condition faster, they are more susceptible to coalescence. On the other hand, evaporation effect at low temperatures delay the film rupture. Based on lubrication theory analysis, the flow in the air gap can be decomposed into Couette and Poiseuille flows. This allowed us to find a correlation between the minimum air gap necessary to balance the droplet weight and surface velocity induced due to Marangoni flow. Beside improving our fundamental understanding of non-coalescence, the outcome of this research will benefit water quality research and demulsification processes such as separation of crude-oil/water emulsion in oil spill or biodegrading of unwanted oils. Further applications in noncontact transportation of droplets for lab-on-achip devices is envisioned.

AUTHOR INFORMATION

Corresponding Authors E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

The author is thankful to R. Capell who inspired this research and improved the quality of this work by her constructive feedback, and Dr. R. Kumar for technical discussions. The author especially thanks the reviewers for their insightful comments.

REFERENCES

(1) Brazier-Smith, P. R.; Jennings, S. G.; Latham, J. Accelerated rates of rainfall. Nature 1971, 232, 112. (2) Velev, O. D.; Prevo, B. G.; & Bhatt, K. H. On-chip manipulation of free droplets. Nature 2003, 426 (6966), 515. (3) Davanlou, A.; Kumar, R. Thermally induced collision of droplets in an immiscible outer fluid,. Sci. Rep. 2015, 5, 9531. (4) Thoroddsen, S. T.; Etoh, T. G.; Takehara, K. High-speed imaging of drops and bubbles. Annu. Rev. Fluid Mech. 2008, 40, 257. (5) Lhuissier, H.; Tagawa, Y.; Tran, T.; Sun, C. Levitation of a drop over a moving surface,. J. Fluid Mech. 2013, 733, R4. (6) Blanchette, F.; Bigioni, T. P. Partial coalescence of drops at liquid interfaces,. Nature Phys. 2006, 2(4), 254. (7) Castillo-Orozco, E.; Davanlou, A.; Choudhury, P. K.; Kumar, R. Droplet impact on deep liquid pools: Formation of Rayleigh jet and daughter droplets,. Phys. Rev. E. 2015, 92(5), 053022. (8) Davanlou, A.; Kumar, R. On the lifetime of non-coalescent levitated droplets,. ASME 13th Heat International Conference on Nanochannels, Microchannels, and Minichannels, San Francisco, 6-9th July 2015. (9) Reynolds O. On drops floating on the surface of water,. Chem. News 1881, 44, 211. (10) Savino, R.; Paterna, D.; Lappa, M. Marangoni flotation of liquid droplets,. J. Fluid Mech. 2003, 479, 307. (11) Couder, Y.; Fort, E.; Gautier, C-H.; Boudaoud A. From bouncing to floating: Noncoalescence of drops on a fluid bath,. Phys. Rev. Lett. 2005, 94 (17), 177801. (12) Sreenivas, K. R.; De P. K.; Arakeri, J. Levitation of a drop over a film flow,. J. Fluid Mech. 1999, 380, 297.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 21

(13) Klyuzhin, I. S.; Ienna, F.; Roeder, B.; Wexler, A.; Pollack, G. H. Persisting Water Droplets on Water Surfaces, J. Phys. Chem. B. 2010, 114(44), 14020-14027. (14) Rayleigh, L. The influence of electricity on colliding water drops,. Proc. R. Soc. London Ser. A 1879, 28, 406. (15) Amarouchene, Y.; Cristobal, G.; Kellay, H. Noncoalescing drops,. Phys. Rev. Lett. 2001, 87 (20), 206104. (16) Jones, A. F.; Wilson, S. D. R. The film drainage problem in droplet coalescence,. J. Fluid Mech. 1978, 87 (02), 263. (17) Monti, R.; Dell’Aversana, P. Microgravity experimentation in non-coalescing systems,. Micrograv. Q. 1994, 4 (2), 123. (18) Phan, C. M. Stability of a floating water droplet on an oil surface,. Langmuir 2014, 30 (3), 768. (19) Alizadeh, A.; Bahadur, V.; Shang, W.; Zhu, Y.; Buckley, D.; Dhinojwala, A.; Sohal, M. Influence of substrate elasticity on droplet impact dynamics,. Langmuir 2013, 29 (14), 4520. (20) Davis, S. H. Thermocapillary instabilities,. Annu. Rev. Fluid Mech. 1987, 19 (1), 403. (21) Schatz, M. F.; Neitzel, G. P. Experiments on thermocapillary instabilities,. Annu. Rev. Fluid Mech. 2001, 33 (1), 93. (22) Kim, H.; Lee, J.; Kim, T. H.; Kim, H. Y. Spontaneous Marangoni Mixing of Miscible Liquids at a Liquid– Liquid–Air Contact Line,. Langmuir 2015, 31 (31), 8726. (23) San Lee, J.; Weon, B. M.; Je, J. H.; Fezzaa, K. How does an air film evolve into a bubble during drop impact?,. Phys. Rev. Lett. 2012, 109 (20), 204501. (24) Neitzel, G. P.; Dell'Aversana, P. Noncoalescence and nonwetting behavior of liquids,. Ann. Rev. Fluid Mech. 2002, 34 (1), 267. (25) Tran, T.; Maleprade, H.; Sun C.; Lohse, D. Air entrainment during impact of droplets on liquid surfaces,. J. Fluid Mech. 2013, 726, R3. (26) Li, E. Q.; Thoroddsen, S. T. Time-resolved imaging of a compressible air disc under a drop impacting on a solid surface,. J. Fluid Mech. 2015, 780, 636. (27) Panton, R. L. Incompressible Flow, 2 ed. John Wiley and Sons, Inc., 1995. (28) Davanlou A.; Kumar, R. Counter-current motion of a droplet levitated on a liquid film undergoing Marangoni convection,. Int. J. Heat Mass Trans. 2015, 89, 345. (29) Sumner, L.B.; Wood, A.M.; Neitzel, G.P. Lubrication analysis of thermocapillary-induced nonwetting. Phys. Fluids 2003, 15(10), 2923-2933. (30) Davanlou, A.; Kumar, R. Passive mixing enhancement of microliter droplets in a thermocapillary environment,. Microfluid Nanofluid 2015, 19(6), 1507-1513. (31) Leidenfrost, J. G. On the fixation of water in diverse fire,. Int. J. Heat Mass Trans. 1966, 9 (11), 1153. (32) Napolitano, L. G.; Monti, R.; Russo, G. Marangoni convection in one-and two-liquids floating zones,. Naturwissenschaften 1986, 73 (7), 352. (33) Davanlou, A. Thermally induced motion, collision and mixing of levitated droplets,. PhD thesis, University of Central Florida, 2015. (34) Davanlou, A.; Lee, J. D.; Basu, S.; Kumar, R. Effect of viscosity and surface tension on breakup and coalescence of bicomponent sprays,. Chem. Eng. Sci. 2015, 131, 243. (35) Phan, C. M.; Allen, B.; Peters, L. B.; Le, T. N.; Tade, M. O. Can water float on oil?,. Langmuir 2012, 28 (10), 4609. (36) Monti R.; Savino, R. Correlation between experimental results and numerical solutions of the Navier-Stokes problem for noncoalescing liquid drops with Marangoni effects. Phys. Fluids 1997, 9 (2), 260. (37) Gilet, T.; Vandewalle, N.; Dorbolo, S. Controlling the partial coalescence of a droplet on a vertically vibrated bath,. Phys. Rev. E 2007, 76 (3), 035302. (38) Hickman K.; Di Luzio F.; Gillam W. S.; Leiserson L. The mechanism of boule flotation on water and other liquids. US Dep. Inter. R & D Prog. Rep. 1966, 200. (39) Weilert, M. A.; Whitaker, D. L.; Maris H. J.; Seidel GM. Magnetic levitation and noncoalescence of liquid helium., Phys. Rev. Lett. 1996, 77 (23), 4840. (40) Yi, N.; Huang, B.; Dong, L.; Quan, X.; Hong, F.; Tao, P.; Song, C; Shang, W.; Deng, T. Temperature-Induced Coalescence of Colliding Binary Droplets on Superhydrophobic Surface,. Sci. Rep. 2014, 4, 4303. (41) Dell’Aversana, P.; Tontodonato, V.; Carotenuto L. Suppression of coalescence and wetting: The shape of the interstitial film. Phys. Fluids 1997, 9 (9), 2475. (42) Dell’Aversana, P.; Banavar, J. R.; Koplik J. Suppression of coalescence by shear and temperature gradients. Phys. Fluids 1996, 8 (1), 15-28.


Page 15 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(43) Shanahan, M. E. R.; Sefiane, K.; Moffat, J. R. Dependence of volatile droplet lifetime on the hydrophobicity of the substrate. Langmuir 2011, 27 (8), 4572.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. Schematic of flow in a narrow gap (H /Lc→0) with inclined (small slope) moving wall which is a combination of Couette and Poiseuille flow. Figure 1. 104x41mm (150 x 150 DPI)

ACS Paragon Plus Environment

Page 16 of 21

Page 17 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 2. Schematic figure of experimental apparatus for droplet levitation. Figure 2. 96x97mm (116 x 110 DPI)


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Levitation of a liquid droplet on the liquid pool of a distinct immiscible fluid. (a) Droplet floats above the air/liquid interface. The inset magnifies the interstice under droplet where the air gap is present. (b) As the temperature of the droplet rises, the air gap shrinks. (c) After thermal equilibrium, the droplet partially submerges within the pool. The vectors inside the liquid pool show the surface tension forces, while the vectors outside show the air flow. Droplet is 3 mm and ∆T= 10 °C between two media. Figure 3. 255x86mm (142 x 121 DPI)


Page 18 of 21

Page 19 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 4. Sequence of drop impact captured by using a high speed camera at 2000 fps. The water droplet is 2.6 mm and the reservoir is FC-43. A ∆T= 15 °C is applied between two media. (a) Impact leads to direct submersion, (b) after bouncing droplet eventually floats at the air/liquid interface. The white spot is the reflection of light. Figure 4. 285x171mm (150 x 150 DPI)


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Measured temperature difference (Tp-Td ) between pool and droplet for different combination of fluids, the first fluid represents the droplet and the second represents the pool. Droplet temperature rise will eventually lead to rupture of the air film. The results are compared with Savino et al 279x178mm (96 x 96 DPI)


Page 20 of 21

Page 21 of 21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

Figure 6. Theoretical relationship between film thickness and temperature difference (Tp – Td) for all three cases. Figure 6. 183x115mm (150 x 150 DPI)


The Role of Liquid Properties on Lifetime of Levitated Droplets

Recommend Documents