Research Papers: Heat and Mass Transfer

Flow Field Inside a Sessile Droplet on a Hydrophobic Surface in Relation to Self Cleaning Applications of Dust Particles

[+] Author and Article Information
Abdullah Al-Sharafi

Department of Mechanical Engineering,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail: alsharafi@kfupm.edu.sa

Bekir S. Yilbas

Department of Mechanical Engineering,
Centre of Excellence for Renewable Energy,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail: bsyilbas@kfupm.edu.sa

Ahmet Z. Sahin

Department of Mechanical Engineering,
Centre of Excellence for Renewable Energy,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail: azsahin@kfupm.edu.sa

H. Ali

Department of Mechanical Engineering,
King Fahd University of Petroleum and Minerals,
Dhahran 31261, Saudi Arabia
e-mail: haiali@kfupm.edu.sa

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 28, 2016; final manuscript received November 9, 2016; published online January 24, 2017. Assoc. Editor: Gennady Ziskind.

J. Heat Transfer 139(4), 042003 (Jan 24, 2017) (16 pages) Paper No: HT-16-1234; doi: 10.1115/1.4035281 History: Received April 28, 2016; Revised November 09, 2016

Internal fluidity of a sessile droplet on a hydrophobic surface and dynamics of fine size dust particles in the droplet interior are examined for various droplet contact angles. The geometric features of the droplet incorporated in the simulations resemble the actual droplet geometry of the experiments, and simulation conditions are set in line with the experimental conditions. The dust particles are analyzed, and the surface tension of the fluid, which composes of the dust particles and water, is measured and incorporated in the analysis. Particle tracking method is adopted experimentally to validate the numerical predictions of the flow field. It is found that heat transfer from the hydrophobic surface to the droplet gives rise to the formation of two counter rotating cells inside the droplet. The Nusselt and the Bond numbers increase with increasing droplet contact angle. The number of dust particles crossing over the horizontal rake, which corresponds to the top surface of the dust particles settled in the droplet bottom, toward the droplet interior increases as the particle density reduces, which is more pronounced in the early period. Experimental findings of flow velocity well agree with its counterparts obtained from the simulations.

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Chandrasekhar, S. , 1961, Hydrodynamic and Hydrodynamic Stability, Oxford University Press, Oxford, UK.
Nakajima, A. , 2011, “ Design of Hydrophobic Surfaces for Liquid Droplet Control,” NPG Asia Mater., 3(5), pp. 49–56. [CrossRef]
Gennes, P. D. , Brochard-Wyard, F. , Quéré, D. , and Reisinger, A. , 2004, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves, Springer, Heidelberg, Germany.
Smith, J. D. , Dhiman, R. , Anand, S. , Reza-Garduno, E. , Cohen, R. E. , McKinley, G. H. , and Varanasi, K. K. , 2013, “ Droplet Mobility on Lubricant-Impregnated Surfaces,” Soft Matter, 9(6), pp. 1772–1780. [CrossRef]
Tam, D. , von Arnim, V. , McKinley, G. , and Hosoi, A. , 2009, “ Marangoni Convection in Droplets on Superhydrophobic Surfaces,” J. Fluid Mech., 624, pp. 101–123. [CrossRef]
Dombrovsky, L. A. , and Sazhin, S. S. , “ A Parabolic Temperature Profile Model for Heating of Droplets,” ASME J. Heat Transfer, 125(3), pp. 535–537. [CrossRef]
Dombrovsky, L. , “ A Simplified non-Isothermal Model for Droplet Heating and Evaporation,” Int. Commun. Heat Mass Transfer, 30(6), pp. 787–796. [CrossRef]
Petsi, A. , Kalarakis, A. , and Burganos, V. , 2010, “ Deposition of Brownian Particles During Evaporation of Two-Dimensional Sessile Droplets,” Chem. Eng. Sci., 65(10), pp. 2978–2989. [CrossRef]
Metya, A. K. , Khan, S. , and Singh, J. K. , 2014, “ Wetting Transition of the Ethanol–Water Droplet on Smooth and Textured Surfaces,” J. Phys. Chem. C, 118(8), pp. 4113–4121. [CrossRef]
Xu, W. , and Choi, C.-H. , 2012, “ Effects of Surface Topography and Colloid Particles on the Evaporation Kinetics of Sessile Droplets on Superhydrophobic Surfaces,” ASME J. Heat Transfer, 134(5), p. 051022. [CrossRef]
Singh, D. P. , and Singh, J. P. , 2011, “ Enhanced Evaporation of Sessile Water Droplet on Vertically Standing Ag Nanorods Film,” J. Phys. Chem. C, 115(24), pp. 11914–11919. [CrossRef]
Weiß, D. , Lienemann, J. , Greiner, A. , Kauzlarić, D. , and Korvink, J. G. , 2011, “ Smoothed Particle Hydrodynamics-Based Numerical Investigation on Sessile, Oscillating Droplets,” Philos. Trans. R. Soc. London A, 369(1945), pp. 2565–2573. [CrossRef]
Kang, K. , Hong, J. , and Dhont, J. , 2014, “ Local Interfacial Migration of Clay Particles Within an Oil Droplet in an Aqueous Environment,” J. Phys. Chem. C, 118(42), pp. 24803–24810. [CrossRef]
Guzowski, J. , Tasinkevych, M. , and Dietrich, S. , 2011, “ Effective Interactions and Equilibrium Configurations of Colloidal Particles on a Sessile Droplet,” Soft Matter, 7(9), pp. 4189–4197. [CrossRef]
Crivoi, A. , and Duan, F. , 2013, “ Amplifying and Attenuating the Coffee-Ring Effect in Drying Sessile Nanofluid Droplets,” Phys. Rev. E, 87(4), p. 042303. [CrossRef]
Schnall-Levin, M. , Lauga, E. , and Brenner, M. P. , 2006, “ Self-Assembly of Spherical Particles on an Evaporating Sessile Droplet,” Langmuir, 22(10), pp. 4547–4551. [CrossRef] [PubMed]
Straube, A. V. , 2011, “ Small-Scale Particle Advection, Manipulation and Mixing: Beyond the Hydrodynamic Scale,” J. Phys.: Condens. Matter, 23(18), p. 184122. [CrossRef] [PubMed]
Dudášová, D. , SjoüBlom, J. , and Øye, G. , 2014, “ Characterization and Suspension Stability of Particles Recovered From Offshore Produced Water,” Ind. Eng. Chem. Res., 53(4), pp. 1431–1436. [CrossRef]
Cai, J. , Ye, J. , Chen, S. , Zhao, X. , Zhang, D. , Chen, S. , Ma, Y. , Jin, S. , and Qi, L. , 2012, “ Self-Cleaning, Broadband and Quasi-Omnidirectional Antireflective Structures Based on Mesocrystalline Rutile TiO2 Nanorod Arrays,” Energy Environ. Sci., 5(6), pp. 7575–7581. [CrossRef]
Zhang, L. , Dillert, R. , Bahnemann, D. , and Vormoor, M. , 2012, “ Photo-Induced Hydrophilicity and Self-Cleaning: Models and Reality,” Energy Environ. Sci., 5(6), pp. 7491–7507. [CrossRef]
Jacobson, M. Z. , Delucchi, M. A. , Bazouin, G. , Bauer, Z. A. , Heavey, C. C. , Fisher, E. , Morris, S. B. , Piekutowski, D. J. , Vencill, T. A. , and Yeskoo, T. W. , 2015, “ 100% Clean and Renewable Wind, Water, and Sunlight (WWS) All-Sector Energy Roadmaps for the 50 United States,” Energy Environ. Sci., 8(7), pp. 2093–2117. [CrossRef]
Yilbas, B. S. , Ali, H. , Khaled, M. M. , Al-Aqeeli, N. , Abu-Dheir, N. , and Varanasi, K. K. , 2015, “ Influence of Dust and Mud on the Optical, Chemical, and Mechanical Properties of a PV Protective Glass,” Scientific Reports, 5, p. 15833.
Blum, J. , 2006, “ Dust Agglomeration,” Adv. Phys., 55(7–8), pp. 881–947. [CrossRef]
Khatib, T. , Kazem, H. , Sopian, K. , Buttinger, F. , Elmenreich, W. , and Albusaidi, A. S. , 2013, “ Effect of Dust Deposition on the Performance of Multi-Crystalline Photovoltaic Modules Based on Experimental Measurements,” http://www.ijrer.com/index.php/ijrer/article/view/876/pdf, 3(4), pp. 850–853.
Siddiqui, R. , and Bajpai, U. , 2012, “ Correlation Between Thicknesses of Dust Collected on Photovoltaic Module and Difference in Efficiencies in Composite Climate,” Int. J. Energy Environ. Eng., 3(1), pp. 1–7. [CrossRef]
Mampallil, D. , Tiwari, D. , van den Ende, D. , and Mugele, F. , 2013, “ Sample Preconcentration Inside Sessile Droplets Using Electrowetting,” Biomicrofluidics, 7(4), p. 044102. [CrossRef]
Xu, X. , and Ma, L. , 2015, “ Analysis of the Effects of Evaporative Cooling on the Evaporation of Liquid Droplets Using a Combined Field Approach,” Scientific Reports, 5, p. 8614.
Al-Sharafi, A. , Sahin, A. Z. , Yilbas, B. S. , and Shuja, S. , 2015, “ Marangoni Convection Flow and Heat Transfer Characteristics of Water–CNT Nanofluid Droplets,” Numer. Heat Transfer, Part A, 69(7), pp. 763–780. [CrossRef]
Al-Sharafi, A. , Ali, H. , Yilbas, B. S. , Sahin, A. Z. , Khaled, M. , Al-Aqeeli, N. , and Al-Sulaiman, F. , 2016, “ Influence of Thermalcapillary and Buoyant Forces on Flow Characteristics in a Droplet on Hydrophobic Surface,” Int. J. Therm. Sci., 102, pp. 239–253. [CrossRef]
COMSOL, 2016, “The Platform for Physics-Based Modeling and Simulation,” COMSOL, Inc., Burlington, MA, http://www.comsol.com/comsol-multiphysics
Buongiorno, J. , 2006, “ Convective Transport in Nanofluids,” ASME J. Heat Transfer, 128(3), pp. 240–250. [CrossRef]
Krause, M. , Blum, J. , Skorov, Y. V. , and Trieloff, M. , 2011, “ Thermal Conductivity Measurements of Porous Dust Aggregates—I: Technique, Model and First Results,” Icarus, 214(1), pp. 286–296. [CrossRef]
Lu, G. , Duan, Y.-Y. , Wang, X.-D. , and Lee, D.-J. , 2011, “ Internal Flow in Evaporating Droplet on Heated Solid Surface,” Int. J. Heat Mass Transfer, 54(19), pp. 4437–4447. [CrossRef]
Morsi, S. , and Alexander, A. , 1972, “ An Investigation of Particle Trajectories in Two-Phase Flow Systems,” J. Fluid Mech., 55(2), pp. 193–208. [CrossRef]
Vand, V. , 1945, “ Theory of Viscosity of Concentrated Suspensions,” Nature, 155(3934), pp. 364–365. [CrossRef]
Fang, Y. , Kuang, S. , Gao, X. , and Zhang, Z. , 2008, “ Preparation of Nanoencapsulated Phase Change Material as Latent Functionally Thermal Fluid,” J. Phys. D, 42(3), p. 035407. [CrossRef]
Holmes, M. , Parker, N. , and Povey, M. , 2011, “ Temperature Dependence of Bulk Viscosity in Water Using Acoustic Spectroscopy,” J. Phys.:Conf. Ser., 269(1), p. 012011.
Reynolds, O. , 1886, “ On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Proc. R. Soc. London, 40(242–245), pp. 191–203. [CrossRef]
Yali, G. , Lan, W. , Shengqiang, S. , and Guiying, C. , 2014, “ Simulation of Dynamic Characteristics of Droplet Impact on Liquid Film,” Int. J. Low-Carbon Technol., 9(2), pp. 150–156. [CrossRef]
Thokchom, A. K. , Gupta, A. , Jaijus, P. J. , and Singh, A. , 2014, “ Analysis of Fluid Flow and Particle Transport in Evaporating Droplets Exposed to Infrared Heating,” Int. J. Heat Mass Transfer, 68, pp. 67–77. [CrossRef]
Maroto, J. , Pérez-Munuzuri, V. , and Romero-Cano, M. , 2007, “ Introductory Analysis of Bénard–Marangoni Convection,” Eur. J. Phys., 28(2), p. 311. [CrossRef]
The Engineering Toolbox, 2016, “  Solids - Specific Heats,” The Engineering Toolbox, http://www.engineeringtoolbox.com/specific-heat-solids-d_154.html
He, Q. , and Jiao, D. , 2014, “ Explicit and Unconditionally Stable Time-Domain Finite-Element Method With a More Than “Optimal” Speedup,” Electromagnetics, 34(3–4), pp. 199–209. [CrossRef]
Cui, Y. , Paxson, A. T. , Smyth, K. M. , and Varanasi, K. K. , 2012, “ Hierarchical Polymeric Textures Via Solvent-Induced Phase Transformation: A Single-Step Production of Large-Area Superhydrophobic Surfaces,” Colloids Surf. A, 394, pp. 8–13. [CrossRef]
Alghamdi, M. A. , Almazroui, M. , Shamy, M. , Redal, M. A. , Alkhalaf, A. K. , Hussein, M. A. , and Khoder, M. I. , 2015, “ Characterization and Elemental Composition of Atmospheric Aerosol Loads During Springtime Dust Storm in Western Saudi Arabia,” Aerosol Air Qual. Res., 15(2), pp. 440–453.
Gelderblom, H. , Bloemen, O. , and Snoeijer, J. H. , 2012, “ Stokes Flow Near the Contact Line of an Evaporating Drop,” J. Fluid Mech., 709, pp. 69–84. [CrossRef]
Wenzel, R. N. , 1936, “ Resistance of Solid Surfaces to Wetting by Water,” Ind. Eng. Chem., 28(8), pp. 988–994. [CrossRef]
Bico, J. , Thiele, U. , and Quéré, D. , 2002, “ Wetting of Textured Surfaces,” Colloids Surf. A, 206(1–3), pp. 41–46. [CrossRef]
Bormashenko, E. , 2009, “ A Variational Approach to Wetting of Composite Surfaces: is Wetting of Composite Surfaces a One-Dimensional or Two-Dimensional Phenomenon?,” Langmuir, 25(18), pp. 10451–10454. [CrossRef] [PubMed]
Cassie, A. B. D. , and Baxter, S. , 1944, “ Wettability of Porous Surfaces,” Trans. Faraday Soc., 40, pp. 546–551. [CrossRef]
Halliday, D. , Resnick, R. , and Walker, J. , 2010, Fundamentals of Physics Extended, Wiley, Hoboken, NJ.


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Fig. 7

SEM micrographs of dust particles: (a) dust particles with different sizes and (b) small dust particles attach at large particle surface (dotted circles shows the attached some small particles)

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Fig. 4

Mesh used in the simulations for two-dimensional case (θ = 120 deg)

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Fig. 5

SEM micrograph and AFM images of crystalized polycarbonate surface: (a) SEM micrograph of textured surface, (b) SEM images of fibrils on the crystalized surface, (c) 3D AFM image of surface texture, and (d) line scan of AFM image

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Fig. 6

Optical image of water droplet and dust particles inside the water droplet, and contact angle images: (a) Optical image of water droplet with dust particles, Δl is the moving particles inside droplet and Δh is the sediment dust particles at droplet bottom, and (b) sessile droplet contact angle images

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Fig. 1

Optical image and droplet geometry used in the simulations: (a) side view of optical image on the hydrophobic surface (θ = 140 deg), (b) geometric configuration used in the simulations and resembling the actual optical image, and (c) top view of optical image of the droplet

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Fig. 2

Velocity field inside droplet for the contact angle of 100 deg: (a) three-dimensional simulation and (b) two-dimensional simulation

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Fig. 3

Surface tension of water–dust mixture for three different concentrations

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Fig. 8

X-ray diffractogram of dust particles

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Fig. 9

Experimental setup for particle analysis in the droplet

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Fig. 10

Microscopic images of particles and tracking for the velocity measurement

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Fig. 11

Velocity and temperature variation along the vertical rake inside the droplet for various durations: (a) velocity variation along the horizontal rake for different durations and (b) temperature variation along the horizontal rake for different durations

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Fig. 12

Velocity contours with and without particles inside the droplet for two contact angles after 30 s duration. The particle density is 857 kg/m3.

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Fig. 13

Temperature contours inside the droplet for two contact angles after 30 s duration

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Fig. 14

Distribution of dust particles inside the droplet for various dust particle densities and two droplet contact angles after 30 s duration

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Fig. 15

Temporal variation of total number of particles crossing over the horizontal rake and inside the droplet for three different densities of the dust particles. The particle diameter is kept 20 μm for all densities and 30 s duration.

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Fig. 18

A schematic view of ray-tracing diagram for a spherical liquid lens [5,29]

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Fig. 16

Variation of the Nusselt and the Bond numbers with droplet contact angle

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Fig. 17

Variation of the Nusselt number with the Ayse number



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