University of Edinburgh
Induction of Marangoni convection in pure water dropsYutaku Kita,1,2 Alexandros Askounis,*,1,2 Masamichi Kohno,1,2,3 Yasuyuki Takata,1,2,3, Jungho Kim4 and Khellil Sefiane51Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan2International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan3CREST, Japan Science and Technology Agency, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan4Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA5School of Engineering, The University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom*To whom correspondence should be addressed: E-mail: a.askounis@i2cner.kyushu-u.ac.jp; Tel.: +81-92-802-3905 Fax: +81-92-802-3905AbstractWe report on experimental observations/visualization of thermocapillary or Marangoni flows in a pure water drop via infrared thermography. The Marangoni flows were induced by imposing a temperature gradient on the drop by locally heating the substrate directly below the center with a laser. Evidently, a temperature gradient along the liquid-air interface of ca. 2.5oC was required for the Marangoni flows to be initiated as twin vortices and a subsequent gradient of ca. 1.5oC to maintain them. The vortices exhibited an oscillatory behavior where they merged and split in order for the drop to compensate for the non-uniform heating and cooling. The origin of these patterns was identified by comparing the dimensionless Marangoni and Rayleigh numbers which showed the dominance of the Marangoni convection. This fact was further supported by a second set of experiments where the same flow patterns were observed when the drop was inverted (pendant drop).The internal flow patterns induced by the evaporation of drops is paramount to numerous applications like inkjet printing, ADDIN EN.CITE <EndNote><Cite><Author>de Gans</Author><Year>2004</Year><RecNum>519</RecNum><DisplayText><style face="superscript">1</style></DisplayText><record><rec-number>519</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1458723247">519</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>de Gans, Berend-Jan</author><author>Schubert, Ulrich S.</author></authors></contributors><titles><title>Inkjet Printing of Well-Defined Polymer Dots and Arrays</title><secondary-title>Langmuir</secondary-title></titles><periodical><full-title>Langmuir</full-title></periodical><pages>7789-7793</pages><volume>20</volume><number>18</number><dates><year>2004</year><pub-dates><date>2004/08/01</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0743-7463</isbn><urls><related-urls><url> DNA chips, ADDIN EN.CITE <EndNote><Cite><Author>Brown</Author><Year>1999</Year><RecNum>501</RecNum><DisplayText><style face="superscript">2,3</style></DisplayText><record><rec-number>501</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1439886758">501</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Brown, Patrick O.</author><author>Botstein, David</author></authors></contributors><titles><title>Exploring the new world of the genome with DNA microarrays</title><secondary-title>Nature Genetics</secondary-title></titles><periodical><full-title>Nature Genetics</full-title></periodical><pages>33 - 37</pages><volume>21</volume><dates><year>1999</year></dates><urls></urls></record></Cite><Cite><Author>Fang</Author><Year>2006</Year><RecNum>432</RecNum><record><rec-number>432</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1405936500">432</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Fang, Xiaohua</author><author>Li, Bingquan</author><author>Petersen, Eric</author><author>Seo, Young-Soo</author><author>Samuilov, Vladimir A.</author><author>Chen, Yong</author><author>Sokolov, Jonathan C.</author><author>Shew, Chwen-Yang</author><author>Rafailovich, Miriam H.</author></authors></contributors><titles><title>Drying of DNA Droplets</title><secondary-title>Langmuir</secondary-title></titles><periodical><full-title>Langmuir</full-title></periodical><pages>6308-6312</pages><volume>22</volume><number>14</number><dates><year>2006</year><pub-dates><date>2006/07/01</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0743-7463</isbn><urls><related-urls><url> medical diagnosis,PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TZWZpYW5lPC9BdXRob3I+PFllYXI+MjAxMDwvWWVhcj48
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ADDIN EN.CITE.DATA 8,9 to name a few. Nonetheless, the exact mechanism governing the evaporation-driven flows is far from understood, especially for water drops.The evaporation of a liquid drop with a pinned contact line leads to an outward capillary flow in order to replenish the fluid lost to evaporation. ADDIN EN.CITE <EndNote><Cite><Author>Deegan</Author><Year>1997</Year><RecNum>41</RecNum><DisplayText><style face="superscript">10</style></DisplayText><record><rec-number>41</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="0">41</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Deegan, Robert D.</author><author>Bakajin, Olgica</author><author>Dupont, Todd F.</author><author>Huber, Greb</author><author>Nagel, Sidney R.</author><author>Witten, Thomas A.</author></authors></contributors><titles><title>Capillary flow as the cause of ring stains from dried liquid drops</title><secondary-title>Nature</secondary-title></titles><periodical><full-title>Nature</full-title></periodical><pages>827-829</pages><volume>389</volume><number>6653</number><dates><year>1997</year></dates><urls><related-urls><url> </url></related-urls></urls></record></Cite></EndNote>10 In the presence of particulate, a “coffee-stain” arises,PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5EZWVnYW48L0F1dGhvcj48WWVhcj4xOTk3PC9ZZWFyPjxS
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ADDIN EN.CITE.DATA 10-12 which are undesirable in applications such as photonic devices ADDIN EN.CITE <EndNote><Cite><Author>and</Author><Year>2000</Year><RecNum>524</RecNum><DisplayText><style face="superscript">13</style></DisplayText><record><rec-number>524</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1458885636">524</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>C. B. Murray and</author><author>C. R. Kagan</author><author>M. G. Bawendi</author></authors></contributors><titles><title>Synthesis and characteriztion of monodisperse nanocrystals and close-packed nanocrystal assembles</title><secondary-title>Annual Review of Materials Science</secondary-title></titles><periodical><full-title>Annual Review of Materials Science</full-title><abbr-1>Annu. Rev. Mater. Sci.</abbr-1><abbr-2>Annu Rev Mater Sci</abbr-2></periodical><pages>545-610</pages><volume>30</volume><number>1</number><keywords><keyword>quantum dot,nanoparticle,superlattice,colloidal crystal,supercrystal</keyword></keywords><dates><year>2000</year></dates><urls><related-urls><url>. The higher evaporation flux at the three-phase contact line leads to a temperature gradient at the liquid-air interface. In turn, this gradient may induce a buoyancy-driven RayleighPEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Ucm91ZXR0ZTwvQXV0aG9yPjxZZWFyPjIwMTI8L1llYXI+
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ADDIN EN.CITE.DATA 14-16 or surface tension driven MarangoniPEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IdTwvQXV0aG9yPjxZZWFyPjIwMDI8L1llYXI+PFJlY051
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ADDIN EN.CITE.DATA 17,18 convection; both being manifested as vortices. There is abundant experimentalPEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IYW1hbW90bzwvQXV0aG9yPjxZZWFyPjIwMTE8L1llYXI+
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ADDIN EN.CITE.DATA 25-31 evidence of convective flows in evaporating drops for highly volatile liquids. However, in the case of water the existence of Marangoni convection remains controversial. Despite the fact that Marangoni convective flows were predicted to be sufficiently strongPEVuZE5vdGU+PENpdGU+PEF1dGhvcj5IdTwvQXV0aG9yPjxZZWFyPjIwMDY8L1llYXI+PFJlY051
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ADDIN EN.CITE.DATA 32,35In this Letter, we attempt to shed light into the controversial issue of the existence of Marangoni flows in pure water drops. As Marangoni flows are highly sensitive to temperature gradients, we impose such a gradient and we follow the evaporation process with a combination of digital and infrared cameras. Potentially, the outcomes of this work should lead to a better understanding of evaporation driven flows and could improve current technologies such as spray cooling, paints or inkjet printing, to name a few.FIG. SEQ FIG. \* ARABIC 1. (a) Schematic illustration of the experimental setup. (b) - (d) IR images showing the imposed temperature gradient on a bare substrate. Dashed line shows the circumference of a 10 ?L drop.Our experimental setup, REF _Ref450574821 \h \* MERGEFORMAT FIG. 1 (a), consists of a FLIR SC4000 mid-infrared (IR) camera (spectral range from 3.0 to 5.0 μm, resolution of 18 mK) and a Sentech STC-MC152USB CCD camera placed perpendicular to each other, allowing simultaneous acquisition of the thermal patterns and the profile of the drops. Copper substrates, with 50 ?m thickness allowing a well-defined and fixed heating pattern, were placed directly below the center of the IR camera. The copper substrates were covered with a thin, 20 nm, Cytop? layer in order to control drop shape. 10 μL drops of deionized water were gently deposited at the substrate center. Initial contact angle and radius were ca. 104o and 1.4 mm. Subsequently, the drop was heated locally, directly under its center with an Integra-MP-30WW diode laser (808 nm wavelength, Spectra-Physics) operating in continuous wave mode. Laser power was kept constant at 1.9 W, as measured with a laser power meter (Vega, Ophir Optronics Solutions Ltd.). REF _Ref450574821 \h \* MERGEFORMAT FIG. 1 (b) – (d) depicts sequential images of the imposed temperature gradient on a bare substrate. It is readily apparent that the heating from the laser is localized to ca. 15% of the drop contact area (drop circumference shown as dashed line). All experiments were carried out in an environmental chamber (PR-3KT, ESPEC Corp.) to keep temperature and relative humidity at 18.0 ± 1.0 °C and 40 ± 10%. Each experiment was carried out a minimum of 10 times in order to establish reproducibility. FIG. SEQ FIG. \* ARABIC 2. Representative IR images of a pure water drop viewed from above (a) prior to heating and (b) – (f) heating at the center. Crosses show the location of the heating spot. Arrows show the motion of the vortices.The thermal activity at the liquid-vapor interface of freely evaporating pure water drop has been reported to be comparatively weak, due to an almost uniform spatial temperature distribution.PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5HaXJhcmQ8L0F1dGhvcj48WWVhcj4yMDA2PC9ZZWFyPjxS
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ADDIN EN.CITE.DATA 20,26,27 Indeed, our experiments corroborate the uniform interfacial thermal distribution, as shown in the IR thermography image in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2 (a) of a freely evaporating pure water drop viewed from above. A dot with a lower temperature is due to reflection of the camera and is therefore neglected. Upon locally heating the substrate directly below the drop center, a temperature gradient in the form of a concentric ring is induced between the apex and the edge of the drop, as seen in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2 (b). This temperature gradient can be attributed to heat transfer from the substrate to the drop and eventually to the air-liquid interface of the drop. Notably, lateral heat conduction within the substrate is minimal due to its thinness (50 ?m), which is verified in REF _Ref450574821 \h FIG. 1 (right column). At the contact line, the liquid layer is much thinner and is heated faster, giving rise to the hotter exterior ring. The longer the path the heat has to travel, the cooler the interface should be, giving rise to a cooler drop apex. Evaporative cooling should also be considered as it is fundamental to the evaporation process. ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>2014</Year><RecNum>661</RecNum><DisplayText><style face="superscript">37</style></DisplayText><record><rec-number>661</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1470980679">661</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Yang, Kai</author><author>Hong, Fangjun</author><author>Cheng, Ping</author></authors></contributors><titles><title>A fully coupled numerical simulation of sessile droplet evaporation using Arbitrary Lagrangian–Eulerian formulation</title><secondary-title>International Journal of Heat and Mass Transfer</secondary-title></titles><periodical><full-title>International Journal of Heat and Mass Transfer</full-title><abbr-1>Int. J. Heat Mass Transfer</abbr-1><abbr-2>Int J Heat Mass Transfer</abbr-2></periodical><pages>409-420</pages><volume>70</volume><keywords><keyword>Droplet evaporation</keyword><keyword>Numerical model</keyword><keyword>ALE</keyword><keyword>Marangoni flow</keyword><keyword>Evaporative cooling</keyword></keywords><dates><year>2014</year><pub-dates><date>3//</date></pub-dates></dates><isbn>0017-9310</isbn><urls><related-urls><url> However, this effect is overcome by substrate heating, leading to the ring in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2(b), similar to previous reports.PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Tw6Flbno8L0F1dGhvcj48WWVhcj4yMDE1PC9ZZWFyPjxS
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ADDIN EN.CITE.DATA 27,31,37 As the convective flows set in, the temperature gradient becomes irregular ( REF _Ref450651232 \h \* MERGEFORMAT FIG. 2(c)) and a pair of counter-rotating vortices emerge which start moving azimuthally, similar to previous reports for alcohols and refrigerants,PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TZWZpYW5lPC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TZWZpYW5lPC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE.DATA 20,21,38 to reach the location shown in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2(d). The arrow in panel (c) shows the direction of the motion of the vortices pair, not of the liquid. Further heating of the drop results in the emergence of twin vortices which move azimuthally ( REF _Ref450651232 \h \* MERGEFORMAT FIG. 2 (d)), similar to previous reports for alcohols and refrigerants.PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TZWZpYW5lPC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5TZWZpYW5lPC9BdXRob3I+PFllYXI+MjAwODwvWWVhcj48
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ADDIN EN.CITE.DATA 20,21,38 Ultimately, the twin vortices begin to sequentially merge and split, ( REF _Ref450651232 \h FIG. 2(d)-(f)) in an oscillatory manner. After ca. 30 sec the thermal patterns become chaotic which is beyond the scope of this work and therefore they are not discussed.FIG. SEQ FIG. \* ARABIC 3: Evolution of the evaporation process of a water drop containing 0.01% w/w tracer particles. Snapshots corresponds to panels in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2. Dashed line in (a) shows the periphery of the drop and arrows in (b) and (c) show liquid flow. The light ring in the center is a reflection of the light source embedded in the lens.To better understand the liquid flow within the droplet and the oscillatory merging and splitting of the vortices, a water drop seeded with 0.01% w/w tracer particles (Vanadyl 2,11,20,29-tetra-tert-butyl-2,3-naphthalocyanine, Sigma Aldrich) and the evaporation process was followed with a CCD camera mounted with a 5x magnification, self-illuminating microscope objective. Care was taken for the particles to have a minimal effect on both the flow patterns and the evaporation process. Representative snapshots are shown in REF _Ref460436813 \h FIG. 3 corresponding to panels in REF _Ref450651232 \h FIG. 2. Notably, the edge of the drop appears brighter than the rest and a bright ring appear at the center of the drop, due to lens lighting and substrate reflectance. Initially, REF _Ref460436813 \h FIG. 3 (a), the particles are almost stationary in the absence of a strong current at the top of the droplet (where the camera is focused), corresponding to REF _Ref450651232 \h FIG. 2 (a). Upon laser irradiation, REF _Ref460436813 \h FIG. 3 (b), the particles start moving from the hot periphery to the cold interior-apex (as shown in REF _Ref450651232 \h FIG. 2(b)) due to the onset of convective flows. As the convective flows set in and given the fact that the air-liquid interface is acting as a boundary/wall to the flow the liquid recirculates along the periphery forming the observed counter rotating vortices in REF _Ref460436813 \h FIG. 3 (c), liquid flow is highlighted with the arrows in same panel. The vortices recirculate the liquid ( REF _Ref460436813 \h FIG. 3 (d)) and eventually a minute quasi-equilibrium is achieved and the convective flows diminish leading to the merging of the vortices ( REF _Ref460436813 \h FIG. 3 (e)). However, the heating continues leading to stronger convective flows and the vortices split in order to compensate ( REF _Ref460436813 \h FIG. 3 (f)). As both fluid recirculation and heating continue, the vortices merge and split in an oscillating manner as the heat recirculates in an attempt for the drop to attain thermal equilibrium. Further studies are underway, both theoretical and experimental, to fully understand the physics governing the observed thermal patterns.FIG. SEQ FIG. \* ARABIC 3 (a) Evolution over time of interfacial temperature difference, . Insets show the corresponding IR images with red arrows pointing at incident . (b) FFT analysis of .Further analysis of the thermographic data allows the depiction in REF _Ref452486025 \h FIG. 3 (a) depicts of the interfacial temperature difference, , which is defined as, with and determined from infrared thermography. Initially, the drop is freely drying on the substrate and is virtually 0oC. Upon heating, the temperature gradients appear in the form of concentric rings leading to sharp increase in . The onset of the twin vortices coincides with the peak of . At this point, sharply drops as fluid vortices attempt to restore thermal equilibrium to the system. However, thermal distribution in the drop is not uniform due to the vortices being located at one side of the drop and hence increases. Once reaches ca. 1.3oC, the twin vortices start to move azimuthally. Notably, another point arises from REF _Ref452486025 \h FIG. 3 (a) which is not clear in the IR images in REF _Ref450651232 \h FIG. 2. At ca. 10 sec. a small oscillation inappears which gradually becomes more prominent as its amplitude increases. At ca. 20 sec. the oscillation becomes significantly more pronounced and fluctuates around 1.25oC. This oscillation could be attributed to the observed sequential merging (valleys) and splitting (peaks) of the vortices. Essentially, every time the vortices merge, the fluid recirculation slows down giving rise to rapid increase which in turn leads to splitting the vortices to recirculate the liquid. The power spectrum of the FFT of is presented in REF _Ref452486025 \h FIG. 3 (b) where the dominant frequency appears to be the first one at 1.05 Hz followed by two minor ones at approx. 2.09 and 2.27 Hz. The minor frequencies could perhaps be attributed to minute temperature instabilities at the drop interface, similar to Marangoni-driven thermal instabilities in capillaries.PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5CdWZmb25lPC9BdXRob3I+PFllYXI+MjAxNTwvWWVhcj48
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ADDIN EN.CITE.DATA 39,40 Further studies are underway, both theoretical and experimental, to fully understand the physics governing the observed thermal patterns.Let us now attempt to elucidate the origin of the thermal patterns in REF _Ref450651232 \h \* MERGEFORMAT FIG. 2, which are essentially convective, either buoyancy or surface tension driven. In order to determine which one is dominant we calculated the non-dimensionless Rayleigh, , and Marangoni, , where and are the characteristic vertical and radial length, respectively, denotes the coefficient of thermal expansion, the acceleration due to gravity, the surface tension, the density, the kinematic viscosity, the thermal diffusivity. was calculated to vary around in accordance with previous reported cases of Marangoni-driven flows, albeit for a pool of water (flat geometry), ADDIN EN.CITE <EndNote><Cite><Author>Ward</Author><Year>2004</Year><RecNum>612</RecNum><DisplayText><style face="superscript">41,42</style></DisplayText><record><rec-number>612</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1464766095">612</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Ward, C. A.</author><author>Duan, Fei</author></authors></contributors><titles><title>Turbulent transition of thermocapillary flow induced by water evaporation</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>056308</pages><volume>69</volume><number>5</number><dates><year>2004</year><pub-dates><date>05/25/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url> app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1464766028">611</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Duan, Fei</author><author>Ward, C. A.</author></authors></contributors><titles><title>Surface excess properties from energy transport measurements during water evaporation</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>056302</pages><volume>72</volume><number>5</number><dates><year>2005</year><pub-dates><date>11/02/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url> whereas was calculated to be below 500 throughout our observation. increases rapidly upon laser irradiation, at 2 sec., from virtually zero to ca. . The emergence of the vortices lowers to ca. as the heat is redistributed within the drop ( REF _Ref450651232 \h FIG. 2 (d)). At approx. 10 sec recovers to and begins oscillating, as described above for . values are in accordance with previous reported cases of Marangoni-driven flows, albeit for a pool of water (flat geometry). ADDIN EN.CITE <EndNote><Cite><Author>Ward</Author><Year>2004</Year><RecNum>612</RecNum><DisplayText><style face="superscript">41,42</style></DisplayText><record><rec-number>612</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1464766095">612</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Ward, C. A.</author><author>Duan, Fei</author></authors></contributors><titles><title>Turbulent transition of thermocapillary flow induced by water evaporation</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>056308</pages><volume>69</volume><number>5</number><dates><year>2004</year><pub-dates><date>05/25/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url> app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1464766028">611</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Duan, Fei</author><author>Ward, C. A.</author></authors></contributors><titles><title>Surface excess properties from energy transport measurements during water evaporation</title><secondary-title>Physical Review E</secondary-title></titles><periodical><full-title>Physical Review E</full-title></periodical><pages>056302</pages><volume>72</volume><number>5</number><dates><year>2005</year><pub-dates><date>11/02/</date></pub-dates></dates><publisher>American Physical Society</publisher><urls><related-urls><url> At the same time, is initially virtually zero and starts to almost linearly increase at the onset of laser irradiation, although it remains below 500 throughout our observation, with a small decrease occurring at the onset of vortices and oscillation occurring later. Determining the dimensionless Bond number, defined as the ratio of buoyancy over surface-tension,, leads to . Combining this result with the fact that the critical value for the onset of natural convection is typically in the order of 103, ADDIN EN.CITE <EndNote><Cite><Author>Chandrasekhar</Author><Year>1961</Year><RecNum>601</RecNum><DisplayText><style face="superscript">33,43</style></DisplayText><record><rec-number>601</rec-number><foreign-keys><key app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1463048289">601</key></foreign-keys><ref-type name="Book">6</ref-type><contributors><authors><author>Chandrasekhar, S.</author></authors></contributors><titles><title>Hydrodynamic and Hydromagnetic Stability</title></titles><dates><year>1961</year></dates><publisher>Dover Publications</publisher><isbn>9780486640716</isbn><urls><related-urls><url> app="EN" db-id="ddw2ravr4vw2z2e9ft3xwwzpatvdta005zvv" timestamp="1464765507">609</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Duan, Fei</author><author>Ward, C. A.</author></authors></contributors><titles><title>Investigation of Local Evaporation Flux and Vapor-Phase Pressure at an Evaporative Droplet Interface</title><secondary-title>Langmuir</secondary-title></titles><periodical><full-title>Langmuir</full-title></periodical><pages>7424-7431</pages><volume>25</volume><number>13</number><dates><year>2009</year><pub-dates><date>2009/07/07</date></pub-dates></dates><publisher>American Chemical Society</publisher><isbn>0743-7463</isbn><urls><related-urls><url> almost twice the value determined above, allows us to claim that the observed heat patterns are a manifestation of Marangoni convection.FIG. SEQ FIG. \* ARABIC 5. (a) Inverted experimental setup, (b)-(e) evolution over time of the interfacial thermal pattern in the water drop induced by localized heating.Nonetheless, this claim was further pursued experimentally with the heating of a pendant drop, using the inverted setup shown in REF _Ref451759982 \h FIG. 5 (a). Essentially, gravity, the main component of natural convection as described in Equation 1, should be inverted in a pendant drop. Evidently, the flows in REF _Ref451759982 \h FIG. 5 (b) – (d) are similar to those in REF _Ref450651232 \h FIG. 2. Analysis of and the dimensionless,showed similar oscillations appearing slightly sooner possibly due to the inverted action of gravity essentially contributing to the interfacial flows. Nonetheless, Marangoni convection is still dominant. In summary, we studied the evaporation of a water drop heated locally directly below its center (~15% of drop contact area), via laser irradiation. We provide the first, to the best of our knowledge, experimental evidence of Marangoni flow in water drops, observed via IR thermography as recirculating twin vortices. Combination of IR thermography and optical imaging allowed the analysis of the flow patterns. The vortices merged and split in an oscillating manner in an attempt to minimize the temperature difference. Moreover, the estimation of the dimensionless Rayleigh and Marangoni numbers unveiled the dominance of Marangoni convection over buoyancy. A second set of experiments was conducted with an inverted setup and a pendant drop (where the effect of gravity is towards the drop apex) which yielded similar flow patterns, providing further evidence that the observed vortices are due to the action Marangoni thermocapillary convection.AcknowledgementsThis work was financially supported in part by the Core Research for Evolutional Science and Technology project of Japan Science and Technology Agency (JST-CREST) and with a Postdoctoral Fellowship for North American and European Researchers from the Japanese Society for the Promotion of Science (JSPS).References ADDIN EN.REFLIST 1B.-J. de Gans and U. S. Schubert, Langmuir 20, 7789 (2004).2P. O. Brown and D. 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