Induction of Marangoni Convection in Pure Water Drops

Induction of Marangoni convection in pure water drops

Yutaku Kita,1,2 Alexandros Askounis,*,1,2 Masamichi Kohno,1,2,3 Yasuyuki Takata,1,2,3, Jungho Kim4and Khellil Sefiane5

1Department of Mechanical Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

2International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

3CREST, Japan Science and Technology Agency, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

4Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA

5School of Engineering, The University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JL, United Kingdom

*To whom correspondence should be addressed: E-mail: ; Tel.: +81-92-802-3905 Fax: +81-92-802-3905

Abstract

We report on experimental observations/visualization ofthermocapillary 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.2.5oCwas required for the Marangoni flows to be initiated as twin vortices and a subsequent gradient ofca. 1.5oCto 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,1 DNA chips,2,3 medical diagnosis,4,5 nanotechnology 6,7 or surface patterning,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.10 In the presence of particulate, a “coffee-stain” arises,10-12which are undesirable in applications such as photonic devices13. The higher evaporation flux at the three-phase contact line leads to a temperature gradientat the liquid-air interface. In turn, this gradient may induce a buoyancy-driven Rayleigh14-16 or surface tension driven Marangoni17,18 convection; both being manifestedasvortices.

There is abundant experimental19-24 and theoretical25-31 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 strong25,31,32 in pure water drops or indirectly concluded,29,33,34there is little corroborating experimental evidence.20,21,35,36 This discrepancy between theory and experiment was attributed to water attracting a high amount of contaminants which negate the Marangoni flow.32,35

In this Letter, we attempt to shed light into the controversial issue ofthe 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 couldimprove current technologies such as spray cooling, paints or inkjet printing, to name a few.

FIG. 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 µL drop.

Our experimental setup, 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 µm thicknessallowing a well-defined and fixed heating pattern,were placed directly below the center of the IR camera. The copper substrates werecovered 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 incontinuous wave mode. Laser power was kept constant at 1.9 W, as measured with a laser power meter (Vega, Ophir Optronics Solutions Ltd.). 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. 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.20,26,27Indeed, our experiments corroborate the uniform interfacial thermal distribution, as shown in the IR thermography image inFIG. 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 heatingthe 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 FIG. 2 (b). This temperature gradient canbe attributed to heat transfer from the substrate to the dropand eventually to the air-liquid interface of the drop.Notably, lateral heat conduction within the substrate is minimal due to its thinness (50 µm), which is verified in FIG. 1 (right column). At the contact line, the liquid layer is much thinnerand 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. 37 However, this effect is overcome by substrate heating, leading to the ring in FIG. 2(b), similar to previous reports.27,31,37As the convective flows set in, the temperature gradient becomes irregular (FIG. 2(c)) and a pair of counter-rotating vortices emerge which start moving azimuthally, similar to previous reports for alcohols and refrigerants,20,21,38 to reach the location shown in 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 (FIG. 2 (d)), similar to previous reports for alcohols and refrigerants.20,21,38Ultimately, the twin vortices begin to sequentiallymerge and split, (FIG. 2(d)-(f)) in an oscillatory manner. Afterca. 30 sec the thermal patterns become chaotic which is beyond the scope of this work and therefore they are not discussed.

FIG. 3: Evolution of the evaporation process of a water drop containing 0.01% w/w tracer particles. Snapshots corresponds to panels in 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 FIG. 3 corresponding to panels in 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, 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 FIG. 2 (a). Upon laser irradiation, FIG. 3 (b), the particles start moving from the hot periphery to the cold interior-apex (as shown in 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 FIG. 3 (c), liquid flow is highlighted with the arrows in same panel. The vortices recirculate the liquid (FIG. 3 (d)) and eventually a minute quasi-equilibrium is achieved and the convective flows diminish leading to the merging of the vortices (FIG. 3 (e)). However, the heating continues leading to stronger convective flows and the vortices split in order to compensate (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. 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 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 tosharp 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 fromFIG. 3 (a) which is not clear in the IR images in FIG. 2. At ca. 10 sec. a small oscillation inappears which gradually becomes more prominent as its amplitude increases. Atca. 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 tosplitting the vortices to recirculate the liquid. The power spectrum of the FFT of is presented in 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.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 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),41,42 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 (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).41,42 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 inthe order of 103,33,43almost twice the value determined above, allows us to claim that the observed heat patterns are a manifestation of Marangoni convection.

FIG. 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 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 FIG. 5 (b) – (d) are similar to those in 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.

Acknowledgements

This 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).

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