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
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We 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,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,10-12 which are undesirable in applications such as photonic devices13. 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 Rayleigh14-16 or surface tension driven Marangoni17,18 convection; both being manifested as vortices.
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,29,33,34 there 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 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. 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.
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.20,26,27 Indeed, our experiments corroborate the uniform interfacial thermal distribution, as shown in the IR thermography image in 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 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 µm), which is verified in 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.37 However, this effect is overcome by substrate heating, leading to the ring in FIG. 2(b), similar to previous reports.27,31,37 As 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.FIG. 2 Ultimately, the twin vortices begin to sequentially merge and split, (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. 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. 4 (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. 4 (a) of the interfacial temperature difference, , 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 FIG. 4 (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. 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 FIG. 4 (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
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.FIG. 2 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 103,33,43 almost twice the value determined above, allows us to claim that the observed heat patterns are a manifestation of Marangoni convection.