Letter pubs.acs.org/JPCL
Chemical Reaction Evolving on a Droplet Kinko Tsuji† and Stefan C. Müller*,‡ †
Shimadzu Europa GmbH, Albert-Hahn-Strasse 6-10, D-47269 Duisburg, Germany Institute of Experimental Physics, Otto-von-Guericke University Magdeburg, D-39106 Magdeburg, Germany
‡
S Supporting Information *
ABSTRACT: A high-speed camera was used to investigate the early stage of a chemical reaction within a few milliseconds. We focus on the process of color change caused by a droplet containing a pH indicator when impinging on the surface of alkaline solution. Contrary to our expectation, this reaction starts along the equatorial line, and not at the protruding edge of the droplet, where it first touches the reaction partner. Small vertical fingers emerge from the front line within 1.5 ms. The results suggest that the observed deformation of the droplet and heat diffusion play major roles during this early reaction stage. Our investigations contribute to the understanding of short-term transport processes across interfaces, including the onset of unstable behavior of reaction fronts. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis
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here are various methods to investigate fast chemical reactions. For kinetic measurements, rapid-flow methods1 or relaxation methods2 are often used. Recent developments in laser application make it possible to measure reactions in the femtosecond range or faster ranges.3 These methods are based on the assumption that the reaction takes place homogeneously in space. However, some chemical reactions are known to develop spatial inhomogeneities.4,5 It is also known that acid− base neutralization may drive hydrodynamic instabilities.6,7 Generally, these phenomena of inhomogeneity occur on longterm scales on the order of a few seconds or even a few minutes. Here, the authors are interested in the very early stage of chemical reactions: if any such reaction starts, it should start at some location. It should be interesting to see how the very initial stage takes place. To study this aspect, the timing of a droplet entering into a solution containing reaction partners can be considered as the start of reaction. In this paper, we chose a reaction system in which color changes occur. We will report a chemical reaction caused by a droplet containing the pH indicator bromothymol blue falling dropwise into a NaOH solution. In order to obtain spatially and temporally resolved data on the reaction process, an ultra high-speed camera is used for the observations. This work is closely related to a plethora of investigations on nonreactive falling droplets, which offer a number of well-established scenarios in hydrodynamic behavior.8−11 A solution for the droplets was prepared from 0.1 mg bromothymol blue (Sigma-Aldrich, Germany) dissolved in 20 mL ethanol, followed by adding distilled water, such that the whole volume amounted to 100 mL. The bromothymol blue concentration was 1.6 × 10−3 M. The color of this solution was yellow. NaOH (pellets) was purchased from Appli Chem (Germany) and dissolved in distilled water. The concentration of the NaOH solution was adjusted to be 0.1 M. The experimental setup is shown in Figure 1. A standard fluorescence cuvette of 1 cm optical path length with a height © 2012 American Chemical Society
Figure 1. Experimental setup.
of 4 cm was filled with 3 mL of 0.1 M NaOH. The tip of a glass pipet was positioned 7 cm above the surface of the liquid. Droplets of bromothymol blue emerging from the tip of the pipet had a volume of 16.8 mm3 (diameter 3.2 mm). The cuvette was illuminated with a 150 W halogen lamp (Volpi, Switzerland) both from the back and the front through optical fibres. A sheet of white paper was attached to the back side of the cuvette in order to get homogeneous illumination. An ultra high-speed camera HPV-2 (Shimadzu Corp., Japan) was placed in front of the cuvette. With a zoom lens attached to the bellows focusing attachment, one can take images of up to 10 times magnification. The spatial resolution of the camera was 312 (horizontal) × 260 (vertical) pixels. (In the images shown in Figures 2 and 3, 1 pixel corresponded to 37 μm.) The dynamic range was 10 bit (black-white). The recording speed Received: February 24, 2012 Accepted: March 20, 2012 Published: March 20, 2012 977
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for droplets) showed a peak at 615 nm, and the extinction coefficient was calculated to be 5.3 × 106 M−1 m−1. Six images labeled A−F in Figure 2 show a sequence of events happening to the droplet of the bromothymol blue and its surrounding solution. It depicts the beginning phase, in the time range from 0.25 to 1.50 ms after the droplet has touched the surface of the 0.1 M NaOH solution (t = 0). The color change is reflected by the gray level: gray (darker than background), and black parts of the droplet right under the meniscus in the images correspond to yellow color (before reaction) and dark blue color (after reaction), respectively. After 1.0 ms, the color change is detected as a thin line just below the meniscus (Figure 2D). Note that any optical distortion due to the meniscus is minor in the region of our interest, which is below the meniscus (see the undistorted background lines in Figure 2 stemming from the paper attached to the backside of the cuvette for orientation purposes). The line soon develops into an equatorial band (Figure 2E,F). The color of an approximately hemispherical volume under the equatorial band remains yellow. The equatorial band moves down and gets broader. Note that the droplet changes its shape from a quasi-sphere to a flat spheroid while entering the NaOH solution. (As shown in extensive Figure 1 of the Supporting Information, there is no change in optical absorption, when the reaction does not take place. This excludes any influence of artifacts such as the optical dispersion.12) Figure 3A,B shows enlarged droplet images at t = 1.5 ms and t = 2.5 ms. They were taken at a recording rate of 16 000 frames/s. In Figure 3A, one can clearly see how a number of vertically oriented small fingers emerge from the front line at quite regular distances. These fingers later develop into a rounder shape, as shown in Figure 3B. Soon afterward (at t ≈ 3 ms), the contours of the fingers are not detectable any more. In the following time the behavior of the droplet is similar to that of a falling drop without chemical reaction (except for its color change). A characteristic scenario known from work on nonreactive droplet,8−11 takes place, including the formation of a crater-like cavity, an upward shooting jet, and, later on, turbulent structures (see extensive Figure 2 of the Supporting Information). These observations, however, will not be further considered in this work. Generally, a chemical reaction occurs in the area where the reactants approach each other within the distance of interaction: in our case, this area is located close to the interface between the droplet and the surrounding alkaline solution. The place where the two solutions first get into touch with each other, that is, the protruding edge of the droplet, is expected to be the first location where the reaction takes place. The high-speed observation reveals, however, that this is not the case: while the color does not change at the bottom of the droplet, a dark band around the equatorial line appears a short time later, at t = 1.0 ms (Figure 2D). Let us assume that the two reactants come close enough to react on the basis of diffusion. The diffusion constant of the used species in aqueous solution13 is on the order of 10−9 m2/s. The diffusion length for a time of 1 ms is then 1 μm. This means that in the time interval of 1 ms, the reaction takes place in an area adjacent to the interface of only 1 μm thickness. Since the extinction coefficient of bromothymol blue in 0.1 M NaOH at λ = 615 nm is 5.3 × 106 M−1m−1, the absorbance of BTB−O− for an optical path length of 1 μm is 8.5 × 10−3. Therefore, the color change of the 1 μm layer is below detectability, not only in our system using white light, but even with a very sensitive spectrophotometer. This is the reason why
Figure 2. Images of the bromothymol blue droplet entering a 0.1 M NaOH solution in the time range from 0.25 to 1.50 ms. (A) t = 0.25 ms, (B) t = 0.50 ms, (C) t = 0.75 ms, (D) t = 1.00 ms, (E) t = 1.25 ms, and (F) t = 1.50 ms. Scale bar: 2 mm. The vertical and horizontal lines seen in the background are drawn on a sheet of white paper attached to the back side of the cuvette for orientation purposes. The arc is the optical image of the meniscus. Camera speed: 8000 frames/s.
Figure 3. Images of the bromothymol blue droplet entering a 0.1 M NaOH solution at t = 1.5 ms (A) and t = 2.5 ms (B). Camera speed: 16000 frames/s, scale bar: 1 mm.
was varied up to 1 × 106 frames/s, and 100 frames were taken successively. The camera was triggered by a transistor− transistor logic (TTL) signal with an appropriate delay. The signal was produced by an optical sensor at the moment when the drop passed across a He−Ne laser beam. The absorption spectra of bromothymol blue were measured with the UV−visible spectrophotometer UV-1800 (Shimadzu Corp., Japan). A 0.1 M NaOH solution becomes dark blue when the pH indicator bromothymol blue (BTB) is added. The pK value of bromothymol blue is 7.0. This reaction is described as: BTB − OH + OH− → BTB − O− + H2O
(1)
The BTB−OH is yellow, while the BTB−O− has a dark blue color. The absorption spectrum of 1.6 × 10−5 M bromothymol blue in 0.1 M NaOH (100 times diluted from the original solution 978
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the work of Almarcha et al.,6 it may play a significant role in a short time range of a few milliseconds. Since the equation of heat conduction is formally analogous to the diffusion equation, heat can cause an instability similar to that due to material diffusion. Only the time scales should be quite different. The thermal diffusion coefficient of water is calculated from the thermal conductivity of water18 (0.6 W/mK) divided by its volume specific heat capacity, to be 1.4 × 10−4 m2/s. Thus, the thermal diffusion coefficient of water is about 105 times larger than its material diffusion coefficient (10−9 m2/s). It is, therefore, likely that an instability due to heat conduction occurs much faster than one due to material diffusion. This is corroborated by the fact that the factor of 105 between the time ranges of the occurrence of the instabilities (on the order of milliseconds and the order of 100 s) coincides with that between the thermal and material diffusion coefficient. It is noteworthy that the location where the fingers appear is characterized by the highest curvature at the edges of the impinging spheroidal droplet. Considering the high curvature at the circumference of the droplet, it is likely that the reaction proceeds favorably in this area, since reactive counterparts are going to interact here more often than at other places of the droplet. This results in the observed vertical broadening of the equatorial band. To what extent effects due to the viscosity of the participating solutions and the interfacial tension at their boundaries would contribute to the observed phenomena certainly poses interesting questions, which have to be elucidated in future experimental studies.
we do not see any color change at the protruding edge of the droplet. For the same reason, we do not see, on the time scale of 1−3 ms, a color change distributed homogeneously all over the interfacial area, although the reaction via diffusion is taking place on the interface area, including the protruding edge. It also suggests that the color change observed along the equatorial line, starting to become visible around 1 ms, is based on effects other than diffusion. In our study, the droplet is the moving object. Differently from the splash of a solid sphere impacting a liquid surface,14 the shape of the liquid sphere changes to form a flat spheroid, when it invades the liquid medium, as shown in Figure 2A−F. Consequently, the vertical velocity of the droplet at that moment is different from the horizontal spreading speed. These differing velocities were calculated from successive high-speed images and are plotted in Figure 4 against time. While the
Figure 4. Plot of the front velocities of the drop in the horizontal direction (●) and in the vertical direction (○) versus time.
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vertical velocity stays constant (≈ 0.6 m/s) in the time interval from 0.3 to 1.5 ms, the horizontal velocity is, at the beginning, about 15 times higher than the vertical one (8.9 m/s). It then decreases quickly and, after 1.0 ms, becomes quasi-constant (≈ 1.5 m/s). This shows that during the initial time of 1 ms, the indicator solution contained in the drop flows mainly in the horizontal direction. Bromothymol blue molecules and OH− ions interact most often along this flow direction, and, therefore, the chemical reaction is expected to occur most often in this region, resulting in the observed equatorial line. Furthermore, we would like to consider the finger formation. Such fingers are observed at the chemical front in the time window between 1 and 3 ms. These fine structures suggest that some type of instability of the chemical front exists on the surface of the droplet.6 In fact, analogous finger formation, although on a much longer time scale, has been found to be caused by concentration-dependent density gradients.6,7,15 Almarcha et al.6 showed the appearance of fingers along a chemical front occurring in an acid−base reaction: HCl + NaOH → NaCl + H2O
ASSOCIATED CONTENT
S Supporting Information *
Bromothymol blue drop inpinging into distilled water and later development of the reaction. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Telephone number: +49-391-6718935. Fax number: +49-3916711205. E-mail address:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Barbara Causemann of Shimadzu Europa GmbH for preparing chemical solutions. They are grateful for the useful suggestions of D. Lohse and M. Versluis of the University of Twente, as well as for the fruitful discussions with A. De Wit and P. Borckmans of the Université Libre de Bruxelles, and with K. Eckert of the Technical University of Dresden.
(2)
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Fingers appeared in the time window of 40−200 s, which is about 105 times slower than in our case, although both our reaction and their reaction are similar redox processes of two reactants. They analyzed the formation of the fingers on the basis of a reaction−diffusion−convection (RDC) model.6,16 However, we can not explain our findings on the basis of this type of model, because, as mentioned above, the reaction coupled to diffusion does not play any role in the relevant time window of 1−3 ms. Most neutralization reactions are exothermic.17 While the effect of heat diffusion is negligible in a long time range like in
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