Propagation Behaviors of an Acid Wavefront Through a Microchannel

Article pubs.acs.org/JPCB

Propagation Behaviors of an Acid Wavefront Through a Microchannel Junction Hideki Nabika,* Takahiko Hasegawa, and Kei Unoura Department of Material and Biological Chemistry, Faculty of Science, Yamagata University, 1-4-12 Kojirakawa, Yamagata 990-8560, Japan ABSTRACT: Waves in reaction-diffusion systems yield a wealth of dynamic self-assembling phenomena in nature. Recent studies have been devoted to utilizing these active waves in conjunction with microscale technology. To provide a compass for controlling reaction-diffusion waves in microspaces, we have investigated the propagation behavior of one specific variety of the reaction-diffusion wave: an acid wave that utilizes an autocatalytic proton-production reaction. Furthermore, the acid wave that we have investigated occurs in a microchannel with a junction connecting circular and straight regions. The obtained results were compared with a neutralization wave that involves only a neutralization reaction. The acid wave was ignited by the addition of the appropriate amount of H2SO4 into the circular region that was filled with a substrate solution, where proton-consuming and proton-producing reactions followed a rapid neutralization reaction. At this stage, the wave penetrated and propagated into the channel region. Comparison between the acid and the neutralization waves clarified that the acid wave required a minimum threshold of H2SO4 concentration in order to be ignited and that the propagation of the acid wave was temporarily delayed because of the presence of intermediate chemical reaction steps. Furthermore, the propagation dynamics was found to be tuned through the configuration of the microchannel. The importance of microchannel configuration, especially for systems with a junction connecting different shapes, is discussed in terms of Fick’s law and in terms of the proton flux from the circular to the straight regions.

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INTRODUCTION Chemical energy is consumed as the driving force of selforganization in nature. We can find a wealth of didactic selforganization phenomena especially in biology, including cell division,1 nerve pulses,2,3 and stripe patterns (which can be found in several different organisms, including angelfish).4 The self-organization in these examples is governed by a sensitive balance between reaction and diffusion among constituent components; thus, they are referred to as reaction-diffusion systems. To gain deep insight into reaction-diffusion systems in nature, the use of model chemical reactions frequently plays an important role.5−7 One particularly famous example of a chemical reaction-diffusion model is the Belouzov-Zhabotinsky (BZ) reaction, which involves the oxidation of organic substrates in an acidic bromate in the presence of metal ion catalysts.8 The propagation of the BZ reaction wave has long been investigated in order to gain insight that could be applied toward understanding the propagation of waves in nature. Although the BZ wave can be considered a solitary wave with a constant velocity and front shape, inevitable chemical reactions and the resultant heat generation at the reaction front induce several characteristic features. For example, the heat-induced density difference at the reaction front forms a nonaxisymmetric interface through convective flow.9 Such convective flow at the reaction front aids the mixing between reacted and © 2015 American Chemical Society

unreacted solutions, thereby increasing both the reaction rate and the propagation velocity. With recent advances in microfabrication technology, BZ wave propagation in well-defined microspaces has stimulated the field of chemistry-based computation, including such aspects as chemical logic gates10−12 and chemical diodes.13,14 In the case of logic gates, the catalyst for the BZ reaction is printed on a thin membrane in specific patterns and with geometries designed to provide various logical operations.11 Two separated glass plates modified with the BZ catalyst are used for the chemical diode, in which the BZ wave can jump at the gap between the two separated plates. By changing the gap distance and geometries of each plate, diode-like unidirectional propagation of the BZ wave becomes possible.13 Well-defined micropatterns with a gap distance of 50−250 μm prepared by photolithographic processes make it possible to precisely control the unidirectional propagation probability and propagation periodicity.15,16 For these reasons, control of the BZ wave propagation in well-defined microspaces is a key technology in achieving high-performance, chemistry-based computation. Received: May 1, 2015 Revised: June 30, 2015 Published: July 1, 2015 9874

DOI: 10.1021/acs.jpcb.5b04210 J. Phys. Chem. B 2015, 119, 9874−9882

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The Journal of Physical Chemistry B

geometrical parameters of the straight-channel region, that is, channel width and height, because the junction between the circular domain and the straight channel may give rise to spatiotemporal fluctuations in reaction or diffusion behavior (or both) of the constituents. For acid wave propagation to be feasibly used for chemistry-based computations (or other technologies) under mild chemical conditions, clarification of the propagation characteristics in complex microspaces is essential. In response to these issues, we have investigated the acid wave propagation dynamics by dividing it into two categories: (1) the early state of propagation near the junction and (2) the stable propagation state far away from the junction. The former region is governed by both reaction-diffusion phenomena and gradient-assisted diffusion, whereas the effect of gradientassisted diffusion becomes less pronounced in the latter region. By distinguishing and comparing these two regions, we have finally articulated some important guidelines for controlling the acid wave propagation behavior through the independent design of chemical and physical conditions.

Stimulated by such requirements, various microspaces have been investigated to clarify the effects of the size, shape, and periodicity of the microspace on the BZ wave propagation characteristics. Examples of such devices consist of large circular domains and narrow channels, gradually narrowing wedgeshaped microreactors, and grid-style microreactors with periodic structural barriers.17 Furthermore, by taking advantage of the fact that, for the BZ reaction, the reaction dynamics are optically controllable,18,19 it is possible to tune the microspace for propagation by using nonhomogeneous light on a thin film.20,21 This method is intriguing because the propagating pathway can be tuned during the experiment by in-situ changes in illumination patterns. Therefore, highly flexible and dynamic control of the BZ wave propagation (and thus computation) can be expected by combining lithographic fabrication techniques with in-situ optical control. Despite a deep understanding of the BZ wave propagation in microspaces, its highly acidified experimental conditions (typically containing submolar levels of H2SO4) reduce its applicability, owing to a limitation of the materials that can be used in the microarchitecture under such low pH conditions. Similar to the BZ wave, proton-producing redox reactions of oxyanions are known to be autocatalytic and to manifest propagating acid fronts.22 Depending on the substrate used, the pH of these acid waves can be designed to range from 3 to 8, which is several orders higher than that of the BZ reaction solution.23,24 Furthermore, such acid waves can be produced by various substrates, such as chlorite-tetrathionate,25−29 chloritethiosulfate,30−32 chlorite-thiourea,33 chlorate-sulfite,34 bromatesulfite,23 bromate-sulfuric acid,35 iodate-arsenous acid,36−38 and iodide-nitric acid.39 Although the substrates and pH conditions are quite different in each case, BZ and acid wave propagations have similar characteristics when considered as reaction-diffusion systems. Because the acid waves also involve a chemical reaction at the propagation front, heat is generated during propagation.32−34 As a result, the buoyancy force at the interface leads to a nonaxisymmetric interface through convective flow,33,35,37,38 as in the case of the BZ wave. However, one critical difference can be found in that most experiments on acid waves have been conducted in simple configurations, such as a cylindrical tube or a thin layer cell, in contrast to BZ wave experiments that have already been performed using well-defined micropatterns with lithographic or optical techniques. Under the use of simple glass tubes or thin layer cells, it is not possible to gain insight into how to control the propagation behavior of acid waves in microspaces with complex configurations, such as a circular domain connected to a straight channel via a junction. Thus, there is only limited information available regarding the acid wave propagation behavior in micropatterned spaces. Recently, acid wave propagation in well-defined microspaces has been reported in a one-dimensional microchannel with a junction connecting a circular domain and a straight channel.40 Systematic design of the microchannel has revealed that the velocity of the acid wave propagation can be controlled by altering the channel width and height. This finding offers a simple way of controlling acid wave propagation through the size of the straight-channel region. However, the experiments mentioned earlier were performed only at an early stage of wave propagation; in other words, the propagation dynamics were observed at close proximity to the junction between the circular domain and the narrow channel. Thus, it is hard to conclude that the obtained relation is purely the result of the

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EXPERIMENTAL SECTION We used straight microchannels with 2 mm diameter pores at each end for solution inlet/outlet (Fluidware Technologies Inc., Japan) (Figure 1). The channel depth was fixed at 100 μm, and

Figure 1. Configuration of the microchannel used in the present experiment.

the channel width varied in the range of 100−2000 μm. Substrate solutions containing 70 mM Na2S2O3, 100 mM KBrO3, 2 mM NaOH, and a small amount of phenol red (a pH indicator) were introduced into the microchannel, whose pH was adjusted to approximately 8, unless otherwise noted. At this stage, 1 μL of H2SO4 solution was added to the inlet to initiate the acid wave propagation. Instead of the substrate solution, we also used a NaOH solution of pH 8 doped with phenol red as a control experiment. In the control experiment, only the neutralization reaction was induced, and it propagated into the microchannel by the addition of 1 μL of the H2SO4 solution. Propagation of both acid and neutralization waves were visualized by the color change of the pH indicator.

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RESULTS AND DISCUSSION Before adding the H2SO4 solution into the inlet, the color of the substrate solution in the microchannel was red (0 s in Figure 2), which is the color of phenol red at a pH of 8. The addition of the H2SO4 solution into the inlet at 15 s resulted in a clear color change to yellow for both neutralization and acid 9875


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Figure 2. Snapshot of wave propagation in a microchannel with w = 300 μm. (a) Neutralization waves initiated with (upper) 0.10 M and (lower) 0.05 M H2SO4. (b) Acid waves initiated with (upper) 0.10 M and (lower) 0.05 M H2SO4. The propagation of the acid wave did not appear under the 0.05 M conditions, although a faint color change from red to yellow was seen close to the junction between the inlet and the channel, as indicated by white arrows. (c) H2SO4 concentration dependence on the appearance of the acid wave in the channel region. The propagation of the acid wave appeared above 0.07 M, although only a faint color change to yellow (indicated by white arrows) was observed below 0.07 M.

Figure 3. (a) Calculated proton concentration profiles at different values of t. (b) Enlarged images of the channel entrance region of Figure 2a. (c) Propagation of neutralization front that can be estimated from the position of pH 7 in a. Because the neutralization wavefront appeared a few seconds after the H2SO4 addition in the experiment, t in the calculation was offset for 5 s.

wavefront characterized by a sharp red/yellow color contrast was observed to penetrate into the channel region immediately after the addition of H2SO4 into the inlet at 15 s. This rapid penetration indicates that there is almost no temporal delay between the proton addition in the inlet and the proton

wave experiments. Because phenol red exhibits a bright color change from red to yellow over the pH range from 8.2 to 7.0, the observed color change indicates a pH decrease in the inlet region upon the addition of H2SO4. In the case of the neutralization wave experiments (Figure 2a), a reaction 9876


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the acid wave penetrated and progressed into the channel region (45 s). Similar to the iodate-sulfite-thiosulfate acid wave system,42 the autocatalytic proton production reaction eq 1 is ignited by a transient formation of bisulfite eq 2 at a relatively low proton concentration:

diffusion into the channel region. Thus, the neutralization wave generation can be described by the following two steps: (1) a rapid neutralization reaction in the inlet and (2) a rapid flux of excess protons from the inlet to the channel. The validity of our assumption that the neutralization wave is driven by proton diffusion can be quantitatively confirmed by a simple calculation in a one-dimensional channel configuration. In the calculation, we used experimental conditions in which 0.1 M H2SO4 was added to the inlet filled with a NaOH solution of pH 8, which is identical to the experiment shown in Figure 2. The addition of H2SO4 changes the proton concentration in the inlet to 3.2 × 10−2 M (pH 1.5) after proton consumption by neutralization with NaOH. Thus, protons diffused from the acidic solution in the inlet to the basic solution in the channel. Because the volume of the inlet (2π mm3: bottom area π mm2, depth 2 mm) is sufficiently large compared with the volume of the channel (0.3 mm3: width 0.3 mm, depth 0.1 mm, length 5 × 105 s), and thus the wave can be regarded as intrinsic velocity of autocatalytic solitary wave without the acceleration effect by proton flux. Quantitative agreement supports our suggestion that the acid wavefront at the constant velocity region is governed only by the autocatalytic reaction.

Figure 6. (a) Histograms of the acid wave propagation velocity at the near-junction region under different H2SO4 concentrations in the microchannel with w = 600 μm. (b) The averaged velocity as a function of channel width. H2SO4 concentrations are 0.07 M (green), 0.1 M (blue), and 0.2 M (red).

varied above the lower limit concentration (0.070 M). The velocity histograms made it clear that the propagation velocity increased by increasing the H2SO4 concentration. These results clarified that the propagation velocity of the acid wave can be controlled by the H2SO4 concentration, presumably owing to the additional proton accumulation effect. However, previous reports using a nitric acid-iron(II) reaction suggested that varying the initiator concentration (protons in our system) affected only the induction period between the addition of the initiator and the wave generation.43 This paper used simple cylindrical tubes containing a reaction mixture, and the wave was initiated by dipping a glass rod into the initiator solution (0.01−0.1 M) and by touching it to the reaction mixture. They observed the wave propagation after an induction period that lasted as long as 5 min, a few times longer than the period associated with our system. Although the reason why they observed the change only during the induction period was not clear, the difference in the propagation configuration and the length of the induction period are nevertheless important factors in resolving this issue. We also investigated the H2SO4 concentration dependence for several channels with different widths. Acceleration with higher concentration was found to be a general feature for any channel width. This experiment demonstrated that the velocity can also be controlled by the channel width. Faster propagation appeared in narrower channels. The channel width dependence has already been discussed on the basis of the relation between c, J, and the channel width.40 Because J is defined as the number of protons that flow through a given unit area during a given unit time, the number of protons per unit time flowing from the inlet to the channel at a given channel configuration is expressed by the product of J and the cross-sectional area of the channel. Therefore, an increase in the channel width caused an outflow of protons at a faster rate. As a result, the proton concentration in the inlet decreased rapidly, which finally led to a rapid decrease in c and J. Their rapid decrease can explain the slower propagation at wider channels. Our results strongly indicate that the acid wave propagation dynamics can be easily and independently tuned by manipulating the H 2 SO 4 9879


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decreasing pH of the substrate solution, the number of protons to be consumed at the initial neutralization reaction would be reduced. As a result, more protons can be left as a proton source for higher c and J, resulting in the observation of a higher propagation velocity. Because the near-junction region will benefit from the highly retained c and J values, a larger effect can be achieved on the near-junction velocity (Figure 7b). As a general feature, we can say that the propagation velocity can be increased 3-fold and 1.5-fold by constraining the pH to be 11 and 8 for the near-junction and far-junction regions, respectively. A similar effect of the initial pH (OH− concentration) on the propagation velocity has been reported in a simple tube system.30 Although such concentration dependence could be calculated by the numerical analysis of reaction-diffusion equations, there is still no information on the rate equations of the present system. Future experimental and theoretical treatments can make it possible to carry out a comprehensive and quantitative analysis by considering both chemical (e.g., H2SO4 and pH) and physical (e.g., proton flux at the junction) parameters that play important roles in controlling the acid wave propagation. Furthermore, it could be an intriguing challenge to couple our strategies with advective and fingering flows in Hele-Shaw cells27,44 or convective surface flows at a liquid/gas interface.45,46 These fluid flow conditions, in conjunction with reaction and diffusion conditions, are expected to offer an additional but dynamic control for the velocity, direction, shape, and interaction of autocatalytic wavefronts.

concentration and the channel configuration, where one uses a microchannel with a junction connecting two domains with different shapes. We have seen that the acid wave is initiated with a rapid neutralization in the inlet and subsequent chemical reactions, which can be ignited above a critical H2SO4 concentration. If the H2SO4 concentration were below a certain lower limit, there were not enough protons left to trigger these reactions, resulting in no propagation. Thus, the acid wave propagation did not appear below a critical H2SO4 concentration. However, if the number of protons consumed at the initial neutralization could be decreased, a larger fraction of protons would be left and could be used to ignite subsequent reactions even under the same H2SO4 concentration conditions. Thus, it can be expected that an increase in the fraction of unused protons would have a similar effect with an increase in the H2SO4 concentration. On the basis of this assumption, we conducted experiments by changing the pH of the substrate solution in the microchannel under the same H2SO4 concentration (Figure 7).

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CONCLUSIONS We have succeeded in clarifying the propagation behavior of an acid wave in a microchannel through a junction connecting different configurations. Temporal image analysis showed that the acid wave propagation was generated via successive chemical reactions: a neutralization reaction, a protonconsumption reaction, and a proton-production reaction, in which the proton-production reaction was ignited only when enough protons were left after the initial neutralization reaction. Numerical analysis on the propagation behavior revealed that the propagation dynamics in the microchannel was controllable by several independent factors. In addition to a factor concerning the chemical conditions of the substrate and the H2SO4 solution (which was to be expected), we must emphasize that special attention must be paid to the configuration of the microchannels when they involve junctions between different shapes. Because the junction was found to have the ability of regulating the proton flux from one side to the other, the propagation velocity can be easily tuned via the design of the junction. Thus, both chemical and physical designs are available for precisely controlling the acid wave propagation. The present findings offer a novel and flexible methodology to control the propagation behavior of acid waves, and also of other reaction-diffusion waves, in microspaces.

Figure 7. (a) Propagation velocity of acid waves under substrate solution with different pH values in the microchannel with w = 300 μm. (b) Averaged propagation velocity at both near-junction (red circle) and far-junction (black cross) regions as a function of the pH of the substrate solution.

As we expected, lowering the pH had the effect of increasing the propagation velocity, which is similar to the effect of an increase in the H2SO4 concentration. Under the highest pH conditions (i.e., a pH of 11.6), the propagation velocity was approximately 2 μm/s at the near-junction region and gradually decreased to a constant velocity of 1.6 μm/s at the far-junction region. On the other hand, a 4-fold increase in the nearjunction velocity was achieved by decreasing the solution pH to 8.1. This phenomenon can be explained similarly to the H2SO4 concentration effect, that is, in terms of the additional proton accumulation effect at higher c and J conditions. With the

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 9880


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ACKNOWLEDGMENTS This work was supported in part by a Grant-in-Aid for Scientific Research (25708012) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

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Propagation Behaviors of an Acid Wavefront Through a Microchannel

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