Guiding chemical pulses through geometry: Y junctions

We study computationally and experimentally the propagation of chemical pulses in complex geometries. The reaction of interest, CO oxidation, takes place on single crystal Pt(110) surfaces that are microlithographically patterned; they are also addressable through a focused laser beam, manipulated through galvanometer mirrors, capable of locally altering the crystal temperature and thus affecting pulse propagation. We focus on sudden changes in the domain shape (corners in a Y-junction geometry) that can affect the pulse dynamics; we also show how brief, localized temperature perturbations can be used to control reactive pulse propagation. The computational results are corroborated through experimental studies in which the pulses are visualized using reflection anisotropy microscopy.

Figure 1

(Color online) Pulse propagation in different Y junction structures. By choosing appropriate geometric parameters, we are able to dictate the pulse transmission patterns. (a) $h=5$, $\theta =\pi$; (b) $h=3.7$, $\theta =\pi$; (c) $h=3.5$, $\theta =\pi$; (d) $h=3.5$, $\theta =\frac{3}{4}\pi$. Other parameters: $W=5$, $w=1.93$, $\alpha =\frac{7}{9}\pi$, $T=535.5\mathrm{K}$, $P_{\mathrm{C}\mathrm{O}}=4.95\times {10}^{-5}\mathrm{mbar}$, $P_{{\mathrm{O}}_2}=2.0\times {10}^{-4}\mathrm{mbar}$. The unit dimensionless length corresponds to a real length of $3.7\mu \mathrm{m}$ throughout the paper except in Fig. 7, where it corresponds to $3.8\mu \mathrm{m}$.

Figure 2

Geometry of a corner structure, $r=\frac{W}{\sin (\pi -\theta )}$.

Figure 3

(Color online) Critical angle ${\theta }_c$ for a pulse to turn around a corner, as a function of dimensionless channel width $W$. For fixed CO pressure, pulses in a geometry with $\theta$ and $W$ chosen “above” the solid lines shown are able to turn around the corner. The solid lines, fitted to data points, are included to guide the eye. The dashed and dotted lines are given by $r_c=\frac{W}{\sin (\pi -{\theta }_c)}$ for different $r_c$. $T=535.5\mathrm{K}$, $P_{{\mathrm{O}}_2}=2.0\times {10}^{-4}\mathrm{mbar}$.

Figure 4

(Color online) (a) A snapshot showing a microdesigned $\mathrm{Ti}{\mathrm{O}}_2∕\mathrm{Pt}$ checkerboard. The inactive $\mathrm{Ti}{\mathrm{O}}_2$ rhombs appear black while pulses (little arcs in the first snapshot) are propagating on the light-gray Pt(110) surface. (b) A blow-up of the checkerboard structure. To its right, a geometry (symmetric around the centerline) we used in the simulations of the rhomb constriction is depicted.

Figure 5

(Color online) Critical angle for pulse turning around the corner as a function of channel width $W$ for the rhomb constriction and the Y-junction structure. For the rhomb constriction structure, we plot ${\varphi }_c∕2+\pi ∕2$ vs $W$ instead of ${\varphi }_c$ vs $W$. For rhomb constriction (Y-junction) structures with values of $W$ and $\varphi ∕2+\pi ∕2\left(\theta \right)$ chosen “above” the corresponding curve, pulses are able to turn around the corner. The solid lines, fitted to data points, are included to guide the eye. Snapshots of a pulse propagating in the rhomb constriction structure at point $a(2.7,0.88)$ and $b(4.0,0.88)$ are shown in the insets. $T=535.5\mathrm{K}$, $P_{\mathrm{C}\mathrm{O}}=4.95\times {10}^{-5}\mathrm{mbar}$, $P_{{\mathrm{O}}_2}=2.0\times {10}^{-4}\mathrm{mbar}$.

Figure 6

(Color online) Using local laser heating to assist the propagation of an O-rich pulse around the corner. Snapshots (a)–(d) show the coverage of oxygen; corresponding instantaneous temperature fields before, after [$\left({\mathrm{a}}^{\prime }\right)$ and $\left({\mathrm{c}}^{\prime }\right)$, respectively], as well as during the laser shot [$\left({\mathrm{b}}^{\prime }\right)$] are plotted in the second row. Laser heating is turned on for a total of $0.4\mathrm{s}$ (from $t=5.0\text{to}5.4\mathrm{s}$) and centered at the lower junction corner; the maximum temperature increase there is $3\mathrm{K}$. The width of the left channel is 6. (a) $t=4.5\mathrm{s}$, (b) $t=5.0\mathrm{s}$, (c) $t=5.5\mathrm{s}$, (d) $t=8.0\mathrm{s}$. $T=535.5\mathrm{K}$, $P_{\mathrm{C}\mathrm{O}}=4.95\times {10}^{-5}\mathrm{mbar}$, $P_{{\mathrm{O}}_2}=2.0\times {10}^{-4}\mathrm{mbar}$.

Figure 7

(Color online) Using local laser heating to prevent the propagation of a CO-rich pulse. Similar to Fig. 6, instantaneous temperature fields [$\left({\mathrm{a}}^{\prime }\right)$–$\left({\mathrm{c}}^{\prime }\right)$] are plotted below the corresponding CO coverage [(a)–(c)]. The local laser heating is turned on for a total of $1\mathrm{s}$ (from $t=12\text{to}13\mathrm{s}$) and centered in the middle of the lower channel entrance with a maximum temperature increase of $5\mathrm{K}$. The width of the left channel is 20. (a) $t=11\mathrm{s}$, (b) $t=12\mathrm{s}$, (c) $t=13\mathrm{s}$, (d) $t=17\mathrm{s}$. $T=540\mathrm{K}$, $P_{\mathrm{C}\mathrm{O}}=4.2\times {10}^{-5}\mathrm{mbar}$, $P_{{\mathrm{O}}_2}=1.33\times {10}^{-4}\mathrm{mbar}$.

Figure 8

(Color online) Using local laser heating to prevent the propagation of an O-rich pulse. The local laser heating is turned on for a total of $0.4\mathrm{s}$ (from $t=1.5\text{to}1.9\mathrm{s}$) and centered in the middle of the lower channel entrance with a maximum temperature increase of $4.5\mathrm{K}$. The width of the left channel is 6. (a) $t=1.0\mathrm{s}$, (b) $t=1.5\mathrm{s}$, (c) $t=2.0\mathrm{s}$, (d) $t=7.0\mathrm{s}$, (e) $t=10.0\mathrm{s}$, (f) $t=12.0\mathrm{s}$. $T=535.5\mathrm{K}$, $P_{\mathrm{C}\mathrm{O}}=4.95\times {10}^{-5}\mathrm{mbar}$, $P_{{\mathrm{O}}_2}=2.0\times {10}^{-4}\mathrm{mbar}$.

Figure 9

(Color online) Schematic image of the experimental setup (not to scale). For details, see text.

Figure 10

Time-lapse images (an interval of $3\mathrm{s}$ between each two snapshots) showing a dying O-rich pulse “rescued” by a laser shot centered at $B$. The arrows indicate the propagation direction of the pulses. $T=455\mathrm{K}$, $P_{{\mathrm{O}}_2}=2\times {10}^{-4}\mathrm{mbar}$, $P_{\mathrm{C}\mathrm{O}}=6.42\times {10}^{-5}\mathrm{mbar}$. (a) No laser shot is applied. The pulse decollates at $B$ and enters the upper right channel. (b) A laser shot is applied for $50\mathrm{ms}$ with a power of $500\mathrm{mW}$ when the lower end of the pulse reaches point $B$. The pulse does not decollate at $B$, and splits into two at $C$ entering both channels.

Figure 11

(Color online) Guidance of CO-rich pulses in a labyrinthine structure. The circles indicate the location where the laser shot is applied. The laser shot duration is $1\mathrm{s}$ with a power of $230\mathrm{mW}$, which destroys any part of the pulse within the circle. $T=451\mathrm{K}$, $P_{{\mathrm{O}}_2}=2\times {10}^{-4}\mathrm{mbar}$, $P_{\mathrm{C}\mathrm{O}}=5.50\times {10}^{-5}\mathrm{mbar}$. (a) No laser shot is applied and the pulse enters all three channels. (b) A laser shot is applied when the lower end of the pulse is at corner $A$ of the crossing. The pulse only enters the upper channel. (c) A laser shot is applied when the upper end of the pulse passes corner $B$ of the crossing. The pulse is thus prevented from entering the channel on the right.