Electrolysis-Driven and Pressure-Controlled Diffusive Growth of Successive Bubbles on Microstructured Surfaces.

TL;DR: It is observed that H2 bubble successions at large gas-evolving substrates first experience a stagnation regime, followed by a fast increase in the growth coefficient before a steady state is reached, which clearly contradicts the common assumption that constant current densities must yield time-invariant growth rates.

Abstract: Control over the bubble growth rates forming on the electrodes of water-splitting cells or chemical reactors is critical with respect to the attainment of higher energy efficiencies within these devices. This study focuses on the diffusion-driven growth dynamics of a succession of H2 bubbles generated at a flat silicon electrode substrate. Controlled nucleation is achieved by means of a single nucleation site consisting of a hydrophobic micropit etched within a micrometer-sized pillar. In our experimental configuration of constant-current electrolysis, we identify gas depletion from (i) previous bubbles in the succession, (ii) unwanted bubbles forming on the sidewalls, and (iii) the mere presence of the circular cavity where the electrode is being held. The impact of these effects on bubble growth is discussed with support from numerical simulations. The time evolution of the dimensionless bubble growth coefficient, which is a measure of the overall growth rate of a particular bubble, of electrolysis-gene...

Summary

■ INTRODUCTION

• At sufficiently large voltages, gas bubbles are produced on the electrodes in electrochemical reactors, 1−3 in water-splitting cells during the electrolysis of water for hydrogen production, 4 in the study of nanobubbles, 5−7 and during photoelectrolysis by solar-driven cells, 8, 9 a topic that recently has gained interest.
• The formation of unwanted nucleation sites or large bubble departure sizes may lead to an excessive coverage of electrodes by bubbles.
• The scaling exponent α is typically 1/2 or 1/3, depending on the experimental conditions.
• The growth is almost entirely driven by the Fickian diffusion of gas into the bubble from the surrounding supersaturated electrolyte.
• It follows that the gas supersaturation near the electrode depends not only on the current density but also on the elapsed time of electrolysis.

■ RESULTS AND DISCUSSION

• The authors begin this section with a theoretical description of the key quantity used to characterize the bubble growth dynamics, namely, the diffusive growth coefficient.
• The experimental results are then discussed, giving special attention to the effect that the different sources of depletion have on the measured growth coefficients.
• R u and k H are the universal gas constant and Henry's constant, respectively.
• Equation 4 allows for the following solution (neglecting surface tension): EQUATION ].
• This solution is essentially that provided by Epstein and Plesset 28 formulated for the nth bubble in the succession and, correspondingly, using the mass-transfer Jakob number 14, 39 related to the nth bubble, EQUATION.
• The Jakob number is a measure of the driving force for bubble growth induced by a solubility parameter Λ, commonly known as the Ostwald coefficient, and the degree of supersaturation ζ n .

■ CONCLUSIONS

• The large surface area of the electrode ensures that the bubble growth is diffusion-limited.
• The authors identify depletion from (i) previous bubbles in the succession, from (ii) unwanted parasitic bubbles forming on the cavity sidewall, and from (iii) the mere presence of the cavity where the electrode is being held.
• A fast growth in β ̃H2 then follows before the steady state is reached.
• Oppositely, CO 2 bubbles experience enhanced growth as they approach detachment.
• The knowledge obtained can be further expanded by conducting electrolysis experiments with two main variations.

Figures

Table 1. Gas Properties under Our Experimental Conditions (T∞ = 20 °C)

Figure 6. Simulation snapshots of (a−c) H2 or (d) CO2 concentration isocontours around four distinct growing bubbles. The contour labels display the local supersaturation value, C/(kHP0) − 1. The simulations are performed for R0 = 7.5 μm, Rp = 15 μm, and Hp = 30 μm. The snapshots correspond to the early growth stage of the bubbles when R = 2Hp = 60 μm. Panels a−c show H2 bubbles growing in an air-saturated electrolyte assuming an effective current density of 1.56 A/m2 that provides a similar H2 flux as the highest nominal current density used in our experiments (Figure 14.) The bubble nucleation time after the start of electrolysis, t0, the corresponding initial degree of H2 supersaturation (in the absence of bubbles), ζ, and the time after nucleation at which the snapshot is taken, t, are (a) t0 = 30 s, ζ ≈ 0, t ≈ 31 s, (b) t0 = 2 min, ζ ≈ 1, t ≈ 16 s, and (c) t0 = 20 min, ζ ≈ 5.3, t ≈ 3 s. Panel (d) portrays a CO2 bubble growing in an initially uniform supersaturated solution, ζ = 0.17 at P0 = 7.75 bar. The bubble is t ≈ 5 s old.

Figure 16. Comparison between simulation (curves) and the experimental growth dynamics for the (a) 48th and (b) 74th bubble of the succession with Hp = 30 μm (cf. Figure 15). The nominal current density is j = 7.8 A/m2, whereas simulations employ an effective current density of 1.04 A/m2. The red dashed curves are expected growth for a bubble in an infinitely long electrode that nucleates at the experimental time t in the absence of any previous bubbles. The initial concentration profile is given by eq 17 evaluated at time t. The resulting local supersaturations are ζ48 ≈ 9.25 and ζ74 ≈ 11.0. For the black curves, the time is adjusted to (a) 0.5t and (b) 0.6t, resulting in ζ48 ≈ 7.25 and ζ74 ≈ 8.4.

Figure 15. Evolution in time of the diffusion growth rate for j = 7.8 A/ m2 for three different experiments. The pit radius is R0 = 5 μm for Hp = 0 and 30 μm, whereas R0 = 1 μm for Hp = 15 μm. The green curve is a theoretical approximate solution given in eq 14, with jeff = 1.04 A/m 2 (same value as in simulations) and Heff = 8 mm.

Figure 8. (a) Pressure-controlled bubble radius dynamics and (b) the corresponding squared radius. The dashed curves are the (extrapolated) fits from which β̃CO2 is computed. The pit and pillar radii are 10 and 15 μm, respectively, whereas the pillar height is 30 μm.

Figure 7. Bubble radius dynamics at three different time periods after the onset of electrolysis with 7.8 A/m2. The measured bubble radii (dots) are plotted in (a, c, and e), whereas the corresponding square of the measured radii are plotted in (b, d, and f). Panels (a and b) correspond to the stagnation regime, (c and d) correspond to the supersaturation regime, and (e and f) correspond to the advected growth regime. The dashed black curves are the fits from which the asymptotic growth coefficient β̃H2 is obtained. The pit and pillar radius are 5 and 15 μm, respectively. The plots in (a−d) belong to the same experiment where Hp = 30 μm. The plots in (e and f) belong to a different experiment where Hp = 15 μm. The dotted horizontal line marks the size below which it was not possible to optically determine the size of the bubble accurately.

Figure 14. Comparison between simulation (curves) and the experimental growth dynamics of the third bubble for three nominal current densities: (a) 7.8, (b) 10.4, and (c) 15.6 A/m2. Simulations employ effective current densities of (a) 1.04, (b) 1.30, and (c) 1.56 A/m2. Using eq 17 in Appendix A, these yield initial supersaturations, ζ, of approximately (a) 1.5, (b) 3.3, and (c) 3.1. The black curves are computed by imposing a zeroconcentration boundary condition at heights of (a) 1.0, (b) 1.3, and (c) 1.3 mm to model the effect of the cavity. The red dashed curves are computed without imposing the aforementioned boundary condition.

Figure 1. SEM image of a micropillar protruding from the silicon substrate. In this particular sample, the pillar height is Hp = 30 μm, the pit (inner) radius is R0 = 5 μm, and the pillar (outer) radius is Rp = 15 μm.

Figure 2. Sketch of the electrolysis setup. The dimensions of the substrate, cavity, and holder are not drawn to scale to highlight, within a single schematic, the different dimensions playing a crucial role in electrolytic bubble growth. Note that the pit and pillar are much smaller in reality.

Figure 10. Diffusive growth coefficient as a function of charge for different current densities (caption of Figure 9). The efficiency of gas evolution in the transient regime increases with the current density j.

Figure 9. β̃H2 for a succession of electrolytic bubbles exposed to constant current densities. Each point corresponds to a distinct bubble in the succession. Time tm is the mean time (after the start of electrolysis) of the fitting period used to compute β̃H2. The bubbles evolved on a pit with a radius of 5 μm, a pillar radius of 15 μm, and a pillar height of 30 μm.

Figure 4. Pressure-controlled growth for a succession of CO2 bubbles for ζ = 0.17 during the first 100 min after the pressure drop. The dotted vertical lines indicate bubble detachment and nucleation of the following bubble. The pit and pillar radii are 10 and 15 μm, respectively, whereas the pillar height is 30 μm.

Figure 3. Time evolution of the bubble radius for a succession of bubbles captured during the first hour after the start of the electrolysis. Each individual curve represents a distinct bubble. Four different experiments are shown, in which the supplied current density is set to (a) 5.2, (b) 7.8, (c) 10.4, and (d) 13.0 A/m2. The pit and pillar radii are 5 and 15 μm, respectively, whereas the pillar height is 30 μm. Using Rd ≈ 0.3 mm and Re = 3.5 mm yields a Damköhler number of De = Re 2/Rd 2 ≈ 136. The dotted horizontal line marks the etching defect size below which it was not possible to optically detect the bubbles.

Figure 17. Universal plot of the time evolution of the 1D concentration profiles for different instants in dimensionless time. The profiles marked in blue correspond to log10(Dt/H 2) = −3, −2, −1, and 0. The profile in red is the steady-state profile.

Figure 18. Invariant, dimensionless plot of the time evolution of the concentration at the electrode wall (z = 0).

Figure 11. (a) Diffusive growth coefficient, β̃CO2, as a function of time for four different P-C experiments. The time measurement for each bubble n is associated with its moment of detachment. (b) Plot of 1/β̃CO2 2 as a function time. The straight solid line shows linear eq 12, with a slope of m = 2πDCO2t/(3Rd 2) = 0.027 s−1.

Figure 12. Photograph showing the parasitic bubbles forming on the circular corner where the electrode (black surface) meets the sidewall of the cavity and at the sharp upper edge of the cavity wall (cf. the large bottommost bubble). These bubbles visibly surround the bubble that forms on top of the micropillar in the center of the electrode. The electrode diameter is 7 mm.

Figure 13. Minimum squared value of β̃H2 plotted versus the product of current density and detachment radius. Each point corresponds to a single bubble in a unique succession. The linear regression fit is also plotted.

Figure 5. Schematic of the simulation grid for a pillar with dimensions Hp/R0 = 4 and Rp/R0 = 2. The simulation points fall on the intersection of the contour lines. The simulation is axisymmetric around the z axis. The bulk region in tangent-sphere coordinates (η, ξ) applies to z > Hp. The microlayer region in pseudocylindrical coordinates (ρ, ζ) applies to 0 < z < Hp. A matching condition is imposed at z = Hp. Coordinates η, ξ, and ρ evolve with the bubble so that ξ = 1 (in blue) always maps the bubble surface, regardless of the actual bubble size. Here, the bubble size has been arbitrarily set to R/ R0 = 3. The separation of the contours is uniform. Here, Δη = Δξ = Δρ = 0.1 and ζ = 0.5. Coordinate η = 0 lies on the z axis, η → ∞, at the contact point.

Frequently asked questions

Q1. What have the authors contributed in "Electrolysis-driven and pressure-controlled diffusive growth of successive bubbles on microstructured surfaces" ?

This study focuses on the diffusion-driven growth dynamics of a succession of H2 bubbles generated at a flat silicon electrode substrate. For electrolytic bubbles and under the range of current densities considered here ( 5−15 A/m ), it is observed that H2 bubble successions at large gas-evolving substrates first experience a stagnation regime, followed by a fast increase in the growth coefficient before a steady state is reached. At sufficiently large voltages, gas bubbles are produced on the electrodes in electrochemical reactors, in water-splitting cells during the electrolysis of water for hydrogen production, in the study of nanobubbles, and during photoelectrolysis by solar-driven cells, a topic that recently has gained interest. This coefficient represents the ratio between the characteristic time of the diffusive transport of the evolved gas across a region of the size of the electrode, tt ≈ Ae/D, and that of the diffusive transport of gas to the bubble, namely, td ≈ Rd/D, which in turn limits the Received: August 22, 2017 Revised: October 6, 2017 Published: October 17, 2017 Article pubs. The gas evolution efficiency, namely, the fraction of gas contained within the departing bubble ( s ) with respect to the total amount of gas produced at the electrode, has been reported to be close to 100 %. Provided that the growing bubble remains spherical as it grows and that the contact angle is small, a simple mass balance yields the following experimentally confirmed relation Moreover, such control should allow us to efficiently harvest the produced gas bubbles without further need of energy input, e. g., in the form of pumpingor vibrationbased mechanical systems. 

Q2. what is the boundary condition for n?

−Δ∞ n P R R T t 4 3n n 0 d3u (22)which acts as a boundary condition to the diffusion equation,θ θ∂ ∂ = ∂ ∂ ∂ ∂ ⎛ ⎝⎜ ⎞ ⎠⎟t D r r r r nnn 2 2(23)together with a second boundary condition θn(r → ∞, t) = 0 and initial condition θn(r, tn = 0) = 0. Let θn̅ be the characteristic solution for θn evaluated at r = δn and t = Δtn. 

Q3. what is the concentration field of the bubble?

It is essentially the concentration field evaluated at the characteristic diffusion length δn and time Δtn corresponding to the previous bubble, where Δtn = td,n − t0,n is the bubble residence time. 

Q4. What is the boundary condition for the nth bubble?

2 = 2RuT∞ΔC̅1/P0 is just the known growth rate of the first bubble (corresponding to the initial, undepleted supersaturation ΔC̅1).