Bubbles in highly porous media: Clogging and unclogging at constrictions

Abstract

Gas bubble transport through highly porous transport layers (PTLs) is a key process in electrochemical devices such as proton exchange membrane water electrolyzers, where bubbles generated at catalyst surfaces must migrate through complex porous networks. To understand this process, we focus on model systems, namely the motion of single, paired and multiple bubbles in capillaries and study these by combining analytical modeling, three-dimensional color-gradient lattice Boltzmann simulations, and X-ray radiography. For single bubbles, we derive an analytical expression for the critical Bond number separating passage from clogging and show that, in the low deformation regime, it accurately predicts this transition in circular capillaries. Extending the study to bubble pairs, we uncover additional clogging and unclogging pathways, including hydrodynamic unclogging driven by pressure buildup in the interbubble film, and coalescence-induced clogging and unclogging. By mapping our results as functions of confinement ratio and Bond number, we define distinct dynamical regimes that control bubble passage. Experiments on bubble chains rising through highly porous nickel foams confirm the predicted clogging and unclogging mechanisms.

Figures (8)

• Figure 1: Schematic of a constricted circular capillary containing two bubbles. The channel has diameter $D$ and length $L$, with a constriction of diameter $d$ and length $l$. Bubbles 1 and 2 have radius $R$ and are separated by a center-to-center distance $r_{21}$. A gravity-induced acceleration $\mathbf{a}$ acts on both bubbles. Note that the dimensions are not drawn to scale.
• Figure 2: Two-dimensional schematic of a bubble entering a constriction. The left and right spherical caps have radii $R_l$ and $R_r$, with maximum distances from the channel inlet $z_l$ and $z_r$. The height of the constriction is $d$ and the cap volumes are $V_l$ and $V_r$. Finally, the background pressure is denoted by $P_0$, and the bubble experiences a gravity-induced acceleration $\mathbf{a}$.
• Figure 3: State diagram of a single bubble passing through a constriction. We identify three different states: Red upward-facing triangles denote clogging of the channel, where the bubble is stuck in front of the constriction and is unable to enter. Green downward-facing triangles denote the passage of the bubble through the constriction. Blue squares correspond to bubble passage, with breakup into two smaller bubbles. Additionally, the gray background patterns indicate the four regions in the confinement ratio. From left to right, we have strong, moderate, weak, and no confinement. The dashed line is the analytical prediction for $\mathrm{Bo}_{\text{cr}}$ (Eq. \ref{['eq:critical-Bond-number-explicit']}).
• Figure 4: Single bubble deformation without passage at moderate Bond number: shown is the bubble profile for a central slice of the simulation box with confinement ratio $\mathrm{C} = 0.5$ and Bond number $\mathrm{Bo} = 1.0$. Only the region of the simulation box containing the bubble is shown and the coordinates of the fluid nodes, $c_x$ and $c_z$, are normalized by the diameter $D$ and length $L$, respectively. The bubble approaches the constriction and clogs after around $25000$ time with the left spherical cap deforming asymmetrically to satisfy the imposed contact angle. Gray rectangles denote regions of increased (A) and reduced (B) curvature with respect to the spherical cap approximation.
• Figure 5: Normalized passage time vs. Bond number (a) and critical Bond number ratio (b) for bubble passage with and without breakup. Open symbols denote passage with breakup, while the closed symbols denote passage without breakup. Colors denote different confinement ratios, where the dashed lines show the critical Bond number, obtained from Eq. \ref{['eq:critical-Bond-number-explicit']}. Two reasons for deviations from the analytical predictions can be identified: viscous effects and violations of the spherical cap approximation.