Two-stage dispersion mechanism of clean spherical bubbles rising in a chain

Abstract

Wake-induced lift is a key mechanism governing the initial destabilization of bubbles rising in a chain (Atasi et al., 2023). Moore's wake model predicts limited interfacial vorticity and a relatively slender, spatially confined wake for clean spherical bubbles, suggesting that wake-mediated interactions weaken as the inter-bubble spacing increases. However, we observed pronounced large-scale lateral dispersion and strong bubble frequency dependence in controlled experiments where bubble diameter and generation frequency were independently varied, even when the inter-bubble separation exceed the characteristic wake length. A reduced-order model incorporating pairwise wake-induced interactions captured the onset of bubble chain destabilization but systematically underpredicted the subsequent emergence of large-scale dispersion. We demonstrate that bubbles rising in a chain collectively generate a mean upward liquid flow that modifies the local shear field, enhancing the lateral migration through shear-induced lift. Incorporating this self-induced weak flow into the model quantitatively reproduced both the dispersion magnitude and its frequency dependence. These results suggest that the dispersion of bubbles rising in a chain involves a two-stage mechanism, with initial chain destabilization mediated by wake interactions, followed by flow modification arising from two-way coupling between bubbles and the liquid. This collective mechanism highlights the importance of self-induced mean flow effects in continuum descriptions of bubble flows.

Figures (18)

• Figure 1: (a) Schematic of the experimental setup of the bubble generation system and three-dimensional high-speed imaging. (b) Definition of dispersion angle $\alpha$ of the recorded bubble trajectories.
• Figure 2: Schematic of the bubble chain model incorporating interactions with adjacent bubbles.
• Figure 3: Assumed upward flow profiles at different heights. The edge regions are modeled by a Gaussian distribution with a standard deviation $\sigma=0.5\,\mathrm{mm}$, while the central flat region expands with height $z$.
• Figure 4: Trajectories of bubbles rising in a chain ($d=0.5\,\mathrm{mm}, \nu=1 \,\mathrm{mm^2/s}$).
• Figure 5: (a) Three-dimensional dispersions and (b) the corresponding bubble passage distributions in cross-sections at 20 mm intervals for bubble generation frequencies of: (i) $f=4\,\mathrm{Hz}$, (ii) $f=8\,\mathrm{Hz}$, (iii) $f=12\,\mathrm{Hz}$, and (iv) $f=20\,\mathrm{Hz}$. The centroid of the distributions in (b) is marked with a cross.