  Series of experiments on turbulent bubbly channel flows observed bubble
clusters near the wall which can change large-scale flow structures. To gain
insights into clustering mechanisms, we study the interaction of a pair of
spherical bubbles rising in a vertical channel through combined experiments and
modeling. Experimental imaging identifies that pairwise bubbles of 1.0 mm
diameter take two preferred configurations depending on their mutual distance:
side-by-side positions for a short distance ($S<5$) and nearly inline, oblique
positions for a long distance ($S>5$), where $S$ is the mutual distance
normalized by the bubble radius. In the model, we formulate the motions of
pairwise bubbles rising at $Re=O(100)$. Analytical drag and lift, and
semi-empirical, spatio-temporal stochastic forcing are employed to represent
the mean acceleration and the fluctuation due to turbulent agitation,
respectively. The model is validated against the experiment through comparing
Lagrangian statistics of the bubbles. Simulations using this model identify two
distinct timescales of interaction dynamics which elucidate the preferred
configurations. For pairs initially in-line, the trailing bubble rapidly
escapes from the viscous wake of the leading bubble to take the oblique
position. Outside of the wake, the trailing bubble travels on a curve-line path
with a slower velocity driven by potential interaction and horizontally
approaches the leading bubble to become side-by-side. Moreover, statistical
analysis identifies that the combination of the wake and the agitation can
significantly accelerate the side-by-side clustering of in-line pairs. These
results indicate positive contributions of liquid viscosity and turbulence to
the formation of bubble clusters.
