Bubble dynamics in an inclined Hele-Shaw cell

Abstract

We report experimental results on the dynamics of large bubbles in a Hele-Shaw cell subject to various inclination angles with respect to gravity. Low Reynolds number cases are studied by injecting bubbles in an stagnant water/UCON mixture in three different Hele-Shaw cell geometry. The leading order rise speed $v_b$ follows the Taylor-Saffman limit which is inversely proportional to the viscosity $η$, but directly proportional to the square of the cell gap $h$ and the effective gravity, accounting for cell tilt angle $θ$. However, when the cell is inclined more and more, the bubble buoyancy in the cell gap leads to a substantial decrease in the rise speed, as compared to the Taylor-Saffman speed. Buoyancy pushes the bubble towards the top channel wall, whereby a difference between the lubrication film thickness on top of and underneath the rising bubble occurs. We attribute these observations to the loss of symmetry in the channel gap, due to cell inclination. Nonetheless, the top lubrication film is observed to follow the Bretherton scaling, namely, $(ηv_b/σ)^{2/3}$, where $σ$ is the liquid surface tension while the bottom film does not exhibit such a scaling. Finally, we illustrate that a model incorporating a friction term to the power balance between buoyancy and viscous dissipation matches well with all experimental data.