Steady shape of a miscible bubble rising below an inclined wall at low Reynolds numbers

When a buoyant volume of fluid impinges a horizontal boundary, it spreads symmetrically in the Stokes flow limit. We investigate the low Reynolds number spreading of a low-viscosity volume of fluid, hereafter called a “bubble”, in the limit that the fluids are miscible and interfacial tension can be neglected; the symmetry of the bubble's spreading is broken by allowing the surface to have a finite slope. We use laboratory experiments, parametrized boundary integral numerical calculations, and a scaling argument to show that there exists a steady bubble shape with an aspect ratio (ratio of the semi-axes of the bubble in the horizontal plane) around 1.4–1.6 for slope angles ranging from 5 to 35°. The existence of a steady shape, together with a rapid shift in aspect ratio as the slope angle ϕ   increases from 0, suggests a continuous phase transition caused by a loss of symmetry when the finite slope is introduced. We show that the time required for the bubble to reach this steady shape and the constant aspect ratio over the range 10<ϕ<3510<ϕ<35 support the analogy to a phase transition.