Driven Cavity Flows in Soap Bubbles: An Illustration of the Spherical Dirichlet Problem

There are few physical objects as beautiful and fascinating as soap bubbles. They exhibit a perfection of geometrical form and an appealing simplicity. Soap bubbles are characterized by the structure of their thin liquid shell of low surface tension. It is well known that the dynamics of the surface of soap bubbles are the resultant of both 1) liquid film thinning under the influence of gravity and 2) the presence of local surface tension gradients which create complex flows (Marangoni flows). In turn, the net motion of the thin liquid shell induces the displacement of gas inside the cavity due to the noslip boundary condition which holds at the liquid-gas interface. Both flows on the liquid shell and within the cavity are incompressible, ∇·u = 0. Moreover, for small soap bubble sizes, O(< 10 m), flows are viscosity dominated and characterized by low-Reynolds numbers (typically Re=O(< 1)). While soap bubbles exhibit intrinsic internal flows [1], thermally-induced Marangoni flows in the liquid film may lead to steady-state forced recirculation inside the cavity. Experimentally, this may be achieved by applying a thermal gradient in the vicinity of the liquid shell, which produces a fixed shear stress at the liquid surface given by τ = ∇σ = (∂σ/∂T )∇T , where σ is the surface tension, and T the temperature. In the present discussion, we will show experimental flow visualizations of the boundary-driven cavity flows inside soap bubbles (Fig. 1), which may be controlled by such thermal forcing schemes. Variations in the number and location of heat sources applied near the liquid shell effectively yield different internal flow topologies.