Marangoni plumes in miscible spreading

Abstract

We present a study of novel, surface tension driven plumes that form at the periphery of fast expanding, circular ethanol-water films that emanate from millimeter sized ethanol-water drops floating at the surface of a deep water layer. Visualizing these plumes that are azimuthally uniformly spaced, using floating particles, we measure their lengths (lp), radial velocities (Up), and mean azimuthal spacings (λp). We show through a model that a balance between the surface tension force across lp and the viscous resistance in an underlying boundary layer results in l p ∼ l σ μ δ b l, where l σ μ is a Marangoni length scale and δbl is the boundary layer thickness. The model also predicts that U p ∼ U σ 3 / U ν, where U σ is a velocity scale balancing inertia and surface tension and U ν = δ b l / t is the velocity scale of momentum diffusion. These predictions are shown to be in agreement with our experimentally observed variations of lp and Up. The observed variation of λp, which we show not to match the predictions of any of the available instability theories, is shown to scale as λ p ∼ r f O h d 2 / 3 / (ζ 1 / 3 χ 3), where Ohd is the drop Ohnesorge number, rf is the film radius, and ζ and χ are the viscosity and the density ratios.