Marangoni plumes in miscible spreading

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 (l(p)), radial velocities (U-p), and mean azimuthal spacings (lambda(p)). We show through a model that a balance between the surface tension force across l(p) and the viscous resistance in an underlying boundary layer results in lp similar to root l(sigma mu)delta(bl), where l sigma mu is a Marangoni length scale and delta(bl) is the boundary layer thickness. The model also predicts that Up similar to root U sigma 3/U nu, where U sigma is a velocity scale balancing inertia and surface tension and U nu=delta bl/t is the velocity scale of momentum diffusion. These predictions are shown to be in agreement with our experimentally observed variations of l(p) and U-p. The observed variation of lambda(p), which we show not to match the predictions of any of the available instability theories, is shown to scale as lambda p similar to rfOhd2/3/(xi 1/3 chi 3), where Oh(d) is the drop Ohnesorge number, r(f) is the film radius, and xi and chi are the viscosity and the density ratios.