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.

Automated summary

We studied the formation of surface tension driven plumes at the periphery of expanding ethanol-water films. Measurements were conducted on the lengths, radial velocities, and azimuthal spacings of the plumes, which were found to agree with the predictions of a model based on the balance of surface tension force and viscous resistance. The observed variation in the azimuthal spacing did not match existing instability theories.