Generation of Fermat's spiral patterns by solutal Marangoni-driven coiling in an aqueous two-phase system.

The solutal Marangoni effect is attracting increasing interest because of its fundamental role in many isothermal directional transport processes in fluids, including the Marangoni-driven spreading on liquid surfaces or Marangoni convection within a liquid. Here we report a type of continuous Marangoni transport process resulting from Marangoni-driven spreading and Marangoni convection in an aqueous two-phase system. The interaction between a salt (CaCl) and an anionic surfactant (sodium dodecylbenzenesulfonate) generates surface tension gradients, which drive the transport process.

Plume-ridge interaction induced migration of the Hawaiian-Emperor seamounts.

The history of the Hawaiian hotspot is of enduring interest in studies of plate motion and mantle flow, and has been investigated by many researchers using the detailed history of the Hawaiian-Emperor Seamount chain. One of the unexplained aspects of this history is the apparent offset of several Emperor seamounts from the Hawaii plume track. Here we show that the volcanic migration rates of the Emperor seamounts based on existing data are inconsistent with the drifting rate of the Pacific plate, and indicate northward and then southward "absolute movements" of the seamounts.

Steady and Unsteady Buckling of Viscous Capillary Jets and Liquid Bridges.

Steady buckling (coiling) of thin falling liquid jets is sensitive to surface tension, yet an understanding of these capillary effects lags far behind what is known about surface-tension-free coiling. In experiments with submillimetric jets and ultralow flow rates, we find that the critical dispensing height H_{c} for coiling decreases with increasing flow rate, a trend opposite to that found previously for inertia-free coiling. We resolve the apparent contradiction using nonlinear numerical simulations based on slender-jet theory which show that the trend reversal is due to the strong effect of surface tension in our experiments.

Liquid ropes: a geometrical model for thin viscous jet instabilities.

Thin, viscous fluid threads falling onto a moving belt behave in a way reminiscent of a sewing machine, generating a rich variety of periodic stitchlike patterns including meanders, W patterns, alternating loops, and translated coiling. These patterns form to accommodate the difference between the belt speed and the terminal velocity at which the falling thread strikes the belt. Using direct numerical simulations, we show that inertia is not required to produce the aforementioned patterns.

Pattern formation in a thread falling onto a moving belt: an "elastic sewing machine".

We study the dynamics of instability and pattern formation in a slender elastic thread that is continuously fed onto a surface moving at constant speed V in its own plane. As V is decreased below a critical value V(c), the steady "dragged catenary" configuration of the thread becomes unstable to sinusoidal meanders and thence to a variety of more complex patterns including biperiodic meanders, figures of 8, "W," "two-by-one," and "two-by-two" patterns, and double coiling. Laboratory experiments are performed to determine the phase diagram of these patterns as a function of V, the thread feeding speed U, and the fall height H.

Meandering instability of a viscous thread.

A viscous thread falling from a nozzle onto a surface exhibits the famous rope-coiling effect, in which the thread buckles to form loops. If the surface is replaced by a belt moving with speed U , the rotational symmetry of the buckling instability is broken and a wealth of interesting states are observed [see S. Chiu-Webster and J.

Dynamics of liquid rope coiling.

We present a combined experimental and numerical investigation of the coiling of a liquid "rope" falling on a solid surface, focusing on three little-explored aspects of the phenomenon: The time dependence of "inertio-gravitational" coiling, the systematic dependence of the radii of the coil and the rope on the experimental parameters, and the "secondary buckling" of the columnar structure generated by high-frequency coiling. Inertio-gravitational coiling is characterized by oscillations between states with different frequencies, and we present experimental observations of four distinct branches of such states in the frequency-fall height space. The transitions between coexisting states have no characteristic period, may take place with or without a change in the sense of rotation, and usually (but not always) occur via an intermediate "figure of eight" state.

Insights into the dynamics of mantle plumes from uranium-series geochemistry.

The long-standing paradigm that hotspot volcanoes such as Hawaii or Iceland represent the surface expression of mantle plumes--hot, buoyant upwelling regions beneath the Earth's lithosphere--has recently been the focus of controversy. Whether mantle plumes exist or not is pivotal for our understanding of the thermal, dynamic and compositional evolution of the Earth's mantle. Here we show that uranium-series disequilibria measured in hotspot lavas indicate that hotspots are indeed associated with hot and buoyant upwellings and that weaker (low buoyancy flux) hotspots such as Iceland and the Azores are characterized by lower excess temperatures than stronger hotspots such as Hawaii.

Periodic folding of viscous sheets.

The periodic folding of a sheet of viscous fluid falling upon a rigid surface is a common fluid mechanical instability that occurs in contexts ranging from food processing to geophysics. Asymptotic thin-layer equations for the combined stretching-bending deformation of a two-dimensional sheet are solved numerically to determine the folding frequency as a function of the sheet's initial thickness, the pouring speed, the height of fall, and the fluid properties. As the buoyancy increases, the system bifurcates from "forced" folding driven kinematically by fluid extrusion to "free" folding in which viscous resistance to bending is balanced by buoyancy.