Low-temperature thermochronology and thermokinematic modeling of deformation, exhumation, and development of topography in the central Southern Alps, New Zealand

Apatite and zircon (U-Th)/He and fission track ages were obtained from ridge transects across the central Southern Alps, New Zealand. Interpretation of local profiles is difficult because relationships between ages and topography or local faults are complex and the data contain large uncertainties, with poor reproducibility between sample duplicates. Data do form regional patterns, however, consistent with theoretical systematics and corroborating previous observations: young Neogene ages occur immediately southeast of the Alpine Fault (the main plate boundary structure on which rocks are exhumed); partially reset ages occur in the central Southern Alps; and older Mesozoic ages occur further toward the southeast. Zircon apparent ages are older than apatite apparent ages for the equivalent method. Three-dimensional thermokinematic modeling of plate convergence incorporates advection of the upper Pacific plate along a low-angle detachment then up an Alpine Fault ramp, adopting a generally accepted tectonic scenario for the Southern Alps. The modeling incorporates heat flow, evolving topography, and the detailed kinetics of different thermochronometric systems and explains both complex local variations and regional patterns. Inclusion of the effects of radiation damage on He diffusion in detrital apatite is shown to have dramatic effects on results. Geometric and velocity parameters are tuned to fit model ages to observed data. Best fit is achieved at 9 mm a−1 plate convergence, with Pacific plate delamination on a gentle 10°SE dipping detachment and more rapid uplift on a 45–60° dipping Alpine Fault ramp from 15 km depth. Thermokinematic modeling suggests dip-slip motion on reverse faults within the Southern Alps should be highest ∼22 km from the Alpine Fault and much lower toward the southeast

Deformation of a free interface pierced by a tilted cylinder

We investigate the interaction between an infinite cylinder and a free fluid-fluid interface governed only by its surface tension. We study the deformation of an initially flat interface when it is deformed by the presence of a cylindrical object, tilted at an arbitrary angle, that the interface "totally wets". Our simulations predict all significant quantities such as the interface shape, the position of the contact line, and the force exerted by the interface on the cylinder. These results are compared with an experimental study of the penetration of a soap film by a cylindrical liquid jet. This dynamic situation exhibits all the characteristics of a totally wetting interface. We show that whatever the inclination, the force is always perpendicular to the plane of the interface, and its amplitude diverges as the inclination angle increases. Such results should bring new insights in both fluid and solid mechanics, from animal locomotion to surface micro-processing.-processing.Comment: 6 pages, 5 figure

When is a surface foam-phobic or foam-philic?

By integrating the Young-Laplace equation, including the effects of gravity, we have calculated the equilibrium shape of the two-dimensional Plateau borders along which a vertical soap film contacts two flat, horizontal solid substrates of given wettability. We show that the Plateau borders, where most of a foam's liquid resides, can only exist if the values of the Bond number ${\rm Bo}$ and of the liquid contact angle $\theta_c$ lie within certain domains in $(\theta_c,{\rm Bo})$ space: under these conditions the substrate is foam-philic. For values outside these domains, the substrate cannot support a soap film and is foam-phobic. In other words, on a substrate of a given wettability, only Plateau borders of a certain range of sizes can form. For given $(\theta_c,{\rm Bo})$, the top Plateau border can never have greater width or cross-sectional area than the bottom one. Moreover, the top Plateau border cannot exist in a steady state for contact angles above 90$^\circ$. Our conclusions are validated by comparison with both experimental and numerical (Surface Evolver) data. We conjecture that these results will hold, with slight modifications, for non-planar soap films and bubbles. Our results are also relevant to the motion of bubbles and foams in channels, where the friction force of the substrate on the Plateau borders plays an important role.Comment: 20 pages, 14 figure

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased

Topological and geometrical disorder correlate robustly in two-dimensional foams

A 2D foam can be characterised by its distribution of bubble areas, and of number of sides. Both distributions have an average and a width (standard deviation). There are therefore at least two very different ways to characterise the disorder. The former is a geometrical measurement, while the latter is purely topological. We discuss the common points and differences between both quantities. We measure them in a foam which is sheared, so that bubbles move past each other and the foam is "shuffled" (a notion we discuss). Both quantities are strongly correlated; in this case (only) it thus becomes sufficient to use either one or the other to characterize the foam disorder. We suggest applications to the analysis of other systems, including biological tissues