Diamond ascent by rift-driven disruption of cratonic mantle keels

Diamonds are erupted at Earth’s surface in volatile-rich magmas called kimberlites1,2,3. These enigmatic magmas, originating from depths exceeding 150 kilometres in Earth’s mantle1, occur in stable cratons and in pulses broadly synchronous with supercontinent cyclicity4. Whether their mobilization is driven by mantle plumes5 or mechanical weakening of cratonic lithosphere4,6 remains unclear. Here we show that most kimberlites spanning the past billion years erupted approximately 25 million years after the onset of continental fragmentation, suggesting an association with rifting processes. Our dynamic models show that physically steep lithosphere-asthenosphere boundaries formed during terminal rifting (necking) generate convective instabilities in the asthenosphere that slowly migrate many hundreds of kilometres inboard of the rift, causing destabilization of cratonic mantle keel tens of kilometres thick. Displaced lithosphere is replaced by hot, upwelling asthenosphere in the return flow, causing partial melting of carbonated mantle and variable assimilation of lithospheric material. The resulting small-volume kimberlite magmas ascend rapidly and adiabatically, exsolving amounts of carbon dioxide (CO2) that are consistent with independent constraints7. Our model reconciles diagnostic kimberlite features including association with cratons and geochemical characteristics that implicate a common asthenospheric mantle source contaminated by cratonic lithosphere8. Together, these results provide a quantitative and mechanistic link between kimberlite episodicity and supercontinent cycles via progressive disruption of cratonic keels.

Critical Solutal Marangoni Number Correlation for Short-Scale Convective Instabilities in Drying Poly(vinyl acetate)-Methanol Thin Films

A new empiric correlation for the critical solutal Marangoni number as function of the Péclet and Schmidt numbers is proposed. It is based on previously published experimental flow field data in drying poly(vinyl acetate)-methanol films with an initial thickness in the range of – and an initial solvent load of to , as well as newly derived concentration profile measurements and 1D drying simulations. The analysis accounts for realistic transient material properties and describes the occurrence of short-scale convective Marangoni (in)stabilities during the entire drying process with an accuracy of 9%. In addition, the proposed correlation qualitatively follows trends known from theory. As convective Marangoni instabilities in drying polymer films may induce surface deformations, which persist in the dry film, the correlation may facilitate future process design for either thin films with uniform thickness or deliberate self-assembly.

Control of stationary convective instabilities in the rotating disk boundary layer via time-periodic modulation

The control of stationary convective instabilities in the rotating disk boundary layer via a time-periodic modulation of the disk rotation rate is investigated. The configuration provides an archetypal example of a three-dimensional temporally periodic boundary layer, encompassing both the von Kármán and Stokes boundary layers. A velocity–vorticity formulation of the governing perturbation equations is deployed, together with a numerical procedure that utilises the Chebyshev-tau method. Floquet theory is used to determine the linear stability properties of these time-periodic flows. The addition of a time-periodic modulation to the otherwise steady disk rotation rate establishes a stabilising effect. In particular, for a broad range of modulation frequencies, the growth of the stationary convective instabilities is suppressed and the critical Reynolds number for the onset of both the cross-flow and Coriolis instabilities is raised to larger values than that found for the steady disk without modulation. An energy analysis is undertaken, where it is demonstrated that time-periodic modulation induces a reduction in the Reynolds stress energy production and an increase in the viscous dissipation across the boundary layer. Comparisons are made with other control techniques, including distributed surface roughness and compliant walls.

Evolution of Surface Morphology of Spin-Coated Poly(methyl methacrylate) Thin Films

The morphology of sub-micron poly(methyl methacrylate) films coated to glass supports by spin coating from toluene is examined using surface profilometry. Wrinkled surfaces with local quasi-sinusoidal periodicity were seen on the surfaces of films with thicknesses of larger than 75 nm. The surface wrinkles had large aspect ratios with wavelengths in the tens of microns and amplitudes in the tens of nanometers. Wrinkles that formed during spin-coating are attributed to surface perturbations caused by Rayleigh–Bénard–Marangoni convective instabilities. The effects of film thickness, coating solution concentration, and drying rate on the thin film surface morphology are investigated. The results can be used to prepare surfaces with controlled morphology, either smooth or with periodic wrinkles.

Numerical Computation of Instabilities and Internal Waves from In Situ Measurements via the Viscous Taylor–Goldstein Problem

We explore numerical methods for the stability analysis of stratified, parallel shear flows considering the effects of small-scale turbulence represented by eddy viscosity and diffusivity. The result is an extension of the classical Taylor–Goldstein problem applicable to oceanic and atmospheric flows. Solutions with imaginary frequency describe shear and convective instabilities, whereas those with real frequency represent internal gravity waves. Application to large observational datasets can involve considerable computation and therefore requires a compromise between speed and accuracy. We compare several numerical methods to identify optimal approaches to various problems.