Earth’s carbon deficit caused by early loss through irreversible sublimation

Carbon is an essential element for life, but its behavior during Earth’s accretion is not well understood. Carbonaceous grains in meteoritic and cometary materials suggest that irreversible sublimation, and not condensation, governs carbon acquisition by terrestrial worlds. Through astronomical observations and modeling, we show that the sublimation front of carbon carriers in the solar nebula, or the soot line, moved inward quickly so that carbon-rich ingredients would be available for accretion at 1 astronomical unit after the first million years. On the other hand, geological constraints firmly establish a severe carbon deficit in Earth, requiring the destruction of inherited carbonaceous organics in the majority of its building blocks. The carbon-poor nature of Earth thus implies carbon loss in its precursor material through sublimation within the first million years.

Freeze-Drying with Structured Sublimation Fronts—Visualization with Neutron Imaging

The particular structure of the sublimation front in vacuum freeze-drying of porous media is, in most situations, not accessible at the pore scale. The classical measurement techniques access the process only globally. Knowledge about the structure of the front, however, is necessary for prescriptive analysis of freeze-drying, as it dictates not only drying velocity, drying time, and overall energy consumption, but also the material properties after drying. This is especially relevant in situations in which the freeze-drying process is carried out close to the collapse temperature of the product. We, therefore, study the sublimation of ice with neutron tomography and analyze the spatial formation of the dry space using the example of frozen cylindrical maltodextrin with drying parameters at the limit of material collapse. We show that the sublimation front forms unique fractal structures that differ strongly from the usual form of a flat front. Distinct dry fingers covering the sample, in addition to a fractal peripheral sublimation front, were observed. The findings are important for the understanding of freeze-drying processes and will serve as a basis for the development of microscale models of freeze-drying.

Planet formation and migration near the silicate sublimation front in protoplanetary disks

Context. The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. Planet formation and migration depend heavily on the structure and dynamics of protoplanetary disks. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. Aims. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. We are especially interested in determining the positions where the drift of pebbles would be stopped, and where the migration of Earth-like planets and super-Earths would be halted. Methods. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. Results. Our results show the temperature and density structure of a gas and dust disk around a young Sun-like star. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Conclusions. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.

Pore network model of primary freeze drying

The pore scale progression of the sublimation front during primary freeze drying depends on the local vapor transport and the local heat transfer as well. If the pore space is size distributed, vapor and heat transfer may spatially vary. Beyond that, the pore size distribution can substantially affect the physics of the transport mechanisms if they occur in a transitional regime. Exemplarily, if the critical mean free path is locally exceeded, the vapor transport regime passes from viscous flow to Knudsen diffusion. At the same time, the heat transfer is affected by the local ratio of pore space to the solid skeleton. The impact of the pore size distribution on the transitional vapor and heat transfer can be studied by pore scale models such as the pore network model. As a first approach, we present a pore network model with vapor transport in the transitional regime between Knudsen diffusion and viscous flow at constant temperature in the dry region. We demonstrate the impact of pore size distribution, temperature and pressure on the vapor transport regimes. Then we study on the example of a 2D square lattice, how the presence of micro and macro pores affects the macroscopic progression of the sublimation front. Keywords: pore size distribution; transitional vapor transport; pore network model; fractured sublimation front.