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Rain drops form in clouds by collision of submillimetric droplets falling under gravity: larger drops fall faster than smaller ones and collect them on their path. The puzzling stability of fogs and non-precipitating warm clouds with respect to this avalanching mechanism has been a longstanding problem. How to explain that droplets of diameter around $10~{\rm \mu m}$ have a low probability of collision, inhibiting the cascade towards larger and larger drops? Here we review the dynamical mechanisms that have been proposed in the literature and quantitatively investigate the frequency of drop collisions induced by Brownian diffusion, electrostatics and gravity, using an open-source Monte-Carlo code that takes all of them into account. Inertia dominates over aerodynamic forces for large drops, when the Stokes number is larger than $1$. Thermal diffusion dominates over aerodynamic forces for small drops, when the P\'eclet number is smaller than $1$. We show that there exists a range of size (typically $1-10~{\rm \mu m}$ for water drops in air) for which neither inertia nor Brownian diffusion are significant, leading to a gap in the collision rate. The effect is particularly important, due to the lubrication film forming between the drops immediately before collision, and secondarily to the long-range aerodynamic interaction. Two different mechanisms regularise the divergence of the lubrication force at vanishing gap: the transition to a noncontinuum regime in the lubrication film, when the gap is comparable to the mean free path of air, and the induction of a flow inside the drops due to shear at their surfaces. In the gap between inertia-dominated and diffusion-dominated regimes, dipole-dipole electrostatic interactions becomes the major effect controlling the efficiency of drop collisions., Comment: 21 pages, 13 figures. Code available at https://gitlab.com/fpoydenot/dropletmicrophysics

The COVID-19 pandemic has given rise to numerous articles from different scientific fields (epidemiology, virology, immunology, airflow physics...) without any effort to link these different insights. In this review, we aim to establish relationships between epidemiological data and the characteristics of the virus strain responsible for the epidemic wave concerned. We have carried out this study on the Wuhan, Alpha, Delta and Omicron strains allowing us to illustrate the evolution of the relationships we have highlighted according to these different viral strains. We addressed the following questions: 1) How can the mean infectious dose (one quantum, by definition in epidemiology) be measured and expressed as an amount of viral RNA molecules (in genome units, GU) or as a number of replicative viral particles (in plaque-forming units, PFU)? 2) How many infectious quanta are exhaled by an infected person per unit of time? 3) How many infectious quanta are exhaled, on average, integrated over the whole contagious period? 4) How do these quantities relate to the epidemic reproduction rate R as measured in epidemiology, and to the viral load, as measured by molecular biological methods? 5) How has the infectious dose evolved with the different strains of SARS-CoV-2? We make use of state-of-the-art modelling, reviewed and explained in the appendix of the article (Supplemental Information, SI), to answer these questions using data from the literature in both epidemiology and virology. We have considered the modification of these relationships according to the vaccination status of the population. We hope that this work will allow a better integration of data from different fields (virology, epidemiology, and immunology) to anticipate the evolution of the epidemic in the case of COVID-19, but also in respiratory pathologies transmissible in an airborne manner., Comment: 26 pages, 5 figures; submitted to Biochimie

The pioneering work of G.I. Taylor on the turbulent dispersion of aerosols is exactly one century old and provides an original way of introducing both diffusive processes and turbulence at an undergraduate level. Light enough particles transported by a turbulent flow exhibit a Brownian-like motion over time scales larger than the velocity correlation time. Aerosols are therefore subjected to an effective turbulent diffusion at large length scales. However, the case of a source of pollutant much smaller than the integral scale is not completely understood. Here, we present experimental results obtained by undergraduate students in the context of the COVID-19 pandemic. The dispersion of a smoke of oil droplets by a turbulent flow is studied in a wind tunnel designed for pedagogical purposes. It shows a ballistic-like regime at short distance, followed by Taylor's diffusive-like regime, suggesting that the continuous cascade is bypassed. Accordingly, measurements show that the CO$_2$ concentration emitted when breathing typically decays as the inverse squared distance to the mouth, which is not the law expected for a diffusion. The experiment offers the possibility for students to understand the role of fluctuations in diffusive processes and in turbulence. The non-linear diffusive equations governing aerosol dispersion, based on a single correlation time, allow us to model the airborne transmission risk of pathogens, indoors and outdoors. We discuss the pedagogical interest of making students work on applied scientific problems, as the results obtained in this study have been used to provide public health policy recommendations to prevent transmission in French shopping malls., Comment: 23 pages, 7 figures; submitted to the American Journal of Physics

When materials freeze, they often undergo damage due to ice growth. Although this damage is commonly ascribed to the volumetric expansion of water upon freezing, it is usually driven by suction of water towards growing ice crystals. The freezing of this additional water can cause a large build up of stress. Here, we study this process by producing a stable ice/water interface in a controlled temperature gradient, and measuring the deformation of the confining boundary. Analysis of the deformation field reveals stresses applied to the boundary with $\mathcal{O}(\mu\mathrm{m})$ resolution. Globally, stresses increase steadily over time as liquid water is transported to more deeply undercooled regions. Locally, stresses increase until ice growth is stalled by the confining stresses. In accordance with the Clapeyron equation, the local limiting stress is proportional to the local undercooling. These results are closely connected to the crystallization pressure for growing crystals and condensation pressure during liquid-liquid phase separation.

Preventive measures to reduce infection are needed to combat the COVID-19 pandemic and prepare for a possible endemic phase. Current prophylactic vaccines are highly effective to prevent disease but lose their ability to reduce viral transmission as viral evolution leads to increasing immune escape. Long term proactive public health policies must therefore complement vaccination with available nonpharmaceutical interventions (NPI) aiming to reduce the viral transmission risk in public spaces. Here, we revisit the quantitative assessment of airborne transmission risk, considering asymptotic limits that considerably simplify its expression. We show that the aerosol transmission risk is the product of three factors: a biological factor that depends on the viral strain, a hydrodynamical factor defined as the ratio of concentration in viral particles between inhaled and exhaled air, and a face mask filtering factor. The short range contribution to the risk, both present indoors and outdoors, is related to the turbulent dispersion of exhaled aerosols by air drafts and by convection (indoor), or by the wind (outdoors). We show experimentally that airborne droplets and CO$_2$ molecules present the same dispersion. As a consequence, the dilution factor, and therefore the risk, can be measured quantitatively using the CO$_2$ concentration, regardless of the room volume, the flow rate of fresh air and the occupancy. We show that the dispersion cone leads to a concentration in viral particles, and therefore a short range transmission risk, inversely proportional to the squared distance to an infected person and to the flow velocity. The aerosolization criterion derived as an intermediate result, which compares the Stokes relaxation time to the Lagrangian time scale, may find application for a broad class of aerosol-borne pathogens and pollutants., Comment: 12 pages, 4 figures; updated manuscript

We report on the structural and magnetic properties of thin Ge(1-x)Mn(x)films grown by molecular beam epitaxy (MBE) on Ge(001) substrates at temperatures (Tg) ranging from 80deg C to 200deg C, with average Mn contents between 1 % and 11 %. Their crystalline structure, morphology and composition have been investigated by transmission electron microscopy (TEM), electron energy loss spectroscopy and x-ray diffraction. In the whole range of growth temperatures and Mn concentrations, we observed the formation of manganese rich nanostructures embedded in a nearly pure germanium matrix. Growth temperature mostly determines the structural properties of Mn-rich nanostructures. For low growth temperatures (below 120deg C), we evidenced a two-dimensional spinodal decomposition resulting in the formation of vertical one-dimensional nanostructures (nanocolumns). Moreover we show in this paper the influence of growth parameters (Tg and Mn content) on this decomposition i.e. on nanocolumns size and density. For temperatures higher than 180deg C, we observed the formation of Ge3Mn5 clusters. For intermediate growth temperatures nanocolumns and nanoclusters coexist. Combining high resolution TEM and superconducting quantum interference device magnetometry, we could evidence at least four different magnetic phases in Ge(1-x)Mn(x) films: (i) paramagnetic diluted Mn atoms in the germanium matrix, (ii) superparamagnetic and ferromagnetic low-Tc nanocolumns (120 K < Tc < 170 K), (iii) high-Tc nanocolumns (Tc> 400 K) and (iv) Ge3Mn5 clusters., Comment: 10 pages 2 colonnes revTex formatted