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 the flow of water toward growing ice crystals that feeds their growth. The freezing of this additional water can cause a large buildup of stress. Here, we demonstrate a technique for characterizing this stress buildup with unprecedented spatial resolution. We create a stable ice–water interface in a controlled temperature gradient and measure the deformation of the confining boundary. Analysis of the deformation field reveals stresses applied to the boundary with O (micrometers) spatial 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. Importantly, we find a strong localization of stresses, which significantly increases the likelihood of damage caused by the presence of ice, even in apparently benign freezing situations. Ultimately, the limiting stress that the ice exerts is proportional to the local undercooling, in accordance with the Clapeyron equation, which describes the equilibrium between a stressed solid and its melt. Our results are closely connected to the condensation pressure during liquid–liquid phase separation and the crystallization pressure for growing crystals. Thus, they are highly relevant in fields ranging from cryopreservation and frost heave to food science, rock weathering, and art conservation.
A quantitative analysis of the viral transmission risk in public spaces al- lows us to identify the dominant mechanisms that a proactive public health policy can act upon to reduce risk, and to evaluate the reduction of risk that can be obtained. The contribution of public spaces to the propa- gation of SARS-CoV-2 can be reduced to a level necessary for a declining epidemic, i.e. an overall reproduction rate below one. Here, we revisit the quantitative assessment of indoor and outdoor transmission risk. We show that the long-range aerosol transmission is controlled by the flow rate of fresh air and by the mask filtering quality, and is quantitatively re- lated to the CO2 concentration, regardless the room volume and the num- ber of people. The short-range airborne transmission is investigated ex- perimentally using dedicated dispersion experiments performed in two shopping malls. Exhaled aerosols are dispersed by turbulent draughts in a cone, leading to a concentration inversely proportional to the squared dis- tance and to the flow velocity. We show that the average infection dose, called the viral quantum, can be determined from epidemiological data in a manner consistent with biological experimental data. Practical implications. The results provide quantitative guidance useful for making rational public health policy decisions to prevent the dominant routes of viral transmission through reinforced ventilation, air purification, mechanical dispersion using fans, and incentivizing the wear- ing of correctly fitted, quality facial masks (surgical masks, possibly cov- ered by another fabric mask, or non-medical FFP2 masks). Taken to- gether, such measures significantly reduce the airborne transmission risk of SARS-CoV-2.
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