Unsteady fragmentation of a fluid bulk into droplets is important for epidemiology as it governs the transport of pathogens from sneezes and coughs, or from contaminated crops in agriculture. It is also ubiquitous in industrial processes such as paint, coating, and combustion. Unsteady fragmentation is distinct from steady fragmentation on which most theoretical efforts have been focused thus far. We address this gap by studying a canonical unsteady fragmentation process: the breakup from a drop impact on a finite surface where the drop fluid is transferred to a free expanding sheet of time-varying properties and bounded by a rim of time-varying thickness. The continuous rim destabilization selects the final spray droplets, yet this process remains poorly understood. We combine theory with advanced image analysis to study the unsteady rim destabilization. We show that, at all times, the rim thickness is governed by a local instantaneous Bond number equal to unity, defined with the instantaneous, local, unsteady rim acceleration. This criterion is found to be robust and universal for a family of unsteady inviscid fluid sheet fragmentation phenomena, from impacts of drops on various surface geometries to impacts on films. We discuss under which viscous and viscoelastic conditions the criterion continues to govern the unsteady rim thickness.

Since the first recording of what we now call Covid-19 infection in Wuhan, Hubei province, China on Dec 31, 2019, the disease has spread worldwide and met with a wide variety of social distancing and quarantine policies. The effectiveness of these responses is notoriously difficult to quantify as individuals travel, violate policies deliberately or inadvertently, and infect others without themselves being detected. Moreover, the publicly available data on infection rates are themselves unreliable due to limited testing and even possibly under-reporting. In this paper, we attempt to interpret and extrapolate from publicly available data using a mixed first-principles epidemiological equations and data-driven neural network model. Leveraging our neural network augmented model, we focus our analysis on four locales: Wuhan, Italy, South Korea and the United States of America, and compare the role played by the quarantine and isolation measures in each of these countries in controlling the effective reproduction number Rt of the virus. Our results unequivocally indicate that the countries in which rapid government interventions and strict public health measures for quarantine and isolation were implemented were successful in halting the spread of infection and prevent it from exploding exponentially. In the case of Wuhan especially, where the available data were earliest available, we have been able to test the predicting ability of our model by training it from data in the January 24 till March 3 window, and then matching the predictions up to April 1. Even for Italy and South Korea, we have a buffer window of one week (25 March - 1 April) to validate the predictions of our model. In the case of the US, our model captures well the current infected curve growth and predicts a halting of infection spread by 20 April 2020. We further demonstrate that relaxing or reversing quarantine measures right now will lead to an exponential explosion in the infected case count, thus nullifying the role played by all measures implemented in the US since mid March 2020.

We have developed a globally applicable diagnostic COVID-19 model by augmenting the classical SIR epidemiological model with a neural network module. Our model does not rely upon previous epidemics like SARS/MERS and all parameters are optimized via machine learning algorithms used on publicly available COVID-19 data. The model decomposes the contributions to the infection time series to analyze and compare the role of quarantine control policies used in highly affected regions of Europe, North America, South America, and Asia in controlling the spread of the virus. For all continents considered, our results show a generally strong correlation between strengthening of the quarantine controls as learnt by the model and actions taken by the regions' respective governments. In addition, we have hosted our quarantine diagnosis results for the top 70 affected countries worldwide, on a public platform.

How do fine modifications to social distancing measures really affect COVID-19 spread? A major problem for health authorities is that we do not know. In an imaginary world, we might develop a harmless biological virus that spreads just like COVID-19, but is traceable via a cheap and reliable diagnosis. By introducing such an imaginary virus into the population and observing how it spreads, we would have a way of learning about COVID-19 because the benign virus would respond to population behaviour and social distancing measures in a similar manner. Such a benign biological virus does not exist. Instead, we propose a safe and privacy-preserving digital alternative. Our solution is to mimic the benign virus by passing virtual tokens between electronic devices when they move into close proximity. As Bluetooth transmission is the most likely method used for such inter-device communication, and as our suggested "virtual viruses" do not harm individuals' software or intrude on privacy, we call these Safe Blues. In contrast to many app-based methods that inform individuals or governments about actual COVID-19 patients or hazards, Safe Blues does not provide information about individuals' locations or contacts. Hence the privacy concerns associated with Safe Blues are much lower than other methods. However, from the point of view of data collection, Safe Blues has two major advantages: - Data about the spread of Safe Blues is uploaded to a central server in real time, which can give authorities a more up-to-date picture in comparison to actual COVID-19 data, which is only available retrospectively. - Sampling of Safe Blues data is not biased by being applied only to people who have shown symptoms or who have come into contact with known positive cases. These features mean that there would be real statistical value in introducing Safe Blues. In the medium term and end game of COVID-19, information from Safe Blues could aid health authorities to make informed decisions with respect to social distancing and other measures. In this paper we outline the general principles of Safe Blues and we illustrate how Safe Blues data together with neural networks may be used to infer characteristics of the progress of the COVID-19 pandemic in real time. Further information is on the Safe Blues website: https://safeblues.org/.

We study the spreading of a film from ethanol–water droplets of radii $0.9~\text{mm}<r_{d}<1.1~\text{mm}$ on the surface of a deep water layer for various concentrations of ethanol in the drop. Since the drop is lighter ($\unicode[STIX]{x1D709}=\unicode[STIX]{x1D70C}_{l}/\unicode[STIX]{x1D70C}_{d}>1.03$), it stays at the surface of the water layer during the spreading of the film from the drop; the film is more viscous than the underlying water layer since $\unicode[STIX]{x1D712}=\unicode[STIX]{x1D707}_{l}/\unicode[STIX]{x1D707}_{d}>0.38$. Inertial forces are not dominant in the spreading since the Reynolds numbers based on the film thickness $h_{f}$ are in the range $0.02<Re_{f}<1.4$. The spreading is surface-tension-driven since the film capillary numbers are in the range $0.0005<Ca_{f}<0.0069$ and the drop Bond numbers are in the range $0.19<Bo_{d}<0.56$. We observe that, when the drop is brought in contact with the water surface, capillary waves propagate from the point of contact, followed by a radially expanding, thin circular film of ethanol–water mixture. The film develops instabilities at some radius to form outward-moving fingers at its periphery while it is still expanding, till the expansion stops at a larger radius. The film then retracts, during which time the remaining major part of the drop, which stays at the centre of the expanding film, thins and develops holes and eventually mixes completely with water. The radius of the expanding front of the film scales as $r_{f}\sim t^{1/4}$ and shows a dependence on the concentration of ethanol in the drop as well as on $r_{d}$, and is independent of the layer height $h_{l}$. Using a balance of surface tension and viscous forces within the film, along with a model for the fraction of the drop that forms the thin film, we obtain an expression for the dimensionless film radius $r_{f}^{\ast }=r_{f}/r_{d}$, in the form $fr_{f}^{\ast }={t_{\unicode[STIX]{x1D707}d}^{\ast }}^{1/4}$, where $t_{\unicode[STIX]{x1D707}d}^{\ast }=t/t_{\unicode[STIX]{x1D707}d}$, with the time scale $t_{\unicode[STIX]{x1D707}d}=\unicode[STIX]{x1D707}_{d}r_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ and $f$ is a function of $Bo_{d}$. Similarly, we show that the dimensionless velocity of film spreading, $Ca_{d}=u_{f}\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$, scales as $4f^{4}Ca_{d}={r_{f}^{\ast }}^{-3}$.