An analytic solution for capillary thinning and breakup of FENE-P fluids

The FENE-P model of a fluid is particularly suitable for describing the rheology of dilute polymer solutions (Newtonian solvents containing small amounts of dissolved polymer) as a result of its ability to capture nonlinear effects arising from the finite extensibility of the polymer chains. In extensional flows, these polymer solutions exhibit dramatically different behavior from the corresponding Newtonian solvents alone, notably through the creation of persistent filaments when stretched. By using the technique of capillary thinning to study the dynamics of the thinning process of these filaments, the transient extensional rheology of the fluid can be characterized. We show that under conditions of uniaxial elongational flow, a composite analytic solution can be developed to predict the time evolution of the radius of the filament. Furthermore we derive an analytic expression for the finite time to breakup of the fluid filaments. This breakup time agrees very well with results obtained from full numerical simulations, and both numerics and theory predict an increase in the time to breakup as the finite extensibility parameter b , related to the molecular weight of the polymer, is increased. As b→∞, the results converge to an asymptotic result for the breakup time which shows that the breakup time grows as t[subscript break]∼ln(M[subscriptW]), where M[subscriptW] is the molecular weight of the dilute polymer solution

Mathematical Models for Estimating the Risk of vCJD Transmission

We present two different simple models for vCJD transmission by blood transfusion. Both models indicate that transfusions alone are unlikely to cause more than a few infections, unless the number of primary cases increases. To improve our models, future work should pursue data collection, empirical estimation of the model parameters, and examination of the underlying assumptions of our frameworks. Further improvements could also include examining susceptibility to vCJD infection by age group and iatrogenic infections introduced through surgical instruments. Regarding the latter, it may be worthwhile to conduct experiments to quantify the transmission of prions from an infected surgical instrument after repeated sterilization procedures

Universal Rim Thickness in Unsteady Sheet Fragmentation

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.United States. Department of Agriculture (Award MDW-2016-04938

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Lagrangian evolution of velocity increments in rotating turbulence: The effects of rotation on non-Gaussian statistics

The effects of rotation on the evolution of non-Gaussian statistics of velocity increments in rotating turbulence are studied in this paper. Following the Lagrangian evolution of the velocity increments over a fixed distance on an evolving material element, we derive a set of equations for the increments which provides a closed representation for the nonlinear interaction between the increments and the Coriolis force. Applying a restricted-Euler-type closure to the system, we obtain a system of ordinary differential equations which retains the effects of nonlinear interaction between the velocity increments and the Coriolis force. A priori tests using direct numerical simulation data show that the system captures the important dynamics of rotating turbulence. The system is integrated numerically starting from Gaussian initial data. It is shown that the system qualitatively reproduces a number of observations in rotating turbulence. The statistics of the velocity increments tend to Gaussian when strong rotation is imposed. The negative skewness in the longitudinal velocity increments is weakened by rotation. The model also predicts that the transverse velocity increment in the plane perpendicular to the rotation axis will have positive skewness, and that the skewness will depend on the Rossby number in a non-monotonic way. Based on the system, we identify the dynamical mechanisms leading to the observations. (c) 2010 Elsevier B.V. All rights reserved

A Scoping Review of Respirator Literature and a Survey among Dental Professionals

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus was discovered in China in late 2019 and subsequently triggered a global pandemic. Dentists, like many other health professionals, are at an increased risk of contracting the virus as they work in close proximity to patients, especially when performing aerosol-generating procedures. Thus, in order for dentists to protect themselves and their patients, it is recommended that practitioners wear filtering facepiece 2 (FFP2) respirators. The prolonged use of these FFP2 respirators has been linked to several side effects. The aim of this paper is to assess the perceived experience associated with N95/FFP2 respirators based on the available literature and data collected through an online survey completed by Italian dental professionals. Articles were included up to May 2020 and literature searches were conducted through The National Library of Medicine, Cochrane Central Register of Controlled Trials, and Embase databases. The search terms included COVID-19, respirators, masks, and discomfort. An online survey was administered to 256 Italian dentists. The results from this survey were in agreement with the available literature. The findings concurred that the prolonged use of respirators was associated with headaches (47.5%), severe exertion and discomfort (50.8%), moderate concentration problems (54.3%), moderate breathing difficulties (63.5%), and consequently, an impaired work ability (85.5%). These findings were not influenced by the number of hours spent wearing the respirator. Despite several side effects, FFP2 respirators are fundamental in protecting dentists and their importance was acknowledged

Practical Indicators for Risk of Airborne Transmission in Shared Indoor Environments and Their Application to COVID-19 Outbreaks

Some infectious diseases, including COVID-19, can undergo airborne transmission. This may happen at close proximity, but as time indoors increases, infections can occur in shared room air despite distancing. We propose two indicators of infection risk for this situation, that is, relative risk parameter (Hr) and risk parameter (H). They combine the key factors that control airborne disease transmission indoors: viruscontaining aerosol generation rate, breathing flow rate, masking and its quality, ventilation and aerosol-removal rates, number of occupants, and duration of exposure. COVID-19 outbreaks show a clear trend that is consistent with airborne infection and enable recommendations to minimize transmission risk. Transmission in typical prepandemic indoor spaces is highly sensitive to mitigation efforts. Previous outbreaks of measles, influenza, and tuberculosis were also assessed. Measles outbreaks occur at much lower risk parameter values than COVID-19, while tuberculosis outbreaks are observed at higher risk parameter values. Because both diseases are accepted as airborne, the fact that COVID-19 is less contagious than measles does not rule out airborne transmission. It is important that future outbreak reports include information on masking, ventilation and aerosol-removal rates, number of occupants, and duration of exposure, to investigate airborne transmission