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

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

Fluid fragmentation shapes rain-induced foliar disease transmission

Plant diseases represent a growing threat to the global food supply. The factors contributing to pathogen transmission from plant to plant remain poorly understood. Statistical correlations between rainfalls and plant disease out- breaks were reported; however, the detailed mechanisms linking the two were relegated to a black box. In this combined experimental and theoretical study, we focus on the impact dynamics of raindrops on infected leaves, one drop at a time. We find that the deposition range of most of the pathogen-bear- ing droplets is constrained by a hydrodynamical condition and we quantify the effect of leaf size and compliance on such constraint. Moreover, we identify and characterize two dominant fluid fragmentation scenarios as responsible for the dispersal of most pathogen-bearing droplets emitted from infected leaves: (i) the crescent-moon ejection is driven by the direct interaction between the impacting raindrop and the contaminated sessile drop and (ii) the inertial detachment is driven by the motion imparted to the leaf by the raindrop, lead- ing to catapult-like droplet ejections. We find that at first, decreasing leaf size or increasing compliance reduces the range of pathogen-bearing droplets and the subsequent epidemic onset efficiency. However, this conclusion only applies for the crescent moon ejection. Above a certain compliance threshold a more effective mechanism of contaminated fluid ejection, the inertial detachment, emerges. This compliance threshold is determined by the ratio between the leaf velocity and the characteristic velocity of fluid fragmentation. The inertial detachment mechanism enhances the range of deposition of the larger con- taminated droplets and suggests a change in epidemic onset pattern and a more efficient potential of infection of neighbouring plants. Dimensionless parameters and scaling laws are provided to rationalize our observations. Our results link for the first time the mechanical properties of foliage with the onset dynamics of foliar epidemics through the lens of fluid fragmentation. We discuss how the reported findings can inform the design of mitigation strategies acting at the early stage of a foliar disease outbreak

Fluid Dynamics of Respiratory Infectious Diseases

The host-to-host transmission of respiratory infectious diseases is fundamentally enabled by the interaction of pathogens with a variety of fluids (gas or liquid) that shape pathogen encapsulation and emission, transport and persistence in the environment, and new host invasion and infection. Deciphering the mechanisms and fluid properties that govern and promote these steps of pathogen transmission will enable better risk assessment and infection control strategies, and may reveal previously underappreciated ways in which the pathogens might actually adapt to or manipulate the physical and chemical characteristics of these carrier fluids to benefit their own transmission. In this article, I review our current understanding of the mechanisms shaping the fluid dynamics of respiratory infectious diseases

Airborne or droplet precautions for health workers treating coronavirus disease 2019?

Cases of coronavirus disease 2019 (COVID-19) have been reported in more than 200 countries. Thousands of health workers have been infected, and outbreaks have occurred in hospitals, aged care facilities, and prisons. The World Health Organization (WHO) has issued guidelines for contact and droplet precautions for healthcare workers caring for suspected COVID-19 patients, whereas the US Centers for Disease Control and Prevention (CDC) has initially recommended airborne precautions. The 1- to 2-meter (≈3–6 feet) rule of spatial separation is central to droplet precautions and assumes that large droplets do not travel further than 2 meters (≈6 feet). We aimed to review the evidence for horizontal distance traveled by droplets and the guidelines issued by the WHO, CDC, and European Centre for Disease Prevention and Control on respiratory protection for COVID-19. We found that the evidence base for current guidelines is sparse, and the available data do not support the 1- to 2-meter (≈3–6 feet) rule of spatial separation. Of 10 studies on horizontal droplet distance, 8 showed droplets travel more than 2 meters (≈6 feet), in some cases up to 8 meters (≈26 feet). Several studies of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) support aerosol transmission, and 1 study documented virus at a distance of 4 meters (≈13 feet) from the patient. Moreover, evidence suggests that infections cannot neatly be separated into the dichotomy of droplet versus airborne transmission routes. Available studies also show that SARS-CoV-2 can be detected in the air, and remain viable 3 hours after aerosolization. The weight of combined evidence supports airborne precautions for the occupational health and safety of health workers treating patients with COVID-19. ©2020NHMRC Centre for Research Excellence (grant no. APP1107393

Discreteness and resolution effects in rapidly rotating turbulence

Rotating turbulence is characterized by the nondimensional Rossby number Ro, which is a measure of the strength of the Coriolis term relative to that of the nonlinear term. For rapid rotation (Ro→0), nonlinear interactions between inertial waves are weak, and the theoretical approaches used for other weak (wave) turbulence problems can be applied. The important interactions in rotating turbulence at small Ro become those between modes satisfying the resonant and near-resonant conditions. Often, discussions comparing theoretical results and numerical simulations are questioned because of a speculated problem regarding the discreteness of the modes in finite numerical domains versus continuous modes in unbounded continuous theoretical domains. This argument finds its origin in a previous study of capillary waves, for which resonant interactions have a very particular property that is not shared by inertial waves. This possible restriction on numerical simulations of rotating turbulence to moderate Ro has never been quantified. In this paper, we inquire whether the discreteness effects observed in capillary wave turbulence are also present in inertial wave turbulence at small Ro. We investigate how the discreteness effects can affect the setup and interpretation of studies of rapidly rotating turbulence in finite domains. In addition, we investigate how the resolution of finite numerical domains can affect the different types of nonlinear interactions relevant for rotating inertial wave turbulence theories. We focus on Rossby numbers ranging from 0 to 1 and on periodic domains due to their relevance to direct numerical simulations of turbulence. We find that discreteness effects are present for the system of inertial waves for Rossby numbers comfortably smaller than those used in the most recent numerical simulations of rotating turbulence. We use a kinematic model of the cascade of energy via selected types of resonant and near-resonant interactions to determine the threshold of Ro below which discreteness effects become important enough to render an energy cascade impossible.Natural Sciences and Engineering Research Council of Canad

Model of a truncated fast rotating flow at infinite Reynolds number

The purpose of this study is to examine the strongly rotating limit of a turbulent flowtheoretically and numerically. The goal is to verify the predictions of asymptotic theories. Given the limitations of experimental and dissipative numerical approaches to this problem, we use classical equilibrium statistical mechanics. We apply the statistical mechanics approach to the inviscid truncated model of strongly rotating turbulence (in the small Rossby number range) and derive the theoretical spectra of the decoupled model. We use numerical simulations to complement these derivations and examine the relaxation to equilibrium of the inviscid unforced truncated rotating turbulent system for different sets of initial conditions. We separate our discussion into two time domains: the discussion of the decoupled phase with time below a threshold time t[subscript ⋆], for which a new set of invariants S are identified, and the coupled phase with a time beyond t[subscript ⋆], for which the quantities S are no longer invariants. We obtain a numerical evaluation of t[subscript ⋆] which is coherent with the theoretical asymptotic expansions. We examine if the quantities S play a constraining role on the coupled dynamics beyond t > t[subscript ⋆]. We find that the theoretical statistical predictions in the decoupled phase capture the horizontal dynamics of the flow. In the coupled phase, the invariants S are found to still play a constraining role on the short-timescale horizontal dynamics of the flow. These results are discussed in the larger context of previous rotating turbulence studies

Numerical and theoretical study of homogeneous rotating turbulence

The Coriolis force has a subtle, but significant impact on the dynamics of geophysical and astrophysical flows. The Rossby number, Ro, is the nondimensional parameter measuring the relative strength of the Coriolis term to the nonlinear advection terms in the equations of motion. When the rotation is strong, Ro goes to zero and three-dimensional flows are observed to two-dimensionalize. The broad aim of this work is to examine the effect of the strength of rotation on the nonlinear dynamics of turbulent homogeneous flows. Our approach is to decompose the rotating turbulent flow modes into two classes: the zero-frequency 2-dimensional (2D) modes; and the high-frequency inertial waves (3D).First, using numerical simulations of decaying turbulence over a large range of Ro we identified three regimes. The large Ro regime is similar to non-rotating, isotropic turbulence. The intermediate Ro regime shows strong 3D-to-2D energy transfers and asymmetry between cyclones (corotating) and anticyclones (couter-rotating), whereas at small Ro regime these features are much reduced.We then studied discreteness effects and constructed a kinematic model to quantify the threshold of nonlinear broadening below which the 2D-3D interactions critical to the intermediate Ro regime are not captured. These results allow for the improvement of numerical studies of rotating turbulence and refine the comparison between results obtained in finite domains and theoretical results derived in unbounded domains.Using equilibrium statistical mechanics, we examined the hypothesis of decoupling predicted in the small Ro regime. We identified a threshold time, t☆ = 2/Ro2, after which the asymptotic decoupling regime is no longer valid. Beyond t ☆, we show that the quasi-invariants of the decoupled model continue to constrain the system on the short timescales.We found that the intermediate Ro regime is also present in forced turbulence and that interactions responsible for it are nonlocal. We explain a steep slope obtained in the 2D energy spectrum by a downscale enstrophy transfer. The energy of the 2D modes is observed to accumulate in the largest scales of the domain in the long-time limit. This is reminiscent of the "condensation" observed in classical forced 2D flows and magnetohydrodynamics

Disease transmission via drops and bubbles

Seasonal influenza was responsible for nearly a million hospitalizations in the US in 2018, and tuberculosis killed more than a million people around the world. Those and other infectious diseases are spread by pathogens, such as bacteria and viruses. An important part of the pathogens' life cycle occurs in liquids, whose fluid dynamics influences transmission from one infected host or environmental reservoir to another. A cough or sneeze, for instance, produces a turbulent cloud of hot, moist air and droplets, as shown in figure 1. That cloud and its droplet payload can span a room up to 8 m long in a few seconds. Droplets can also be spread from bursting bubbles or splashed from a wet, contaminated surface. To predict and model disease transmission at both population and individual scales, and to develop efficient mitigation innovations and strategies against the spread of infectious diseases, understanding the role of the underlying fluid dynamics is critical. Yet little is known about the factors affecting the source, transport, and persistence of pathogen-bearing droplets. This Quick Study focuses on the example of bursting air bubbles to illustrate the rich physics and close coupling of biology and fluid dynamics in the context of disease transmission