Droplets and aerosols: An artificial dichotomy in respiratory virus transmission.

In the medical literature, three mutually non-exclusive modes of pathogen transmission associated with respiratory droplets are usually identified: contact, droplet, and airborne (or aerosol) transmission. The demarcation between droplet and airborne transmission is often based on a cut-off droplet diameter, most commonly 5 µm. We argue here that the infectivity of a droplet, and consequently the transmissivity of the virus, as a function of droplet size is a continuum, depending on numerous factors (gravitational settling rate, transport, and dispersion in a turbulent air jet, viral load and viral shedding, virus inactivation) that cannot be adequately characterized by a single droplet diameter. We propose instead that droplet and aerosol transmission should be replaced by a unique airborne transmission mode, to be distinguished from contact transmission.

Excess thermal energy and latent heat in nanocluster collisional growth.

Nanoclusters can form and grow by nanocluster-monomer collisions (condensation) and nanocluster-nanocluster collisions (coagulation). During growth, product nanoclusters have elevated thermal energies due to potential and thermal energy exchange following a collision. Even though nanocluster collisional heating may be significant and strongly size dependent, no prior theory describes this phenomenon for collisions of finite-size clusters. We derive a model to describe the excess thermal energy of collisional growth, defined as the kinetic energy increase in the product cluster, and latent heat of collisional growth, defined as the heat released to the background upon thermalization of the nonequilibrium cluster. Both quantities are composed of a temperature-independent term related to potential energy minimum differences and a size- and temperature-dependent term, which hinges upon heat capacity and energy partitioning. Example calculations using gold nanoclusters demonstrate that collisional heating can be important and strongly size dependent, particularly for reactive collisions involving nanoclusters composed of 14-20 atoms. Excessive latent heat release may have considerable implications in cluster formation and growth.

Regulating particle number measurements from the tailpipe of light-duty vehicles: The next step?

Light-duty vehicle emission regulation in the European Union requires the dilution of the whole exhaust in a dilution tunnel with constant volume sampling prior to emission measurements. This methodology avoids measurement uncertainties associated with direct raw exhaust emission measurements from the tailpipe, such as exhaust flow determination, exhaust flow pressure pulsations, differences in the response time between exhaust flow and instrument signals, or their misalignment. Transfer tubes connecting the tailpipe to the dilution tunnel of different lengths, and mixing of the exhaust gas with the dilution air in the dilution tunnel may increase differences in measurements performed at different facilities. Recently, the light-duty vehicle regulation was complemented by on-road measurements with Portable Emissions Measurement Systems (PEMS). PEMS measurements are conducted from the vehicle tailpipe. Differences between tailpipe and full dilution tunnel measurements have not been adequately addressed so far. In this study we compare particle number emissions measured at the full dilution tunnel or directly at the tailpipe. The measurements covered solid particles with diameter larger than 23 nm, as required by the current regulation, but also solid particles larger than 10 nm, as recommended for future regulations. The studied vehicle technologies were diesel, gasoline, and compressed natural gas. The differences between tailpipe and dilution tunnel particle number emissions were found to be small (<15%) for both size ranges, with the exception of engine cold start (up to 35% in some cases). Theoretical estimates showed that agglomeration in the transfer line from the vehicle to the dilution tunnel might reduce particle concentrations by up to 17%. Exhaust flow rate determination and time misalignment of exhaust flow and particle concentration signals can introduce uncertainties of ±10% and ±5%, respectively, to the tailpipe measurements. The results suggest that tailpipe sampling is not only possible, but it can additionally give more representative ("real") emissions of the vehicle and should be considered in post Euro 6 regulations.

Morphology and mobility of synthetic colloidal aggregates.

The relationship between geometric and dynamic properties of fractal-like aggregates is studied in the continuum mass and momentum-transfer regimes. The synthetic aggregates were generated by a cluster-cluster aggregation algorithm. The analysis of their morphological features suggests that the fractal dimension is a descriptor of a cluster's large-scale structure, whereas the fractal prefactor is a local-structure indicator. For a constant fractal dimension, the prefactor becomes also an indicator of a cluster's shape anisotropy. The hydrodynamic radius of orientationally averaged aggregates was calculated via molecule-aggregate collision rates determined from the solution of a Laplace equation. An empirical expression that relates the aggregate hydrodynamic radius to its radius of gyration and the number of primary particles is proposed. The suggested expression depends only on geometrical quantities, being independent of statistical (ensemble-averaged) properties like the fractal dimension and prefactor. Hydrodynamic radius predictions for a variety of fractal-like aggregates are in very good agreement with predictions of other methods and literature values. Aggregate dynamic shape factors and DLCA individual monomer hydrodynamic shielding factors are also calculated.

Indirect transmission and the effect of seasonal pathogen inactivation on infectious disease periodicity.

The annual occurrence of many infectious diseases remains a constant burden to public health systems. The seasonal patterns in respiratory disease incidence observed in temperate regions have been attributed to the impact of environmental conditions on pathogen survival. A model describing the transmission of an infectious disease by means of a pathogenic state capable of surviving in an environmental reservoir outside of its host organism is presented in this paper. The ratio of pathogen lifespan to the duration of the infectious disease state is found to be a critical parameter in determining disease dynamics. The introduction of a seasonally forced pathogen inactivation rate identifies a time delay between peak pathogen survival and peak disease incidence. The delay is dependent on specific disease parameters and, for influenza, decreases with increasing reproduction number. The observed seasonal oscillations are found to have a period identical to that of the seasonally forced inactivation rate and which is independent of the duration of infection acquired immunity.

Spatial dynamics of airborne infectious diseases.

Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003 and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for airborne transmission in indoor environments. Respirable pathogen-carrying droplets provide a vector for the spatial spread of infection with droplet transport determined by diffusive and convective processes. An epidemiological model describing the spatial dynamics of disease transmission is presented. The effects of an ambient airflow, as an infection control, are incorporated leading to a delay equation, with droplet density dependent on the infectious density at a previous time. It is found that small droplets (∼0.4µm) generate a negligible infectious force due to the small viral load and the associated duration they require to transmit infection. In contrast, larger droplets (∼4µm) can lead to an infectious wave propagating through a fully susceptible population or a secondary infection outbreak for a localized susceptible population. Droplet diffusion is found to be an inefficient mode of droplet transport leading to minimal spatial spread of infection. A threshold air velocity is derived, above which disease transmission is impaired even when the basic reproduction number R(0) exceeds unity.

On the friction coefficient of straight-chain aggregates.

A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, aggregate-average or individual, are related to the molecule-aggregate collision rate that is obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of straight chains are in very good agreement with previous results, suggesting that the friction coefficients may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that the diffusive motion of straight-chain aggregates may be described either by a monomer-dependent or an aggregate-average random force, if the shielding factors are appropriately chosen.

Langevin agglomeration of nanoparticles interacting via a central potential.

Nanoparticle agglomeration in a quiescent fluid is simulated by solving the Langevin equations of motion of a set of interacting monomers in the continuum regime. Monomers interact via a radial rapidly decaying intermonomer potential. The morphology of generated clusters is analyzed through their fractal dimension df and the cluster coordination number. The time evolution of the cluster fractal dimension is linked to the dynamics of two populations: small (k≤ 15) and large (k>15) clusters. At early times monomer-cluster agglomeration is the dominant agglomeration mechanism (d(f)=2.25) , whereas at late times cluster-cluster agglomeration dominates (d(f)=1.56). Clusters are found to be compact (mean coordination number of ∼5), tubular, and elongated. The local compact structure of the aggregates is attributed to the isotropy of the interaction potential, which allows rearrangement of bonded monomers, whereas the large-scale tubular structure is attributed to its relatively short attractive range. The cluster translational diffusion coefficient is determined to be inversely proportional to the cluster mass and the (per-unit-mass) friction coefficient of an isolated monomer, a consequence of the neglect of monomer shielding in a cluster. Clusters generated by unshielded Langevin equations are referred to as ideal clusters because the surface area accessible to the underlying fluid is found to be the sum of the accessible surface areas of the isolated monomers. Similarly, ideal clusters do not have, on average, a preferential orientation. The decrease in the numbers of clusters with time and a few collision kernel elements are evaluated and compared to analytical expressions.

Dynamics of infectious disease transmission by inhalable respiratory droplets.

Transmission of respiratory infectious diseases in humans, for instance influenza, occurs by several modes. Respiratory droplets provide a vector of transmission of an infectious pathogen that may contribute to different transmission modes. An epidemiological model incorporating the dynamics of inhalable respiratory droplets is developed to assess their relevance in the infectious process. Inhalable respiratory droplets are divided into respirable droplets, with droplet diameter less than 10 microm, and inspirable droplets, with diameter in the range 10-100 microm: both droplet classes may be inhaled or settle. Droplet dynamics is determined by their physical properties (size), whereas population dynamics is determined by, among other parameters, the pathogen infectivity and the host contact rates. Three model influenza epidemic scenarios, mediated by different airborne or settled droplet classes, are analysed. The scenarios are distinguished by the characteristic times associated with breathing at contact and with hand-to-face contact. The scenarios suggest that airborne transmission, mediated by respirable droplets, provides the dominant transmission mode in middle and long-term epidemics, whereas inspirable droplets, be they airborne or settled, characterize short-term epidemics with high attack rates. The model neglects close-contact transmission by droplet sprays (direct projection onto facial mucous membranes), retaining close-contact transmission by inspirable droplets.

Brownian motion of finite-inertia particles in a simple shear flow.

Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time limit. The classical fluctuation dissipation theorem is used to calculate the amplitude of random-force correlations, thereby neglecting corrections of the order of the molecular relaxation time to the inverse shear rate. In the diffusive limit (time much greater than the particle relaxation time) the fluctuating particle-velocity autocorrelations functions are found to be stationary in time, the correlation in the streamwise direction being an exponential multiplied by an algebraic function and the cross correlation nonsymmetric in the time difference. The analytic, nonperturbative, evaluation of the particle-phase total pressure, which is calculated to be second order in the Stokes number (a dimensionless measure of particle inertia), shows that the particle phase behaves as a non-Newtonian fluid. The generalized Smoluchowski convective-diffusion equation, determined analytically from a combination of the particle-phase pressure tensor and the inertial acceleration term, contains a shear-dependent cross derivative term and an additional term along the streamwise direction, quadratic in the particle Stokes number. The long-time diffusion coefficients associated with the particle flux relative to the carrier flow are found to depend on particle inertia such that the streamwise diffusion coefficient becomes negative with increasing Stokes number, whereas one of the cross coefficients is always negative. The total diffusion coefficients measuring the rate of change of particle mean-square displacement are always positive as expected from general stability arguments.

Classical nucleation theory revisited.

A field-theoretic derivation of the correction to classical nucleation theory due to translational invariance of a nucleating droplet is proposed. The correction is derived from a functional integral representation of the classical partition function, where the two-body interaction potential is decomposed into a short-range repulsive part and a long-range attractive part. The functional integral is evaluated in the mean-field approximation, and the spatially nonuniform density solution of the Euler-Lagrange equation is approximated by a physically motivated hyperbolic tangent profile. Leading-order effects of the nonlocal attractive interaction are highlighted through a density-gradient expansion. The capillarity approximation to the droplet free energy of formation is obtained by performing a density resummation of the uniform state, low-density expansion of the Helmholtz free energy density, and by retaining the leading-order density-gradient term. The resulting translational-invariance correction modifies the droplet free energy by an additive mixing-entropy term. The additional contribution, which contains a logarithmic correction to the surface-energy term, defines a scaling volume that depends on the range of the coarse-grained attractive potential.