Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number Stc below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the non-dimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and St > Stc, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell

Aerosol dynamics simulations of the anatomical variability of e-cigarette particle and vapor deposition in a stochastic lung

Electronic cigarette (EC) aerosols are typically composed of a mixture of nicotine, glycerine (VG), propylene glycol (PG), water, acidic stabilizers and a variety of flavors. Inhalation of e-cigarette aerosols is characterized by a continuous modification of particle diameters, concentrations, composition and phase changes, and smoker-specific inhalation conditions, i.e. puffing, mouthhold and bolus inhalation. The dynamic changes of inhaled e-cigarette droplets in the lungs due to coagulation, conductive heat and diffusive heat/convective vapor transport and particle phase chemistry are described by the Aerosol Dynamics in Containment (ADiC) model. For the simulation of the variability of inhaled particle and vapor deposition, the ADiC model is coupled with the IDEAL Monte Carlo code, which is based on a stochastic, asymmetric airway model of the human lung. We refer to the coupled model as "IDEAL/ADIC_v1.0". In this study, two different ecigarettes were compared, one without any acid ("no acid") and the other one with an acidic regulator (benzoic acid) to establish an initial pH level of about 7 ("lower pH"). Corresponding deposition patterns among human airways comprise total and compound-specific number and mass deposition fractions, distinguishing between inhalation and exhalation phases and condensed and vapor phases. Note that the inhaled EC aerosol is significantly modified in the oral cavity prior to inhalation into the lungs. Computed deposition fractions demonstrate that total particle mass is preferentially deposited in the alveolar region of the lung during inhalation. While nicotine deposits prevalently in the condensed phase for the "lower pH" case, vapor phase deposition is dominating the "no acid" case. The significant statistical fluctuations of the particle and vapor deposition patterns illustrate the inherent anatomical variability of the human lung structure.Peer reviewe

Stochastic representation of the Reynolds transport theorem: revisiting large-scale modeling

We explore the potential of a formulation of the Navier-Stokes equations incorporating a random description of the small-scale velocity component. This model, established from a version of the Reynolds transport theorem adapted to a stochastic representation of the flow, gives rise to a large-scale description of the flow dynamics in which emerges an anisotropic subgrid tensor, reminiscent to the Reynolds stress tensor, together with a drift correction due to an inhomogeneous turbulence. The corresponding subgrid model, which depends on the small scales velocity variance, generalizes the Boussinesq eddy viscosity assumption. However, it is not anymore obtained from an analogy with molecular dissipation but ensues rigorously from the random modeling of the flow. This principle allows us to propose several subgrid models defined directly on the resolved flow component. We assess and compare numerically those models on a standard Green-Taylor vortex flow at Reynolds 1600. The numerical simulations, carried out with an accurate divergence-free scheme, outperform classical large-eddies formulations and provides a simple demonstration of the pertinence of the proposed large-scale modeling

Prediction and evolution of drop-size distribution of an ultrasonic vibrating microchannel

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.We report in this paper the evolution of a physically-based drop size-distribution coupling the Maximum Entropy Formalism and the Monte Carlo method to solve the distribution equation of a spray. The atomization is performed by a new Spray On Demand (SOD) device which exploits ultrasonic generation via a Faraday instability. The Modified Hamilton’s principle is used to describe the fluid structure/interaction with a vibrating micro-channel conveying fluid excited by a pointwise piezoactuator. We combine to the fluid/structure description a physically based approach for predicting the drop-size distribution within the framework of the Maximum Entropy Formalism (MEF) using conservation laws of energy and mass coupling with the three-parameter generalized Gamma distribution. The prediction and experimental validation of the drop size distribution of a new Spray On Demand print-head is performed. The dynamic model is shown to be sensitive to operating conditions, design parameter and physico-chemical properties of the fluid and its prediction capability is good. We also report on a model allowing the evolution of drop sizedistribution. Deriving the discrete and continuous population balance equation, the Mass Flow Algorithm is formulated taking into account interactions between droplets via coalescence. After proposing a kernel for coalescence, we solve the time dependent drop size distribution using a Monte Carlo Method which is shown to be convergent. The drops size distribution upon time shows the effect of spray droplets coalescence

Basic concepts for convection parameterization in weather forecast and climate models: COST Action ES0905 final report

The research network “Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models” was organized with European funding (COST Action ES0905) for the period of 2010–2014. Its extensive brainstorming suggests how the subgrid-scale parameterization problem in atmospheric modeling, especially for convection, can be examined and developed from the point of view of a robust theoretical basis. Our main cautions are current emphasis on massive observational data analyses and process studies. The closure and the entrainment–detrainment problems are identified as the two highest priorities for convection parameterization under the mass–flux formulation. The need for a drastic change of the current European research culture as concerns policies and funding in order not to further deplete the visions of the European researchers focusing on those basic issues is emphasized