Note on the method of matched-asymptotic expansions for determining the force acting on a particle

This paper is an addendum to the article by Candelier, Mehaddi & Vauquelin (2013) where the motion of a particle in a stratified fluid is investigated theoretically, at small Reynolds and P\'eclet numbers. We review briefly the method of matched asymptotic expansions which is generally used in order to determine the force acting on a particle embedded in a given flow, in order to account for small, but finite, inertia effects. As part of this method, we present an alternative matching procedure, which is based on a series expansion of the far-field solution of the problem, performed in the sense of generalized functions. The way to perform such a series is presented succinctly and a simple example is provided.Comment: 8 page

The history force on a small particle in a linearly stratified fluid

The hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck-Boussinesq approximation, and in the limit of small Reynolds and small P\'eclet numbers. The force acting on the particle is obtained by using matched asymptotic expansions in which the small parameter is given by a/l where a is the particle radius and l is the stratification length defined by Ardekani & Stocker (2010), which depends on the Brunt-Vaisala frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular-frequency corresponding to the Brunt-Vaisala frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified-fluid.Comment: 16 page

Etude d'un jet de faible densité destiné à reproduire un panache thermique pour des applications de simulation d'incendie sur maquette à échelle réduite

International audiencePar analogie aéraulique, un panache thermique d'incendie en tunnel peut être simulé sur maquette par le rejet continu d'un mélange d'air et d'hélium à température ambiante. Le débit d'hélium est fixé par la puissance de l'incendie simulé tandis que la masse volumique peut être déduite des niveaux de température simulés. Cet article présente des résultats expérimentaux pour un jet d'air et d'hélium axisymétrique impactant le plafond d'un canal. Des mesures de masse volumique ont été réalisées au point d'impact pour différents diamètres d'injection, débits d'hélium et masses volumique du fluide injecté. L'objectif est d'établir une "méthodologie" expérimentale permettant de reproduire des niveaux de température équivalente au point d'impact en jouant sur les conditions d'injection. On montre que ces niveaux de température peuvent être reproduits soit en ajoutant de l'air à l'injection, soit en augmentant le diamètre d'injection

Etude expérimentale des mécanismes thermo-aérauliques lors d'un feu dans une charge de bois

International audienceNous proposons une étude expérimentale de la combustion d'une charge de copeaux de bois confinés dans une enceinte ventilée ou non ventilée. Nous avons étudié l'influence des paramètres relatifs au combustible (type de bois) et à l'aération (apport d'oxygène) sur l'évolution de la structure de la flamme et de sa température, de la perte de masse du bois et de la nature des émissions gazeux de sa combustion. Ce travail permet d'améliorer les connaissances disponibles sur les mécanismes thermo-aérauliques accompagnant la combustion du bois et offre un outil de validation aux modèles numériques disponibles

Etude numérique et expérimentale de la propagation de fumées entre deux locaux

International audienceCette étude est relative à la compréhension et à la description du phénomène de propagation dans une structure confinée et ventilée mécaniquement. Ceci est réalisé en utilisant deux maquettes à échelle réduite au 1/5, d'un dispositif composé de deux compartiments communiquant par une ouverture verticale. Des simulations numériques ont été menées sur deux codes afin de juger leurs performances vis-à-vis de ce problème

Effet des variations massique et dynamique d'un jet vertical à flux de gravité fixé sur la masse volumique mesurée au point d'impact sur une paroi horizontale

Cet article présente des essais expérimentaux pour un jet vertical axisymétrique d'air et d'hélium impactant une paroi horizontale. Pour différents nombres de Richardson initiaux (2×10-3 - 908) et de Reynolds initiaux (47 - 22780), des visualisations de l'écoulement ont été réalisées et la masse volumique au point d'impact a été mesurée. Il apparaît que, sous certaines conditions, cette masse volumique peut décroître alors que la masse volumique du mélange injecté est augmentée par ajout d'air. L'étude montre que ce résultat est lié au caractère instable de l'écoulement (bouffées), pouvant être caractérisé par une condition sur le nombre de Richardson initial

The influence of drug distribution and drug-target binding on target occupancy: The rate-limiting step approximation

The influence of drug-target binding kinetics on target occupancy can be influenced by drug distribution and diffusion around the target, often referred to as "rebinding" or "diffusion-limited binding". This gives rise to a decreased decline of the drug-target complex concentration as a result of a locally higher drug concentration that arises around the target, which leads to prolonged target exposure to the drug. This phenomenon has been approximated by the steady-state approximation, assuming a steady-state concentration around the target. Recently, a rate-limiting step approximation of drug distribution and drug-target binding has been published. However, a comparison between both approaches has not been made so far. In this study, the rate-limiting step approximation has been rewritten into the same mathematical format as the steady-state approximation in order to compare the performance of both approaches for the investigation of the influence of drug-target binding kinetics on target occupancy. While both approximations clearly indicated the importance of kon and high target concentrations, it was shown that the rate-limiting step approximation is more accurate than the steady-state approximation, especially when dissociation is fast compared to association and distribution out of the binding compartment. It is therefore concluded that the new rate-limiting step approximation is to be preferred for assessing the influence of binding kinetics on local target site concentrations and target occupancy

The influence of drug distribution and drug-target binding on target occupancy: The rate-limiting step approximation

The influence of drug-target binding kinetics on target occupancy can be influenced by drug distribution and diffusion around the target, often referred to as "rebinding" or "diffusion-limited binding". This gives rise to a decreased decline of the drug-target complex concentration as a result of a locally higher drug concentration that arises around the target, which leads to prolonged target exposure to the drug. This phenomenon has been approximated by the steady-state approximation, assuming a steady-state concentration around the target. Recently, a rate-limiting step approximation of drug distribution and drug-target binding has been published. However, a comparison between both approaches has not been made so far. In this study, the rate-limiting step approximation has been rewritten into the same mathematical format as the steady-state approximation in order to compare the performance of both approaches for the investigation of the influence of drug-target binding kinetics on target occupancy. While both approximations clearly indicated the importance of kon and high target concentrations, it was shown that the rate-limiting step approximation is more accurate than the steady-state approximation, especially when dissociation is fast compared to association and distribution out of the binding compartment. It is therefore concluded that the new rate-limiting step approximation is to be preferred for assessing the influence of binding kinetics on local target site concentrations and target occupancy

A two-state model for the kinetics of competitive radioligand binding

© 2018 The Authors. British Journal of Pharmacology published by John Wiley & Sons Ltd on behalf of British Pharmacological Society. Background and Purpose: Ligand–receptor binding kinetics is receiving increasing attention in the drug research community. The Motulsky and Mahan model, a one-state model, offers a method for measuring the binding kinetics of an unlabelled ligand, with the assumption that the labelled ligand has no preference while binding to distinct states or conformations of a drug target. As such, the one-state model is not applicable if the radioligand displays biphasic binding kinetics to the receptor. Experimental Approach: We extended the Motulsky and Mahan model to a two-state model, in which the kinetics of the unlabelled competitor binding to different receptor states (R 1 and R 2 ) can be measured. With this extended model, we determined the binding kinetics of unlabelled N-5′-ethylcarboxamidoadenosine (NECA), a representative agonist for the adenosine A 1 receptor. Subsequently, an application of the model was exemplified by measuring the binding kinetics of other A 1 receptor ligands. In addition, limitations of the model were investigated as well. Key Results: The kinetic rate constants of unlabelled NECA were comparable with the results of kinetic radioligand binding assays in which [ 3 H]-NECA was used. The model was further validated by good correlation between simulated results and the experimental data. Conclusion: The two-state model is sufficient to analyse the binding kinetics of an unlabelled ligand, when a radioligand shows biphasic association characteristics. We expect this two-state model to have general applicability for other targets as well