I am interested in the mathematical analysis and modelling of suspension of particles in a viscous fluid. Precisely, it consists in the rigorous derivation of mesoscopic models (kinetic description) by performing a mean-field analysis of the microscopic model (ODEs system for a large number of particles). This asymptotic analysis is related to the homogenization of Stokes equation in a perforated domain. I am also interested in the analysis of the limit model which is a Stokes-transport coupled system. The main interesting aims are existence and uniqueness results for irregular data, modeling and analysis of the surface of a falling drop in a viscous flow. The modelling of sedimentation of particles in a Stokes flow involves also the rigorous justification of some effective phenomena such as the effective viscosity. A challenging issue is to extend the well-known Einstein's effective viscosity formula for high order terms of the suspension volume fraction. I also collaborated on a work regarding fluid-kinetic modelling for respiratory aerosols that takes into account the radius growth of aerosol particles due to humidity in the respiratory system. This work includes 2D numerical simulations of aerosol deposit in the trachea in order to investigate the hygroscopic effects on the aerosol.
Scientific contributions
A. Mecherbet. On the sedimentation of a droplet in Stokes flow. 2020 To appear in Comm Math Sci.
D. Gérard-Varet and A. Mecherbet. On the correction to Einstein's formula for the effective viscosity. 2020. To appear in Annales de l'IHP (C)-ANL.
L. Boudin, C. Grandmont, B. Grec, S. Martin, A. Mecherbet and F. Noël. Fluid-kinetic modelling for respiratory aerosols with variable size and temperature. 2019. ESAIM: Proceedings and Surveys.
A. Mecherbet. A model for suspension of clusters of particle pairs. 2019. ESAIM: Mathematical Modelling and Numerical Analysis.
A. Mecherbet. Sedimentation of particles in Stokes flow. Kinetic & Related Models, 2019, 12 (5) : 995-1044.
A. Mecherbet and M. Hillairet. Lp estimates for the homogenization of Stokes problem in a perforated domain. Journal of the Institute of Mathematics of Jussieu, 1-28. 2018.
Talks in conferences
Oberwolfach workshop on Classical and Quantum Mechanical Models of Many-Particle Systems (30/11-4/12/2020)
Vorticity, Rotation and Symmetry (V) - Global Results and Nonlocal Phenomena, 6-10 april 2020, CIRM Marseille. sessions parallèles. Speaker.
EDDy Seminar, 16 July 2020, RWTH Aachen University, digital talk
Workshop The mathematical theory of particle suspensions, Bonn university, 20-22 January 2020.
Modélisation, analyse et simulation - Le Laboratoire Jacques-Louis Lions fête ses 50 ans. 27-29 november 2019. Poster session.
Séminaire analyse appliquée, I2M Aix-Marseille Université, 02 July 2019. Invited speaker.
SMAI 9ème biennale, may 2019, Guidel. sessions parallèles. Analyse de EDP. Speaker.
Workshop RheoSuNN, 27-28 March 2019, Ecole Polytechnique, Palaiseau. Poster session
Séminaire EDP, 15 January 2019, IECL Nancy. Invited speaker.
ABPDE III, 28-31 August 2018, Lille, Poster session
CEMRACS 2018, August 2018, CIRM Marseille. Size-varying respiratory aerosols modeling. Speaker with Frédérique Noël.
Séminaire ACSIOM 2016, Montpellier universitiy, IMAG. Lp estimates for the homogenization of Stokes problem in a perforated domain
Education
2019 - 2020 PostDoc Position at Laboratoire Jacques-Louis Lions, Sorbonne university.In collaboration with Anne-Laure DALIBARD and David GERARD-VARET.
2016 - 2019 Ph.D. student at Institut Montpelliérain Alexander Grothendieck, Montpellier university. PhD thesis: Modeling of multiphase flows
Advisor : Matthieu HILLAIRET
Referees: Laurent DESVILLETTES, Pierre-Emmanuel JABIN
Thesis Committee : Kleber CARRAPATOSO, Anne-Laure DALIBARD, Laurent DESVILLETTES, Pierre-Emmanuel JABIN, Aline LEFEBVRE-LEPOT, Charlotte PERRIN.
2014 - 2016 Master's degree of Applied Mathematics, University of Montpellier. Major of the promotion. Master thesis: Homogénéisation du problème de Stokes et estimations Lp
Advisor : Matthieu HILLAIRET
2011 - 2014 Bachelor degree in Mathematics, University of Tlemcen, Algeria. Major of the promotion.