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.

## I am currently a Postdoctoral researcher

at Laboratoire Jacques-Louis Lions (LJLL)

Sorbonne Université

4 Place Jussieu, 75005 Paris, France

## Research interests

## Scientific contributions

A. Mecherbet. On the sedimentation of a droplet in Stokes flow. (In progress)

D. Gérard-Varet and A. Mecherbet. On the correction to Einstein's formula for the effective viscosity. 2020. arXiv:2004.05601.

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. hal-02092574. To appear in ESAIM: Proceedings and Surveys.

A. Mecherbet. A model for suspension of clusters of particle pairs. 2019. hal-02171615. To appear in ESAIM: Mathematical Modelling and Numerical Analysis.

A. Mecherbet. Sedimentation of particles in Stokes flow. Kinetic & Related Models, 2019, 12 (5) : 995-1044.arXiv:1806.07795

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. hal-01398706

## Talks in conferences

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.