A New Algorithm to Solve Condensation/Evaporation Growth and Coagulation of Nanoparticles Marion Devilliers 1,2, Christian Seigneur 2, Edouard Debry 1, Karine Sartelet 2 1 National Institute of Industrial Environment and Risk (INERIS), Verneuil en Halatte, France 2 Atmospheric Environnement Center (CEREA), Joint Laboratory École des Ponts ParisTech/EDF R&D, Université Paris-Est, France European Geosciences Union General Assembly 2011 Vienna | Austria | 05 April 2011

Nanoparticles : a health concern Definition : at least one of the dimensions of the particle is less than 100 nm Potential adverse effects on human health Multiple sources : – indoor air (domestic activities) – outdoor air (road traffic,...)

Objectives of this study To be accurate with both number (important for nanoparticles) and mass (important for fine and coarse particles) To correctly account for phenomena specific to nanoparticles such as Kelvin effect, van der Waals forces, electric forces for charged particles, and fractal aspect → development of an aerosol model suitable for both indoor and outdoor applications

The sectional approach Development of a 0D model with particle size distribution discretized in N sections Each section is characterized by a representative mean diameter, a number concentration and/or a mass concentration of particles Hypotheses are: – temperature and particle density are constant – all particles have the same composition – particles are spherical

Initial distribution : regional pollution number distributionvolume distribution

Initial distribution : diesel vehicles number distributionvolume distribution

Condensation/Evaporation The volume variation at each time step for the section i is calculated using the following formula: with the Kelvin effect calculated as follows: and the partial gas pressure being updated at every time step because of mass conservation

Redistribution of the particles To keep the representative diameter in the section, particles which are too large or too small are moved to the next or the previous section To redistribute particles among sections, different schemes have been tested and compared

Standard redistribution schemes Euler-Mass: Euler-Number:

Advanced redistribution schemes Moving-Diameter redistribution when diameter changes section (based on Jacobson scheme) Full-Moving no redistribution, cannot be used in 3D but here as the reference (with 500 sections)

New schemes Euler-Hybrid number redistribution for nanoparticles, mass redistribution for fine and coarse particles Euler-Couple redistribution conserving both mass and number

Results : regional pollution Moving-Diameter and Euler-Hybrid show the best results

Results : diesel vehicles Moving-Diameter shows the best results Euler-Hybrid is better than the other Euler schemes

Performance statistics Comparing to our reference using the formula (for the number) : DistributionErrorEuler- Mass Euler- Number Euler- Hybrid Euler- Couple Moving- Diameter Regional pollution logN M Diesel vehicules logN M

Coagulation Coagulation has been added to the model that simulate c/e with the Euler-Hybrid scheme (using a splitting method)

Future work Comparison of different coagulation kernels: – integrated over the section – based on representative diameter Van der Waals forces will be taken into account for coagulation A new other scheme: Euler - Irregular using a finer discretization for nanoparticles

Thank you for your attention