A New Algorithm to Solve Condensation/Evaporation Growth and Coagulation of Nanoparticles

Marion Devilliers1,2, Christian Seigneur2, Edouard Debry1, Karine Sartelet2

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 UnionGeneral 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 distribution volume distribution

Initial distribution : diesel vehicles

number distribution volume 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 schemesEuler-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-Coupleredistribution conserving both mass and

number

Results : regional pollution

Moving-Diameterand Euler-Hybridshow 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) :

Distribution Error Euler-Mass

Euler-Number

Euler-Hybrid

Euler-Couple

Moving-Diameter

Regional pollution

logN 1.24 0.32 0.30 0.41 0.19

M 0.21 0.72 0.05 0.15 0.14

Diesel vehicules

logN 0.89 0.92 0.81 0.80 0.29

M 0.63 1.41 0.63 1.21 1.24

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