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Welcome to the bin-diffusion-model wiki!
Example output for diffusion coefficient of 10-17 growing dynamically
each of the above plots can be created from the output, in Matlab (with mexcdf installed):
i=30;
pcolor(nc{'time'}(:),squeeze(nc{'r'}(:,i,:))',squeeze(nc{'c'}(:,i,1,:))' ...
./(squeeze(nc{'c'}(:,i,1,:))'+3.*squeeze(nc{'c'}(:,i,2,:))'));shading flat;
set(gca,'YScale','log');
Coupling diffusion and cloud formation processes on aerosol particles is a difficult problem. The problem of the formation of cloud on aerosol particles alone is a so called stiff problem alone. Whereas diffusion is a moving boundary or Stefan problem. Representing these processes in a model is difficult, but has been done here.
The model is research-grade in that it is quite slow to run, and we do not yet understand all the effects.
The aerosol particles are represented in a spherically symmetric coordinate system. We found it appropriate to space the shells logarithmically in radius space.
The last shell is coincident with the boundary of the particle and it position is update as the particle grows / shrinks.
Diffusion through the particle is solved using an implicit method to solve the finite difference equation approximating Fick's 2nd law.
Diffusion through the aerosol particles had to be solved at every iteration in the parcel model ODE (Ordinary Differential Equation) solver. This was a key step in making the model stable, and accurate; however, it slows the integration down significantly.
In addition, once the ODE solver exits a time-step at time texit, a final call to the diffusion solver is required (because the last call inside the solver is not necessarily at time texit).
This is currently represented according to the Koop et al. (2000, Nature) formulation. Rather than be calculated according to the mole fraction of water (or activity) averaged over the whole particle nucleation probability is calculated in each shell and summed up for each bin. For low diffusion coefficients, water can be concentrated in certain regions of the particle, which may enhance the nucleation rate in solution droplets at low temperatures.