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Photobleaching of a dye in droplet, meshing problem
Posted May 28, 2014, 8:36 a.m. EDT Mesh Version 4.4 1 Reply
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Hey,
I've been trying to simulate the absorption of light by a dye molecule in solution, followed by photoreactions.
I've set the model up using General form PDE for light, and the model has worked fine in 1D and 2D.
Now I wanted to simulate a spherical droplet of water in an organic phase. The dye is only present in the aqueous phase. I'm using 2D axial symmetry.
The light is coming from below, and the governing equation is
dI/dz = - eps*c(dye)*I
where I is the intensity of the light, eps is the extinction coefficient of the dye, and c is the dye concentration. Basically this equation describes the absorption in a case where the concentration is not constant (otherwise the equation gives the Lambert-Beer law as solution). For r direction there is no light, so the system is anisotropic.
The problem is that even though I increase the number of elements in the mesh and decrease the relative tolerance, the solution has a lot of oscillations. It seems to me that the the problem is that the triangular elements do not work very well with anisotropic systems. It seems to me that too much light is absorbed from r direction.
Indeed, when I replaced the sphere with a cylinder (square in 2d axial symmetry), and used mapped mesh to make the meshing from rectangles at r-z direction, the model worked perfectly.
However, I don't know how to create a similar mesh with a semicircle, as I always get curving elements.
If anybody has some ideas, please let me know.
I've been trying to simulate the absorption of light by a dye molecule in solution, followed by photoreactions.
I've set the model up using General form PDE for light, and the model has worked fine in 1D and 2D.
Now I wanted to simulate a spherical droplet of water in an organic phase. The dye is only present in the aqueous phase. I'm using 2D axial symmetry.
The light is coming from below, and the governing equation is
dI/dz = - eps*c(dye)*I
where I is the intensity of the light, eps is the extinction coefficient of the dye, and c is the dye concentration. Basically this equation describes the absorption in a case where the concentration is not constant (otherwise the equation gives the Lambert-Beer law as solution). For r direction there is no light, so the system is anisotropic.
The problem is that even though I increase the number of elements in the mesh and decrease the relative tolerance, the solution has a lot of oscillations. It seems to me that the the problem is that the triangular elements do not work very well with anisotropic systems. It seems to me that too much light is absorbed from r direction.
Indeed, when I replaced the sphere with a cylinder (square in 2d axial symmetry), and used mapped mesh to make the meshing from rectangles at r-z direction, the model worked perfectly.
However, I don't know how to create a similar mesh with a semicircle, as I always get curving elements.
If anybody has some ideas, please let me know.
1 Reply Last Post May 28, 2014, 8:53 a.m. EDT
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Posted:
1 decade ago
Naturally I do not know your problem, but I had an analogous one with material diffusing into a nanometer scale droplet where it undergoes a chemical reaction. I made the problem dimensionless by scaling distances with the droplet radius and time with the first order reaction rate constant k, t replaced by k*t. I wonder if anything like that would be feasible for you.
Use mapped mesh if possible.
Wish this helps.
best regards
Lasse
Use mapped mesh if possible.
Wish this helps.
best regards
Lasse