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The minium density in a particular cell of the volumetric object. In most cases you should leave this value at 0 as you don't want any visible density where there are no particles.
Max final density
The max allowable density in a particular cell of the volumetric object. Note that this parameter is also influenced by the Density Multiplier - a small density multiplier will not make the volumetric look more dense, even if the Max final density is very large. In fact, you should avoid setting this setting very high (for example more than a few hundred), especially if the density multiplier value is small. This will result in a similar look as if a smaller max final density value was used, with the downside that the render time will be substantially slower. As you can see in the example renders below, if the Density multiplier is already fairly large, then a Max final density value of around 100 will be enough even for the most "solid" volumetric simulations.
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The cell size should be considered as the "resolution" of the volumetric object. The smaller the cell size, the finer the resolution. Just as a bitmap image can reveal more detail when zoomed in if it contains a lot of pixels. The cell size parameter is necessary in order to keep the RAM usage under control. So the final RAM consumption is not influenced by the number of particles in your simulation, but instead on the number of cells which are created at render time, which define the resolution of the volumetric object.
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The above illustration shows a particle that happens to have the same size of its the cell. But even in this case, it isn't certain that this cell will show any density, if the density multiplier and final density settings are too small, because the cell still has a certain distance to search before finding this particle. The longer this search distance is, the more faded the density becomes.
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A 10cm large cube of particles, where each particle is 2cm in diameter, and each cell is 1cm in size (setting of 0.01). The cells are small, so a smaller search distance inside the cell is needed to find a particle, thus we see the some density created by in each individual particle cell in this case. Notice that we are not seeing the round shape of the particleparticles, but rather the square shape of each of the cells. The cells (the "resolution") would need to be even smaller to start mimicking the round shape of the particles.
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Now the cell size is 3cm and we start seeing some density again. This can seem very unintuitive at first, but looking at the grid of cells, it is clear that now that some corners of some cells are actually closer to a particle compared to when the grid was set to 2cm. So we start seeing a very rough, square representation of these particles, because the cell size is so large.
All renders with cell size of 2mm, radius 1cm, Max Final Density at 500. Only the Density Multiplier changed: 10000, 3000, 1000.
This series of images is ment to show that with a small enough cell size, each particle can be very well defined (in these renders the cell size was reduced to 2mm (a setting of 0.002), and secondly, how the Density Multiplier parameter can act as a sort of falloff between areas of density and no density. The Max Final Density was 500 for all renders. You can see that as the Density Multiplier decreases, there is a larger falloff between no density to the areas of maximum density. When the Density Multiplier is very high, there is a very sharp falloff, making the volumetric shape have much sharper contours.
Extra particles