Dye-based ink actually soaks into the cellulose fibres, giving a far richer colour and a wider Gamut of colours. The trade-off is that absolute sharpness in not achievable.
Pigment-based ink behaves completely differently. The ink is projected at the paper, the carrier body then evaporates, and the pigment adheres to the paper fibres. This results in a clear sharp image, but the colour does not have the same saturation as for dye-based inks.
Different grades or quality of paper will give different results for the same ink type. There are special photographic papers that only give the right result when matched with a specific ink. The ink has a solvent that etches into the paper and the pigment fills the etched area.
Paper left out in areas exposed to high humidity absorb moisture and alter the water content of the paper. This can adversely affect the way ink is absorbed into the paper and Bleeding results. The ink is often blamed, where in fact the problem is with the humidity or paper type.
It is important to set the printer's properties to match the paper being used and the type of print job. The printer automatically adjusts the amount of ink being delivered to match the settings.
Using a basic copy paper and setting the print properties to 'high resolution' or 'photo paper', 'gloss paper' etc. can cause quite extensive bleeding problems. Black will often penetrate
