E. Sanger-Shepherd and O.M. Barlett were perhaps the 1st to propose the use of a relief matrix to produce dye-imbibition prints in 1902. US Patent #728,310
One of Ives' most important contributions to the art, one that was used in all subsequent schemes, was the effect of the pH of the dye-bath on contrast. Since acid raises gelatin's affinity for the dye, lower pH will cause more dye to enter the matrix, thus, higher contrast will be obtained. To have 3 or 4 dye-solutions of each color, each with differing acid contents, would be an excellent method to have contrast control in the transferring stage. This is described in the British Journal of Photography, Vol 46 (1899), p. 409, 470 & 537.
Some of Ives' Patents are: USP1,106,816 & USP1,160,288, Ger.P.308030, Eng.P. 15823/13 & 15823/14, Fr.P. 463,737.
My explanation of why the dye transfers into the receiving paper might've been somewhat misleading The main reason for the transfer, according to Friedman, is that the matrix is necessarily very hard (tanned) comapared to the receiving sheet, which will have softer gelatin, and thus the migration.
The acid rinse after soaking the matrices in their dye baths should be a 10% solution of acetic acid, not 2%. This highly acidic bath will remove the excess dye on the matrix, but will cause the gelatin in the matrix to adhere tightly. The matrices can be left in this, registered if necessary, until ready for transfer. This prevents the possibility of them drying out between transfers.
A recommendation for testing textile dyes is a 2% dye solution in 5% acetic acid. However, this was for the purpose of making transparencies, so for prints the 2% concentration of dye could be reduced significantly.
Mat or Semi-Mat fixed out photo papers will work best as receiving papers.
A UV-restraining dye (yellow) has been added to matrices historically as standard practice to limit the depth of the relief. This might be something to explore in the future. Unfortunately, the K-dichromate stain is not sufficient to have a great affect, according to Friedman.
Lastly, if anyone is confused or needs clarification on something, it would be my pleasure to talk about it.