The action of acids in this context is very similar to their effect as accentuators , but in reverse. This applies to both tissue groups and those on the dye. In effect, the acid used to differentiate will compete with the anions of the tissue for the dye cations. Since the differentiating acid is deliberately chosen to be a stronger anion than the tissue groups, it will dissociate more thoroughly and will invariably win the competition. The result is that the dye is preferentially removed from the tissue by dissolving it out.
Bases work much the same with acid dyes.
They compete with tissue cations for the anions of dyes and disrupt their attachment to the tissue. The dye is removed by dissolving into the differentiating solution. Controlling this process is quite simple. Alternatively, a weaker acid that dissociates less could be substituted. Likewise, a less polar solvent will tend to slow down the differentiation due to lower ionisation of the acid.