When I was running a few days ago I thought of an analogy that does a really good job illustrating the workings and behavior of pH buffers and what happens when they are mixed.
Envision a system where there is a reservoir that has a large diameter at a certain height and that diameter then reduces to a narrow tube above and below it. Connected to that reservoir is a sight glass.
Now think of the pH of the system as the water level seen though the sight glass. Just looking at that water level will not tell you how much water the reservoir can hold. This is the same with pH. pH does not tell you how well it is held in place. You’ll have to add a measured amount of water to the system to judge the size of the reservoir by observing the change in water level. A small reservoir will result in a large change of the water level while a large reservoir will cause only a small change in water level.
The same is true for pH and what happens to pH when you add a known amount of an acid or a base to a substance of unknown buffer capacity.
It is also true that the buffer capacity of that model with the reservoir depends on the current height of the water level. As seen below the bulge, where the water level will only change a little, may sit at different heights for different systems. Just like a pH buffer has its best buffer capacity at a certain pH range.
Now use this model to represent malt and water:

Malt has a large buffer capacity and in this case its “natural” pH is 5.5 This is the distilled water mash pH. Water , on the other hand, is a weaker buffer than malt. And in this case the added water has a pH of 8.

When you dough-in you connect both systems and the water level (I.e. pH) settles at a point between the grist’s pH and the water’s pH. At what point exactly depends on the size of the respective reservoirs (i.e. the buffer capacities). For the malt that buffer capacity is largely determined by its weight and for the water it is determined by its volume and alkalinity.
I think I’ll have to expand further in these models in the future since they do seem to work better than the model with the springs that I have been using before.
Kai