My banana Muffins won’t rise like I want – Why

It sounds like your bananas might not be ripe enough. If they're really ripe, you can mash with a fork and with very little effort turn them into a nice smooth goopy mush. There shouldn't be any pieces left to sink. You want to wait until they're so ripe you wouldn't want to eat them - blackening skin, very very soft.

First, you must assume a spherical muffin. This is a silly but fun question, so lets think about the limiting factors.

What if you could scale down everything (the pan, the size of the ingredients, the size of the gas cells, everything else) uniformly.

If that could be done, muffin tops would be a uniform phenomenon at any size.

So, what can we not scale down uniformly?

It seems to me that there are to major factors that cannot be uniformly scaled down in actual practice:

1. The cell-size of the starch matrix that is expanded by the leavening. It has a minimum size, and one would imagine that muffins must be macro-scaled compared to the cell size in order to work.

   Since the cell size is visible as the grain in an actual muffin, the muffin has an internal structure on the order of millimeters, typically (I haven't baked muffins just now to measure their structure size) based on my best guess and recollection. This is taking into account some of the larger scale structures within the muffin, like bubbles, and that "grain" which is composed of even finer "grains".

   So one limiting factor would be that the muffin would have to be several orders of magnitude larger than tenths of millimeters, say three orders of magnitude. That would bring the limiting size of muffin-topped muffins to about a centimeter across.

2. Heat penetration.

   We can assume the rate of cooking in the muffin is proportional to the radius of the muffin at any given size, as a first order approximation, for any given temperature.

   At some point, the muffin will either cook through before it can expand, or burn on the outside before it cooks through.

   The problem with tiny baked goods is that they are outside any effective balance of temperatures. Either they cook through and start drying out without any good crust development, or the outside is overdone before the inside gets cooked.

   The requirement for muffins is even more balanced: it has to heat the inside enough to trigger the oven spring from the leavening before the outside is set enough that it cannot expand, while still being able to cook all the way through, set the outside, and get decent crust development.

   This is very hard to manage.

Practically, it is likely that the current mini-muffin pan size (a couple of centimeters across) is about as small as you can go without having to start taking drastic measures with the recipe. The main problem is heat management: getting good oven spring without the muffin setting too fast, while cooking it through, and yet having nice crust development on the outside.

You can have smaller baked goods, but they have a much simpler structure. They are called cookies. Most muffin batters would make an effective drop cookie, again probably down to about 2 cm. They would be essentially all muffin top.

For a look at some of these practical factors, see:

See also: How to adapt brownie recipe to cook well in a mini-muffin tin?