Immersion vs Drip
Some brew methods are hybrids like the Aeropress and Clever Dripper, but in general, an immersion brew is any brew method which hits its maximum dilution level at the beginning of the brewing process, while a drip brew is any gravity fed brew method that involves the erosion of solids through some kind of strainer/filter.
The Sedimentary Filter Bed
A fundamental difference between drip and immersion brews is that drip coffee forms a sedimentary filter bed and with a few exceptions (notably the Clever Dripper and the Aeropress) while immersion brews do not. The filter bed helps clarify brews and is best left relatively static after an initial wetting phase. If you vigorously agitate the coffee bed after the pre-wetting phase, you promote a dramatic rearrangement of coffee particles where all the finest particles gather at the bottom of the coffee bed. This causes the flow rate to dramatically slow down. Some agitation such as the Rao Spin during the drawdown of a pour-over can be very effective. (For a single cup pour-over, Scott performs this spin at 1min. 45sec.) This can help to flatten the coffee bed to prevent channelling and to ensure grinds aren’t left to under extract above the water line. However, as a general rule, we don’t advocate excessive stirring of the coffee bed after it is formed.
The filter bed depth has a significant effect on the flow rate in drip coffee. If you upscale a brew on the same ratio but maintain the same grind setting, invariably the brew cycle will take longer. One explanation for this is Darcy’s Law, an equation which describes the movement of liquid through a porous medium — in this case, water through a coffee bed. According to this, the flow rate of water through the bed decreases with the distance it has to travel — if you have a deeper bed, it’ll take longer to flow through.