the way i picture it, latrines would work like beds and tables, you go to it in (q)uery mode and define a bathroom, you would also be able to (d)esignate, or (i)dentify, or perhaps make a stock(p)ile for solid, and liquid waste, that is where dwarfs would go for doing their necessities in the absence of a bathroom within a reasonable distance.
You would also be able to tag latrines as well as bathroom buckets and the non-bathroom areas for bathroom related activities for usage with only liquid and only solid waste (so you don't have to separate the two later on to use them.
Solid waste (aka shit) without enough water would go first muddy, then solid, muddy would not move much distance on it's own, and solid would just stay where it is. You would need to keep a constant flow of fresh water in he sewers or else risk the sewer getting clogged, and if too much solid was is being deposited in proportion to the water flow, the water wouldn't be enough and the sewer would get clogged too. Solid waste touching more solid waste would diffuse it's humidity, going in the direction of the least moist ones, the driest ones sucking moisture faster than the less dry ones, you can "melt" a wall of solid waste with enough water, but if there too much solid waste coming in proportion to the the inflow of water, the water would just get absorbed and distributed among the growing volume of not all that moist solid waste. When a liquefied solid waste flows over a tile with solidified solid waste, the moisture level of the two is mixed and the result of both the volume and the moistness of the solid waste in the tile is assigned to the tile in place of what was there before (so they will mix, if there are equal volumes but opposite extremes of moistness getting in contact with each other, the result would be both would become muddy, but if there one of them has more volume than the other, then the the one with the least volume would have it's moistness changed more, if they are equal volume but one is almost muddy, then the one that is almost changing would change to muddy, and the other one would just be much less moist or dry). The flow of moistness would be divided if there are more than one neighbor tile with solid waste, weighted by the moistness level of each neighbor in comparison with the tile in question
edit: oh, and solidified solid waste would affect which way things flow, if the it's too high in comparison to mud and liquified solid waste they would tend to flow around it (though still exchanging moistness.