How does a maple syrup evaporator work? Some background info on what an evaporator is:
It is a system of metal pans set over a heat source.  Sap constantly enters the first pan controlled by a float valve to keep a constant depth.  The pans have channels which are open to each other at alternating ends, so that the sap flows back and forth in a serpentine pattern.  At the end of the pan system there is a manual valve where you periodically draw off finished syrup.  From the beginning of the pan system to the end there is a ever-increasing concentration of sugar.  
My question is, how does the sap get more concentrated towards the end of the pan?  Or conversely, how is it that the sap doesn't maintain a homogenous sugar concentration throughout?  (If you let the fire go out, once the sap cools it will redistribute itself until it is homogenous.) 
I think somebody will probably tell me it has to do with the distance the sap has flowed through the pan by the time it gets to the other end (it would be a linear distance of about 24 feet in my system) but I don't think that answers the question because when you first start a batch, you flood the whole system with cold, fresh sap, all of uniform sugar content, and then you start the fire.  It doesn't take long before there is a visible color difference between each channel of the final pan, with the darkest one being next to the draw-off valve.  
And no, it's not flow caused by the pans being angled downwards either (a BS answer posted on yahoo!answers to a similar question).  The pans are perfectly level.  And as far as I can tell the heat intensity from the fire below is uniform at least for the final four channels, which are where you really begin to see visible color graduation as it becomes syrup.

There is one detail that I didn't describe at first because I couldn't figure out how to without a drawing, so now that I've added the drawing I'll elaborate on that.  The first pan, where the sap goes in, has flues, which are deep, narrow vertical pockets in the bottom of the pan, which reach all the way down into the stove itself.  The flames actually pass between the flues on their way to the stovepipe.  This (obviously) greatly increases the surface area being heated.  I don't know if this changes anything but I thought I should add it.  
 
 A: I can't vouch for the answer here, but it purports to be the reason.

The evaporator is perfectly level. If
  that's the case, visitors often wonder
  how it is that sap moves through the
  pan. Forgotten is the fact that rising
  steam is the equivalent of dipping or
  draining liquid from the pan. A level
  bottom means that sap moves under the
  pull of gravity as water leaves the
  pan as steam. (That, of course, is the
  whole objective of the process!) The
  sugar stays behind forming a syrup of
  increasing sweetness to make the
  finished product. At that point, the
  sugar concentration is at 60% and the
  boiling point is elevated about 7
  degrees. The difference in viscosity
  coupled with the baffles in the pan
  allows finished syrup to accumulate in
  the last section without our ever
  having to mechanically separate the
  final product. At the end of the
  season or if, for some reason, we wish
  to shut down the process and empty the
  pans, it is possible to draw off
  virtually all the syrup. One could
  not, of course, simply drain the pan.
  The fire would cause melt-down in a
  matter of seconds. Instead, soft water
  from the farm pond takes the place of
  the entering raw sap and supplies the
  necessary cooling liquid. Boiling
  continues, and because of their
  different viscosities, the syrup and
  pond water do not mix significantly.
  This same situation occurs when oils
  of different densities flow
  sequentially in a transcontinental
  pipeline. Very little mixing occurs at
  the interface between the two
  products. Virtually all the syrup can
  be drawn off before the pond water
  arrives at the discharge valve.

I suppose the big question is why doesn't the liquid become homogeneous?  That's probably due to the baffles limiting the interface significantly - reducing the the ability of the most concentrated fluid to mix with the most diluted.  
A: In answer to how does your evaporator work:  in the pan there is a frontal boundary of sugar concentrations, the long narrow compartments minimize this frontal boundary.  The effectiveness of the evaporator is determined by the travel speed through the compartments versus the migration of sugar as it attempts to dissolve into the solution, thus segregating the fresh incoming sap from that boiled for a period of time allowing us to draw syrup continuously as sap is added continuously.  Keeping steady feed, steady heat, minimal foam, and steady draw minimizes the intermixing that might occur.  The density or the viscosity of the product has absolutely no bearing on this process.  
A: What's going on is that there are two flows here, a gas flow (produced by boiling) and a liquid flow. The liquid flow is from the entrance to the exit while the gas flow is to the air. The gas flow is controlled by allowing only one exit for the gas, near the place where you add syrup.
The longer the fluid spends in the contraption the more water is boiled out of it and the more sugar that is left. So by the time the liquid gets to the output spigot it's spent a lot of time boiling and has lost a lot of water.
The process is similar to distillation in that the steam preferentially carries off water rather than sugar. This suggests that a more efficient method of processing maple syrup is distillation, and that designing an evaporator so that it mimics the distillation process as much as possible is a good idea. The US Forest Service agrees:
Processing Maple Syrup with a Vapor Compression Distiller: An Economic Analysis Lawrence D. Garrett, Forest Service Research Paper NE-385, 1977
Forest Service, U.S. Department of Agriculture,
Northeastern Forest Experiment Station
6816 Market Street, Upper Darby, PA 19082

A test of vapor compression distillers
  for processing maple syrup revelaed
  that (1) vapor compression equipment
  tested evaporated 1 pound of water
  with 0.047 pounds of steam equivalent
  (electrical energy); open-pan
  evaporators of similar capacity
  required 1.5 pounds of steam
  equivalent (oil energy) to produce 1
  pound of water; (2) vapor compression
  evaporators produced a syrup of equal
  quality to that from a conventional
  open-pan evaporation plant; and (3) a
  central plant producing 8,000 gallons
  of syrup per year should yield a
  return of 16 percent on investment.
  Increasing annual product output
  should increase the return on
  investment.

A: 
(If you let the fire go out, once the
  sap cools it will redistribute itself
  until it is homogenous.) I think
  somebody will probably tell me it has
  to do with the distance the sap has
  flowed through the pan by the time it
  gets to the other end (it would be a
  linear distance of about 24 feet in my
  system)

As You write, the pans all have a level "floor". This enables the 
concentrated (and higher density) sap from the last pan to flow 
as a stream close to the bottom backwards, the lighter sap from 
the first compartments will stream on top "downwards". 
(This is similar to salt water streaming "upward" at the mouth of 
a river from sea. ) In case the evaporator then rests for longer time, 
diffusion will equalize the sugar concentration vertically. That will 
take days I think. The stream "downward" of the low concentration sap 
on top at high temperature (fire just went out) is faster, and that 
is what You "see" or taste when testing with a finger dipped in. 

but I don't think that answers the
  question because when you first start
  a batch, you flood the whole system
  with cold, fresh sap, all of uniform
  sugar content, and then you start the
  fire. It doesn't take long before
  there is a visible color difference
  between each channel of the final pan,
  with the darkest one being next to the
  draw-off valve. And no, it's not flow
  caused by the pans being angled
  downwards either (a BS answer posted
  on yahoo!answers to a similar
  question). The pans are perfectly
  level. And as far as I can tell the
  heat intensity from the fire below is
  uniform at least for the final four
  channels, which are where you really
  begin to see visible color graduation
  as it becomes syrup.

This part I refuse to "believe".The problem I see is Your idea of 

uniform heat intensity from the fire

The process of evaporation in such a pan is controlled by the heat flux 
into the pan. (For every Joule of heat energy forced through the bottom,
You get a certain amount of water evaporated into steam). 
Maybe that heat flux is homogenous, maybe not, this is a very tricky business 
of construction. Without inspecting details of the fire grate / stack gas ducts / 
details of pans from below, I have no idea on "truth". 
In general and terms of chemical technology that pan(s) is a flow tube reactor (evaporator).
The bubbles generated by evaporation make the medium turbulent. 
Such a flow is rather easy to treat mathematically, because it can be 
approximated rather exactly by assuming plug flow with perfect mixing across 
the flow, and some minor mixing along (in direction of) flow. 
The channels conecting the pans are some restriction to longitudinal mixing.
The approximation is done by replacing this flow tube reactor by a cascade of the proper 
number of stirred reactors for each pan, and that cascades are cascaded to 
make tha model of the entire evaporator. 
The medium (sap) is getting denser along the path of flow, due to increasing 
sugar concentration. But at the same time the temperature increases, this will 
reduce the density due to thermal expansion. The net effect of concentration and 
temperature will lead to a flow as explained above (after shut down) This flow 
counter to net product flow would impair the evaporation efforts. So, if I had to 
construct such an apparatus, I would use a little bit of inlination and
more baffles to reduce this effect.
This is the theory You need to make an "ansatz" :=). 
In practice, I would try to find someone producing such evaporators, 
that people might know quantitatively what I can say only qualitative. 
There is some risk, that nobody ever developed those evaporators,
but all was done in small steps starting with pans from kitchen 
by village blacksmiths, then nobody knows exactly. 
PS
I just googeled for "maple syrup evaporator" to find a lot of pictures 
and some very instructive videos as well. 
One thing is important to Your question: 
All the evaporators use countercurrent heat exchange. 
(Sap flow is opposite to the flow of stack gas) 
This is done very simply by pouring the sap from bin to bin
with the most primitive tinkered evaporators, 
others have a continuous flow as You described. 
This means that 
Your idea of "uniform heat intensity from the fire" is not reality.
A: I have been boiling sap all weekend and have been wondering the exact same thing.  When you are not drawing off syrup, and only adding sap to one end of the pan, why is the concentration of sugar more at the end (where the syrup tap is) and the lowest where you drip the sap in?  
Okay - visualize the zig zag pattern of the pan as a long trough that goes left to right.  You dump sap in the left side only.  You are not drawing out of the right side yet.  Equivalent boiling is occurring over the entire surface.  Although there is no liquid coming out of the pan, the net flow of sap is from left to right because you are adding it to the right side, and it is being lost to the air at an even rate over the whole thing.  The speed of the water flow is the fastest on the left side, and the slowest on the right side.  As the water moves to the right, it also goes up, into the air as steam.  As the sugar in the water moves to the right is does not go up, it only stays in the pan.  The water/sugar on the left is moving faster, so it "leaves less sugar behind" and the water on the right moves slower, so "more sugar is left behind" leaving the sugar concentration on the right (or the end of the pan) greater than the concentration on the left (the beginning of the pan).
I will illustrate an analogy: Imagine a 1000 meter running race.  No imagine that the runners (the sap) have pockets full of sand with a holes in their pockets.  As soon as they start running, the sand starts running out of the holes in their pockets.  They are running really fast at first and the amount of sand on the ground represents the sugar content in the liquid in the evaporator pan.  They are getting tired half way through the race, thus leaving more sand per square inch on the ground.  At the end, they are pooped, and moving really slowly.  The sand is still spilling out onto the ground at the same rate (equal boiling rate over the whole pan).  The speed of each runner approaches zero as the near the end of the race.  The race track is covered with sand at the end.  More runners keep starting the race at you dribble sap in and they all run the same way - fast in the beginning, slow at the end.  Sand spills out at the same rate throughout the race.  Sprinkles of sand in the beginning, piles at the end.
I'm pretty sure this is whats going on here.  Osmosis is what describes why it becomes a uniform concentration when you stop dripping sap in and let it boil without taking any syrup off.
