Likely lots of people have wondered about this question,
as indeed that's exactly what happens when liquid is first
added to a fat and flour mixture. The purpose of the fat
is to coat the flour particles, to keep them from clumping
together so they swell independently as the liquid is
a sauce begins to thicken, the starches within each
flour particle take up liquid. Initially, however, there
is much less liquid in proportion to the number of thirsty
starch grains. Thus, the mixture becomes very thick,
very quickly. When the starch granules initially swell
by absorbing liquid, you've basically made a thickened
paste. Once they've been exposed to liquid and dampened,
starch granules are primed to swell more as additional
liquid is added.
As the proportion of liquid increases, the starch granules
continue to absorb more liquid and swell in a process
called "gelatinizing." This mixture becomes a sauce
(or thickened liquid). Stirring is important to keep
the starch granules, as well as starch that spills from
ruptured granules, suspended and moving, which reduces
the formation of lumps. Stirring also keeps the temperature
of the sauce uniform so the sauce stays smooth as each
starch granule takes up its share of water.
Though sauce-making is a basic task in cooking, the
process by which they thicken is quite fascinating.
Thanks for asking the question.