consider two wires of different diameter. when current enters from that of greater diameter to lesser diameter drift velocity increases. which force causes it to increase?
it is really simple.
we have,current(I) through a conductor of the crossectional area of A is the product of the drift velocity(v) of the moving charges ,the area(A) and number of electrons(n)*the charge of a electron(e).hence
I=venA
or, v=I/(enA)
this relation shows that drift5 velocity is inversely proportional to the area of crosssection of the conductor.Hence if area decreases drift velocity increases.
HOPE THIS HELPS HIMAL
I don't think there's an external force involved, as it seems you have in mind, rather conservation of energy causes the drift velocity to increase, similar to http://en.wikipedia.org/wiki/Bernoulli%27s_principle" in fluid dynamics.