Rotational flow through narrow axial channels is considered in connection with a proposed technique to sort and separate particles according to sedimentation velocities. Nonlinear and linear axisymmetric flow through two channels connected by a slot in the vertical wall is studied numerically. A linearized formulation for the three-dimensional flow through a circumferentially blocked channel, with arbitrary positioning of the inlets and outlets, is examined analytically. Both approaches indicate that to have a sharp criteria for fractionation, the vertical shear layers on the channel walls must overlap. Otherwise, Coriolis effects, accompanying a strong azimuthal motion, make the sorting less precise. Results of an exploratory experiment with a simple two-stage machine demonstrate the feasibility of the basic process for simultaneous and continuous separation and fractionation.