Particles are separated from a source viscoplastic fluid by flowing streams of the viscoplastic fluid and a destination fluid in parallel streamed relationship inside a rotating cylindrical annulus (FIG. 16 (106, 102b) by using baffles (112, 114) to introduce each fluid independently at an inlet lower end of the annulus and for separating the upper streams consisting of an un-yielded source and destination flow proximate the radially innermost side of the annulus, a bulk axial flow in a more central region and a yielded layer destination flow adjacent the radial outermost side of the annulus which contains the particles that have separated. Inlet and outlet baffles are provided at each end of the vertically oriented device to maintain the flows discrete on entry and to maintain the separated flows discrete on exit so as to facilitate removal of the component flows from the fractionator. The flow is maintained as laminar Poiseuille flow by adjusting the flow rates of the source and destination fluids. Supporting theory is provided with derived parameters for controlling the flow and predicting results. Two major embodiments are presented the first based on axial inlet flows (FIG. 17) and the second based on radial inlet flows (FIG. 8). Pump blades (170), (176) (FIG. 17) may be provided for the axial inlet/outlet embodiment in the region of the separated flow channels. Modular construction is shown in FIGS. 1-3.