The present invention provides apparatuses and methods for continuously separating particles of interest from a heterogenous particle population. the heterogeneity can be based on, for example, magnetic susceptibility, particle size, thermal diffusion, phase solubility, and combinations of the preceding. Based on the heterogeneity, a separation force capable of exploiting the separand (i.e., particles subject to the separation process) is provided. The various embodiments of the present invention preferably employ an annular separation channel, appropriate separation force and flow compartments. In a first embodiment, an annular separation channel having semi-permeable inner and outer cylindrical walls is used to generate lateral convection forces. In a second embodiment of the present invention, an annular separation chanel having heat conductive inner and outer cylindrical walls is used to generate thermal diffusion forces. In a third embodiment, an annular separation channel having non-permeable inner and outer cylindrical walls is used to generate a solubility difference separation force based on solubility coefficient differences between phases of flow compartments. In a fourth embodiment, an annular separation channel having electrically conductive inner and outer cylindrical walls is used to generate an electrophoretic separation force. In a fifth embodiment, an annular separation channel having electrically conductive inner and outer cylindrical walls is used to generate a dielectrophoretic separation force. Yet other embodiments of the present invention provide for the combination of separation forces including lateral convection, thermal diffusion, solubility difference, electrophoretic, dielectrophoretic, and magnetic separation forces.