This paper examines particle trapping and release in confined microvortex flows, including those near a solid surface due to variations in the electrokinetic slip velocity and those at a liquid-gas interface due to an external momentum source. We derive a general analytical solution for a two-dimensional microvortex flow within a semicircular cap. We also use a bifurcation theory on the kinetic equation of particles under various velocity and force fields to delineate the conditions for a vortex trap, a point trap, a limit cycle trap, and the selective sorting of the particles into different traps. In the presence of only divergence-free forces on suspended particles, we find that two parameters, such as those related to Stokes drag, gravity, and flow vorticity, are sufficient to classify all the trap topologies for a given slip velocity distribution. We also show that nondivergence-free forces such as nonuniform repulsion or attraction can capture suspended particles in one trap and selectively sort a binary suspension into different traps.

In this article, we investigate theoretically electro-osmotic flow set up by charged strips on an otherwise uncharged surface. Starting with a single-strip problem we demonstrate that for simple polynomial surface charge distributions several basic solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provide a more lucid way of revealing the flow features. These solutions reveal two types of flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and antisymmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions. We further extend the analysis to two uniformly charged strips and show how the flow characteristics vary with the strips' dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic vortices is also investigated theoretically for the first time. We show that in collaboration with short-range attraction effects the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.