The paper presents theoretical and experimental investigations of the behavior of an electrolyte solution with three types of ions near an ion-selective microparticle with electrokinetically and pressure-driven flow. A special experimental cell has been developed for the investigations. An anion-selective spherical particle composed of ion-exchange resin is fixed in the center of the cell. An enriched region with a high salt concentration appears at the anode side of the particle when an electric field is turned on, according to the nonequilibrium electrosmosis behavior. A similar region exists near a flat anion-selective membrane. However, the enriched region near the particle produces a concentration jet that spreads downstream akin to a wake behind an axisymmetrical body. The fluorescent cations of Rhodamine-6G dye are chosen as the third species in the experiments. The ions of Rhodamine-6G have a 10-fold lower diffusion coefficient than the ions of potassium while bearing the same valency. This paper shows that the concentration jet behavior is described accurately enough with the mathematical model of a far axisymmetric wake behind a body in a fluid flow. The third species also forms an enriched jet, but its distribution turns out to be more complex. The concentration of the third species increases in the jet with an increase in pressure gradient. The pressure-driven flow stabilizes the jet, yet electroconvection has been observed near the microparticle for sufficiently strong electric fields. The electrokinetic instability and the electroconvection partially destroy the concentration jet of salt and the third species. The conducted experiments show good qualitative agreement with the numerical simulations. The presented results could be used in future for implementing microdevices based on membrane technology for solving problems of detection and preconcentration, and thus simplifying chemical and medical analyses utilizing the superconcentration phenomenon. Such devices are called membrane sensors, and are actively being studied.