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In this work, experimental observations of the microstructure of neutralized polyacrylic acid (Carbopol) in water by confocal microscopy under both static and flow conditions are presented. In the former case, a Carbopol-rich phase made by swollen particles dispersed in a water-rich continuous phase is found, so that the system will be henceforth referred to as a suspension, as long as particles are observed. The swollen particles form dendritic-like aggregates, which span the entire solution volume above a critical concentration. In such conditions, a percolated network can be formed, leading to the onset of a yield stress behavior. By separating the dispersed and continuous phase through centrifugation, we provide evidence of a miscibility gap in the phase behavior of Carbopol in water. When the Carbopol suspensions flow in a microfluidic capillary, a particle-concentrated plug core can be distinguished from a less concentrated layer corresponding to a steep velocity decrease. Confocal imaging also shows that the apparent slip found in Carbopol suspensions is due to a particle-concentrated near-wall region, where no flow is observed. Such flow-induced microstructure is responsible for the different nature of the yield stress values measured by classical rheometry and by flow velocimetry. While the yield stress measured by the former can be here related to the presence of a percolated network, the yield stress obtained from the velocity profile is due to the heterogeneous particle distribution along the capillary radius. These results provide a novel insight on the mechanisms governing yield stress in complex fluids. [ABSTRACT FROM AUTHOR]