[en] The plasmodium of the unicellular slime mould Physarum polycephalum forms an extended vascular network in which protoplasm is transported through the giant cell due to peristaltic pumping. The flow in the veins is always parabolic and it performs shuttle streaming, i.e., the flow reverses its direction periodically. However, particles suspended in the protoplasm are effectively and rapidly distributed within the cell. To elucidate how an effective mixing can be achieved in such a microfluidic system with Poiseuille flow, we performed micro-particle imaging velocimetry experiments and advected virtual tracers in the determined time-dependent flow fields. Two factors were found to be crucial for effective mixing: (i) flow splitting and flow reversals occurring at junctions of veins and (ii) small delays in the reversals of flows in the veins at a junction. These factors enhance the distribution of fluid volumes and hence promote mixing due to chaotic advection. From the residence time distributions of particles at a junction, it is estimated that about 10% of the volume is effectively redistributed at a junction during one period of the shuttle streaming. We presume that the principles of mixing unravelled in P. polycephalum represent a promising approach to achieve efficient mixing in man-made microfluidic devices. (paper)