The paper is focused on the mechanism of mixing process in a manifold which mimics the geometrical properties of vascular systems. The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. However, in contrast to biological vascular networks, which are composed of circular pipes, microfluidic manifolds are fabricated using a range of processes (photolithography, wet or dry etching, surface micromachining), which result in channels of rectangular or trapezoidal sections and constant depth throughout the device. The paper focuses on constant-depth rectangular channels often employed in lab-on-a-chip systems and provides comprehensive numerical studies of mixing in such geometry. It also presents simplified analytical estimation on how the coefficient of mixing depends on the number of generations and Reynolds number. The main goal of the paper is to describe the concept of a mixer which provides almost perfect mixing at the outlet regardless of the value of Re and for a minimal number of manifold's generations.