This paper is concerned with the investigations and modeling of the unsteady diffusion process along a straight micro-channel with a cross section of 380 mu m x 360 mu m. The studied process is characterized by small Reynolds numbers (Re < 10) and high Peclet number (Pe > 1000). The 3D computations of the coupled momentum and diffusion equations for isochoric motions are performed with the FLUENT code using the unsteady solvers for both equations. In the limit of stationary solutions, the numerical results are validated by direct flow visualizations and experimental data using confocal microscopy. The computed distributions of concentration provide qualitative and quantitative information on the transitory diffusion process and the rate of solute spreading with in the investigated geometry. In particular, the pattern of the "butterfly effect" is represented and analyzed during the non-stationary dynamical process. The work is relevant for the design of novel microfluidics applications where the control of diffusion processes at the walls are important (absorption, extraction, capture of molecules or nano-particles). (C) 2011 Elsevier Ltd. All rights reserved.