The Microfluidic probe (MFP) is a mobile channel-less microfluidic system where a liquid is injected from one aperture into one open space and re-aspirated from a second aperture at a higher aspiration flow rate forming a Hydodynami-cally Confined Stream (HCS). In this work, we characterize both analytically and numerically the geometry of the HCS and the shear stress at the bottom substrate with respect to the ratio of aspiration to injection flow rates, gap size, and the diffusion coefficients of the injected liquid in the solute. The finite element method is used to simulate numerically the flow confinement, and dimensionless analysis is employed to characterize the concentration and shear stress profiles. We found that width and length of the HCS increases linearly with increasing gap size, and it shrinks linearly with respect to the ratio of aspiration to injection flow rates. Thanks to the establishment of the scaling laws and the numerical model we developed here, the parameters of the MFP can be predicted easily through simulation instead of having to determine them experimentally by trial and error.