We validate the use of non-linear signal phase evolution to estimate the susceptibility and orientation of sub-voxel structures. Capillary tubes filled with ferritin solutions of varying susceptibility were positioned in a water phantom. Multi-echo gradient-echo scans (100 echoes, echo-spacing=0.6ms) were acquired for multiple orientations of the capillaries with respect to the magnetic field. Fitting a 2-compartment model to the complex signal, processed using frequency difference mapping (FDM), resulted in susceptibility and signal fraction estimates in good agreement with theoretical predictions. Non-linear phase evolution, processed using FDM, may provide new insight into microvascular structure and physiology.