Experiments and numerical simulations are conducted in order to study the causes and solutions for the Ti inhomogeneity problem in Ti doped sapphire Micro-Pulling-Down (mu-PD) growth. The measurement and modeling of the thermal and flow fields, electromagnetic field, Ti concentration in the molten zone and along the fibre axis are compared. For the mean Ti concentration along the fibre and temperature along the iridium crucible, the modeling results are consistent with experiments. Results showed that for high pulling rate, the mass transfer in the capillary is dominated by convection. Marangoni convection is strong in the meniscus due to the large temperature gradient, which has great impact on the Ti distribution for different fibre radii. For high pulling rate, Ti concentration increases quickly from the seed along the fibre axis, and reaches a constant value after about 0.5-2 mm. Radial segregation is high for large diameter fibres. The constant Ti concentration along the fibre axis is increasing when increasing the fibre radius from 0.2 to 0.6 mm. For 0.8 mm, it decreases due to the change of the vortex. At low growth rate, the transport in the capillary is diffusive, back to the crucible, which leads to a Scheil-like Ti distribution, in full agreement with the experimental results.