Three recent microgravity experiments have been hampered by convection caused by unwanted voids and/or bubbles in the melt. In this work, we present a numerical study to describe how thermocapillary convection generated by a void or bubble can affect a typical microgravity solidification process. A detailed numerical model for the Bridgman solidification of a doped single crystal from its dilute binary melt is developed which solves the. quasi-steady Navier Stokes equations together with the conservation equations for transport of energy and species. The complicating effects of thermocapillary convection generated by the void and solutal rejection at the melt-solid interface are included, Numerical simulations indicate that void-generated thermocapillary convection can affect segregation patterns drastically, especially, if the thermocapillary vortex penetrates the solutal boundary layer at the growth interface. Two lateral void positions are considered with the void placed either in the center of the ampoule or on the side wall. From a transport point of view, three different segregation regimes are identified for each lateral void location based on the distance between the void and the growth interface. These range from a diffusion-controlled regime where most of the radial nonuniformity in the interfacial composition is due to the interface curvature with minimal convective effects to a fully mixed regime where the penetration of the solutal boundary layer by the thermocapillary vortex tends to homogenize the interfacial compositions drastically. Naturally, the extent of each of three regions will not only depend on the size and lateral position of the void but also on the material and growth properties of the system under consideration.