Thermocapillary　convection　and　its　stability　are　of　particular　importance　during　the　floating　zone　crystal　growth　process.　In　this　paper,　three-dimensional　(3D)　transient　numerical　simulations　are　conducted　to　study　the　onset　and　general　features　of　thermocapillary　instabilities　in　half　zone　liquid　bridges　of　low　Prandtl　fluid　(Pr　=　0.01)　with　non-equal　disks　under　microgravity.　The　effect　of　disk　radius　ratio　on　the　critical　conditions　is　investigated.　The　results　reveal　that　both　the　first　critical　Reynolds　number　Rec1　and　the　second　critical　Reynolds　number　Rec2　are　sensitive　to　the　disk　radius　ratio.　However,　for　a　liquid　bridge　with　fixed　length　and　volume,　varying　the　disk　radius　ratio　does　not　change　the　critical　azimuthal　wave　number　of　the　first　bifurcation,　as　well　as　the　critical　oscillation　mode　of　the　second　bifurcation.　Characteristics　of　the　3D　steady　thermocapillary　convection　and　the　3D　oscillatory　thermocapillary　convection　are　presented.　For　the　supercritical　state　at　Re　=　1.2Rec1　after　the　first　bifurcation,　the　flow　is　3D　steady.　The　deviations　between　the　amplitudes　of　azimuthal　flow　in　liquid　bridges　with　different　disk　radius　ratios　are　insignificant.　For　the　supercritical　state　at　Re　=　1.2Rec2　after　the　second　bifurcation,　the　flow　is　3D　oscillatory.　The　oscillating　frequency　decreases　with　disk　radius　ratio.　The　oscillating　frequency　in　a　liquid　bridge　with　a　convex　free　surface　is　higher　than　that　in　one　with　a　concave　free　surface.　©　2021　Elsevier　B.V.