As you are working with a 3 dimensional mesh, the vector function space has three components:
T_S_1 = interpolate(S_11, T)
T_S_2 = interpolate(S_12, T)
T_s_0 = Function(T) # Function containing 0 values
assigner = FunctionAssigner(V, [T, T, T])
assigner.assign(v, [T_S_1, T_S_2, T_s_0])