  We explore length segregation in binary mixtures of spherocylinders of
lengths $L_1$ and $L_2$ with the same diameter $D$ which are tangentially
confined on a spherical surface of radius $R$. The orientation of
spherocylinders is constrained along an externally imposed direction field on
the sphere which is either along the longitude or the latitude lines of the
sphere. In both situations, integer orientational defects at the poles are
imposed. We show that these topological defects induce a complex segregation
picture also depending on the length ratio factor $\gamma$=$L_2/L_1$ and the
total packing fraction $\eta$ of the spherocylinders. When the binary mixture
is aligned along longitudinal lines of the sphere, shorter rods tend to
accumulate at the topological defects of the polar caps whereas longer rods
occupy central equatorial area of the spherical surface. In the reverse case of
latitude ordering, a state can emerge where longer rods are predominantly both
in the cap and in the equatorial areas and shorter rods are localized in
between. As a reference situation, we consider a defect-free situation in the
flat plane and do not find any length segregation there at similar $\gamma$ and
$\eta$, hence the segregation is purely induced by the imposed topological
defects. It is also revealed that the shorter rods at $\gamma$=4 and $\eta
\ge$0.5 act as obstacles to the rotational relaxation of the longer rods when
all orientational constraints are released.
