  We study the tensor structure function $b_1\xq$ in deep inelastic scattering
(DIS) of an electron from a polarized deuteron target. We model the
electron-nucleon cross section at the starting point for $Q^2$ evolution by
vector-meson-dominance (VMD). Shadowing due to the double-scattering of vector
mesons, along with the presence of a d-state admixture in ground state deuteron
wave function gives rise to a non-vanishing contribution to $b_1\xq$. Although
significant at large Bjorken $x$, the restoration of rotational symmetry for
small $x$ ($\leq10^{-3}$) requires that $b_1^{(2)}\xq$ approach zero as $x\to
0$ in this model. If the model is valid, it should apply within the range of
present fixed target experiments.
