  We have studied the shear and bulk viscosities of asymmetric nuclear matter
in the mechanical and chemical instability region based on IBUU transport
simulations in a box system. The Green-Kubo method is used to calculate these
viscosities with a prepared dynamically equilibrated nuclear system with hot
clusters. While the behavior of the shear viscosity is largely affected by
energy-dependent nucleon-nucleon cross sections, the bulk viscosity increases
significantly in the presence of nuclear clusters compared to that in uniform
nuclear matter. Increasing isospin asymmetry generally increases both
viscosities, while their behaviors are qualitatively modified once the isospin
asymmetry is large enough to affect significantly the spinodal region. Our
calculation shows that the bulk viscosity is more sensitive to the nuclear
clustering than the shear viscosity, and is thus a robust quantity related to
the phase diagram of asymmetric nuclear matter.
