We consider a planar interface between strongly-segregated homopolymer
s subjected to steady shear in the plane of the interface. We develop
a constitutive equation for stress relaxation in an inhomogeneous syst
em for chains obeying Rouse dynamics. Using this equation, the interfa
cial viscosity for a symmetric blend is found to be zeta b(2)/(6 chi n
u(0)) in agreement with a scaling prediction due to de Gennes, where z
eta is the bead friction coefficient, b is the segment length, nu(0) i
s the segment volume and chi is the Flory-Huggins interaction paramete
r driving the phase separation. We generalize our results to asymmetri
c blends and describe a phenomenological extension to entangled melts.