  In this work we study the influence of orbital viscosity on the dynamics of
the order parameter texture in the superfluid B-phase of $^3$He near a moving
bounda ry. Based on the redistribution of thermal quasiparticles within the
texture, we develop a model which bestows a significant effective mass on the
interface, an d gives a new mechanism for friction as the boundary moves. We
have tested the model against existing data of a moving A-B interface whose
motion was controlled using magnetic field. The model allows some predictions
in experimental situations which involve texture rearrangement due to the
B-phase boundary motion.
