  We investigate the van der Waals friction between graphene and an amorphous
SiO$_2$ substrate. We find that due to this friction the electric current is
saturated at a high electric field, in agreement with experiment. The
saturation current depends weakly on the temperature, which we attribute to the
quantum friction between the graphene carriers and the substrate optical
phonons. We calculate also the frictional drag between two graphene sheets
caused by van der Waals friction, and find that this drag can induce a voltage
high enough to be easily measured experimentally.
