  We develop an analytical theory of adhesive interaction of viscoelastic
spheres in quasistatic approximation. Deformations and deformation rates are
assumed to be small, which allows for the application of the Hertz contact
theory, modified to account for viscoelastic forces. The adhesion interactions
are described by the Johnson, Kendall, and Roberts theory. Using the
quasistatic approximation we derive the total force between the bodies which is
not sufficiently described by the superposition of elastic, viscous and
adhesive contributions, but instead an additional cross-term appears, which
depends on the elastic, viscous and adhesive parameters of the material. Using
the derived theory we estimate the contribution of adhesive forces to the
normal coefficient of restitution and derive a criterion for the validity of
the viscoelastic collision model.
