  In this paper we study the dynamics of a layer of incompressible viscous
fluid bounded below by a rigid boundary and above by a free boundary, in the
presence of a uniform gravitational field. We assume that a mass of surfactant
is present both at the free surface and in the bulk of fluid, and that
conversion from one species to the other is possible. The surfactants couple to
the fluid dynamics through the coefficient of surface tension, which depends on
the the surface density of surfactants. Gradients in this concentration give
rise to Marangoni stress on the free surface. In turn, the fluids advect the
surfactants and distort their concentration through geometric distortions of
the free surface. We model the surfactants in a way that allows absorption and
desorption of surfactant between the surface and bulk. We prove that small
perturbations of the equilibrium solutions give rise to global-in-time
solutions that decay to equilibrium at an exponential rate. This establishes
the asymptotic stability of the equilibrium solutions.
