The atomic (microscopic) diffusion of individual elements in stellar interiors and atmospheres lead to their accumulation or depletion in specific layers. The selective radiative accelerations on individual elements, which work in opposition to the effects of the pressure and thermal gradients, have important consequences. When acting on elements like iron or nickel, which are important contributors to the opacity in some stellar layers, the resulting overabundance can lead to global macroscopic effects, like extra convective zones or wave excitation by kappa mechanism. The competition between atomic diffusion and independent hydrodynamical processes including turbulent (macroscopic) diffusion has been extensively studied in previous years using parametrized computations. An important macroscopic consequence of atomic diffusion was however ignored: the double-diffusive mixing, also referred to as fingering or thermohaline convection, directly induced by μ-gradient inversion created by local heavy element accumulation. Taking this process into account will modify the studies of the element abundance variations inside stars and in their atmospheres.