  We introduce two 2D mechanical models reproducing the evolution of two
viscous tissues in contact. Their main property is to model the swirling cell
motions while keeping the tissues segregated, as observed during vertebrate
embryo elongation. Segregation is encoded differently in the two models: by
passive or active segregation (based on a mechanical repulsion pressure). We
compute the incompressible limits of the two models, and obtain strictly
segregated solutions. The two models thus obtained are compared. A striking
feature in the active segregation model is the persistence of the repulsion
pressure at the limit: a ghost effect is discussed and confronted to the
biological data. Thanks to a transmission problem formulation at the
incompressible limit, we show a pressure jump at the tissues' boundaries.
