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We introduce two 2D mechanical models reproducing the evolution of twoviscous tissues in contact. Their main property is to model the swirling cellmotions while keeping the tissues segregated, as observed during vertebrateembryo elongation. Segregation is encoded differently in the two models: bypassive or active segregation (based on a mechanical repulsion pressure). Wecompute the incompressible limits of the two models, and obtain strictlysegregated solutions. The two models thus obtained are compared. A strikingfeature in the active segregation model is the persistence of the repulsionpressure at the limit: a ghost effect is discussed and confronted to thebiological data. Thanks to a transmission problem formulation at theincompressible limit, we show a pressure jump at the tissues' boundaries.

Multi-species viscous models for tissue growth: incompressible limit and qualitative behaviour