Viscous vertex model for active epithelial tissues

We present a rotationally invariant viscous vertex model that accounts for both cortical and bulk dissipation of cells. The vanishing substrate-friction limit is enforced via Lagrange multipliers, which also provides a framework for implementing various boundary conditions, such as fixed boundaries and prescribed tractions. Building on this formulation, we introduce a slab-shear rheology protocol to extract an effective, coarse-grained tissue shear viscosity. Under polar or nematic activity, viscosity regulates the formation of elongated, spatially correlated cell-shape textures and stabilizes well-defined topological defects. Because the model remains well-posed at zero substrate friction, it is naturally suited to describing free-floating epithelia and organoids.