Linear viscoelastic properties of the vertex model for epithelial tissues
Fig 2
Storage and loss shear moduli in the solid (top row) and fluid phase (bottom row) for hexagonal tilings.
(a-b) An overlay of the representative reference (grey) and sheared (yellow) configurations in (a) the solid and (b) the fluid phase. The magnitude of the shear is highly exaggerated for demonstration purposes. (c-d) Representative storage (G′) and loss (G″) shear moduli as functions of the shearing frequency, ω0, for different values of the cell-shape parameter, p0. Dashed curves are the fits based on (c) the Standard Linear Solid (SLS) model in the solid phase [see Eq (5)] and (d) the Burgers model in the fluid phase [see Eq (8)]. (e-f) The collapse of the moduli curves for different values of p0 for (e) the solid phase and (f) the fluid phase. The insets show the representation of (e) the SLS model and (f) the Burgers model in terms of the springs and dashpots. The majority of the data corresponds to the system of nearly square shape with Nx = 15 cells in the horizontal direction, and we also show examples of larger systems with Nx = 37 and Nx = 51 cells in the horizontal direction.