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A recent experiment on zebrafish blastoderm morphogenesis showed that theviscosity ({\eta}) of a non-confluent embryonic tissue grows sharply until acritical cell packing fraction ({\phi}S). The increase in {\eta} up to {\phi}Sis similar to the behavior observed in several glass-forming materials, whichsuggests that the cell dynamics is sluggish or glass-like. Surprisingly, {\eta}is a constant above {\phi}S. To determine the mechanism of this unusualdependence of {\eta} on {\phi}, we performed extensive simulations using anagent-based model of a dense non-confluent two-dimensional tissue. We show thatpolydispersity in the cell size, and the propensity of the cells to deform,results in the saturation of the available free area per cell beyond a criticalpacking fraction. Saturation in the free space not only explains the viscosityplateau above {\phi}S but also provides a relationship between equilibriumgeometrical packing to the dramatic increase in the relaxation dynamics.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis