We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. The new model is able to capture both qualitatively and quantitatively experiments by Katsunuma et al. (2016) [J. Cell Biol. 212(5), pp. 561--575]. We also review some of the applications of these models in other areas of tissue growth in developmental biology. We finally explore the resulting qualitative behavior due to cell-cell repulsion. These are the videos related to our recent preprint in arXiv:1901.02919.
EPSRC grant number EP/P031587/1. JSPS KAKENHI Grant Numbers 26287025, 15H03635 and 17K05368, and JST CRESTGrant No. JPMJCR14D3. JSPS KAKENHI Grant Numbers 18K06219,18H04764, and a grant from the Takeda Science Foundation.