Boundary geometry drives three-dimensional defect transitions in a polar fluid*

Confinement is a prominent driver of collective phenomena in anisotropic matter. Hence, understanding its role in the emergence of order is crucial for the control of complex structures such as topological defects. Using a minimal continuum model, we address the role of boundaries—with emphasis on their geometry—in the surface induced ordering of a 3D confined polar fluid. We define a dimensionless parameter that allows us to adjust the geometry of the system continuously, and use a weak anchoring energy to account for nonuniform boundary conditions. We find that, although material parameters are responsible for the creation of defects in the order parameter field, their location and structure are determined by the system geometry. We test our results in the experimental context of the mouse epiblast, where cells gradually align along their apico-basal axis and eventually form a fluid filled cavity (lumen) at their apical sides. Since field defects represent regions where the apical sides of the cells meet, changes in defect position can be relevant to lumen formation in the biological system. We compare our predictions with imaging data of the morphogenetic process for wildtype and genetically perturbed mice, finding a remarkable quantitative agreement without any fitting parameters. Our work provides insights into luminogenesis and embryonic viability, while paving the way for defect control by geometry manipulation in more general settings.