  We describe a viscocapillary instability that can perturb the spherical
symmetry of cellular aggregates in culture, also called multicellular
spheroids. In the condition where the cells constituting the spheroid get their
necessary metabolites from the immediate, outer microenvironment, a permanent
cell flow exists within the spheroid from its outer rim where cells divide
toward its core where they die. A perturbation of the spherical symmetry
induces viscous shear stresses within the tissue that can destabilise the
aggregate. The proposed instability is viscocapillary in nature and does not
rely on external heterogeneities, such as a pre-existing pattern of blood
vessels or the presence of a substrate on which the cells can exert pulling
forces. It arises for sufficiently large cell-cell adhesion strengths,
cell-renewal rates, and metabolite supplies, as described by our model
parameters. Since multicellular spheroids in culture are good model systems of
small, avascular tumours, mimicking the metabolite concentration gradients
found in vivo, we can speculate that our description applies to microtumour
instabilities in cancer progression.
