In addition to generating forces and reacting to mechanical cues, cell assemblies and tissues are characterized by their capacity to actively pump fluid, thanks to active ion transport. By pumping fluid, multicellular structures can nucleate and grow fluid-filled cavities called lumens. In this talk, I will present a continuum description of a spherical cell assembly that takes into account fluid pumping, electric currents and electric fields to explore the physical mechanisms of lumen formation. I will highlight in particular the role of the coupling between tissue bending and electric fields, called tissue flexoelectricity, in the lumen nucleation process. This description of cell assemblies can also be used to examine how a hydraulic or electrical perturbation, imposed for instance by a drain of micrometric diameter, can be used to perturb tissue growth. I will show that a sufficiently strong imposed flow or electric current can for instance drive a growing spheroid to decay.