Fig. 3: A simple model captures the domain size.
a In the geometry considered, the aggregate and background have, respectively, radius a and b, and cell density ρa and ρb, while the mean cell density \(\bar{\rho }\) is fixed. The aggregate surface fraction is ϕ ≡ a2/b2, with maximal value \({\phi }_{\max }=\bar{\rho }/{\rho }_{{{{{{{{\rm{a}}}}}}}}}\). b, c Oxygen concentration field c (r, z) around an aggregate. Here \(\bar{\rho }=1{0}^{6}\) cm−2, h = 1 mm, \(\phi=0.16\,{\phi }_{\max }\) and the size domain is a = 130 μm. The minimal concentration, reached at the origin, is the target concentration \(\hat{c}\), i.e., \(c(0,0)/{c}_{{{{{{{{\rm{s}}}}}}}}}=\hat{c}/{c}_{{{{{{{{\rm{s}}}}}}}}}=0.01\). d Aggregate size \(a(\bar{\rho },h,\phi )\) predicted when \(\bar{\rho }\) and h are independent parameters, obtained from numerically solving Eq. (2). The continuous and dashed lines correspond to surface fraction \(\phi={\phi }_{\max }\) and \(0.16\,{\phi }_{\max }\), respectively. e Aggregate size a(h, ϕ) predicted when accounting for the thickness dependence of mean cell density \(\bar{\rho }\). The black lines are solutions of Eq. (4). Graphically, they correspond to the intersection between the colored oblique lines, reproduced from panel (d), and the vertical line at a film height h solution of \({\bar{\rho }}_{\exp }(h)=\bar{\rho }\). As above, \(\phi={\phi }_{\max }\) and \(0.16\,{\phi }_{\max }\) for solid and dashed lines, respectively. The shaded area shows the aggregate size expected in experiments.
