Fig. 5: Effect of adhesion heterogeneity on the critical stress.

a Critical stress normalized by that for the case of homogeneous adhesion, \({{\rm{\sigma }}}_{{\rm{cr}}}^{* }\), as a function of the coefficient of variation, \({{\rm{CV}}}_{{\rm{\gamma }}}\), of the distribution of adhesion. b, c Snapshots showing initial wrinkling patterns for the uniform adhesion case (\({{\rm{CV}}}_{{\rm{\gamma }}}=0\)) and a heterogeneous adhesion case (\({{\rm{CV}}}_{{\rm{\gamma }}}=0.2\)), respectively, both with \(\bar{{\rm{\gamma }}}=46\,{\rm{\mu }}{\rm{J}}\,{{\rm{m}}}^{-2}\) and \({D}_{{\rm{b}}}^{\mathrm{on}}=360\,{\rm{n}}{{\rm{m}}}^{2}\,{{\rm{h}}}^{-1}\). The homogeneous case shows wrinkles distributed across the biofilm center, while the heterogeneous one displays significantly fewer wrinkles, localized in regions with weak adhesion.