Mechanical and Civil Engineering Seminar

Wrinkling instability of compressed stiff thin films bound to soft substrates has been studied for many years and the formation and evolution of wrinkles is well understood. Similar wrinkling instabilities also play important role in biology during the development of organs, such as brains and guts, and during the formation of bacterial biofilms grown on soft substrates. In recent years, the wrinkling instability has been exploited to create structures with tunable drag, wetting, adhesion, and to create a template for wire formation. While these studies successfully demonstrated the proofs of concepts, the quantitative understanding is still lacking, because very little is known about how wrinkled surfaces deform in response to interactions with environment. To address this issue, we investigated the linear response of wrinkled structures to external forces. By mapping the problem to the Landau theory of phase transitions, we demonstrated that the linear response to external forces diverges near the onset of wrinkling instability with the usual mean field exponent found in critical phenomena. Interactions with environment also dictate the morphology of wrinkled patterns in growing biological systems. I will discuss the formation of wrinkling patterns in bacterial biofilms grown on agar substrates, which usually have radial stripe patterns near the outer edge and zigzag herringbone-like patterns in the core. The observed wrinkling patterns result from uneven stress distribution in the biofilm as a consequence from the depletion of slowly diffusing nutrients underneath the biofilm, which are required for the bacterial growth.