Hierarchical wrinkling in a confined permeable biogel

Confined thin surfaces may wrinkle as a result of the growth of excess material. Elasticity or gravity usually sets the wavelength. We explore new selection mechanisms based on hydrodynamics. First, inspired by yoghurt-making processes, we use caseins (a family of milk proteins) as pH-responsive building blocks and the acidulent glucono-δ-lactone to design a porous biogel film immersed in a confined buoyancy-matched viscous medium. Under specific boundary conditions yet without any external stimulus, the biogel film spontaneously wrinkles in cascade. Second, using a combination of titration, rheology, light microscopy, and confocal microscopy, we demonstrate that, during continuous acidification, the gel first shrinks and then swells, inducing wrinkling. Third, taking into account both Darcy flow through the gel and Poiseuille flow in the surrounding solvent, we develop a model that correctly predicts the wrinkling wavelength. Our results should be universal for acid-induced protein gels because they are based on pH-induced charge stabilization/destabilization and therefore could set a benchmark to gain fundamental insights into wrinkled biological tissues, to texture food, or to design surfaces for optical purposes.