# Mathematics Colloquia and Seminars

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### Getting Stuck: Kinetics, Elastohydrodynamics, and Soft Adhesion

**Mathematical Biology**

Speaker: | Arvind Gopinath, Haverford College |

Location: | 2112 MSB |

Start time: | Mon, Mar 30 2015, 3:10PM |

We consider the sticking of a fluid-immersed colloidal particle with a substrate coated by polymeric tethers, a model for soft, wet adhesion in many natural and artificial systems. Our theory accounts for the kinetics of binding, the elasticity of the tethers, and the hydrodynamics of fluid drainage between the colloid and the substrate, characterized by three dimensionless parameters: the ratio of the viscous drainage time to the kinetics of binding, the ratio of elastic to thermal energies, and the size of the particle relative to the height of the polymer brush. For typical experimental parameters and discrete families of tethers, we find that adhesion proceeds via punctuated steps, where rapid transitions to increasingly bound states are separated by slow aging transients, consistent with recent observations.