**Bryan Quaife, Department of Scientific Computing, Florida State University**

*The Role of Permeability in Biomembranes*

Biomembranes permeate small molecules into a cell while not allowing large molecules to pass through. Even in the absence of osmolarity, a biomembrane can exchange large amounts of fluid if enough mechanical force is applied. I will discuss two mathematical constructs for semipermeable membranes: a modification of a well-studied continuum model and a coarse-grained model. Both models require solving the Stokes equations in unbounded domains, and high-order accuracy is achieved by reformulating the governing equations as an integral equation. I will draw comparisons between impermeable and semipermeable membranes when subjected to large mechanical forces, and I will quantify permeability with the coarse-grained model. Finally, the coarse-grained model will be used to quantify slip between the layers of a biomembrane.