Modeling the interface between bristle elastic structures and fluids

N.D.Botkin, K.-H.Hoffmann, V.N.Starovoitov, and V.L.Turova
center of advanced european studies and research, DE

Keywords: HPSW biosensor, solid-fluid interface, homogenization, dispersion relations

Abstract:
The interaction of a solid multi-layered structure with a fluid is studied. Such a problem arises when modeling HPSW sensors operating in liquids. The surface of HPSW biosensors is covered by specific receptors called aptamers. One can impress the aptamer layer as a bristle structure interacting with the surrounded liquid. The thickness of the aptamer layer is about $4$ nm and the number of bristles per surface unit is enormous large. Therefore, the direct numerical modeling of such a structure using solid-fluid interface conditions is impossible. Proper models can be derived using a homogenization technique along with the strict treatment of the solid-fluid interface conditions. We propose a homogenized model of the bristle structure where the interaction between the bristles and fluid is replaced by an averaged material whose properties are derived using the passage to the limit in the model based on the solid-fluid interface conditions when the number of bristles goes to infinity whereas their thickness goes to zero. The height of the bristles remains constant. Using the model of the new material, we compute dispersal relations which express the dependence of the surface shear wave velocity on the excitation frequency. Based on the dispersal relations, one can compute many useful characteristics, for example, the sensitivity of the biosensor with respect to adhering ligand-biomolecules. Numerical algorithm developed by the authors works for any number of anisotropic layers. The precision of the method enables to estimate the sensitivity regarding nanoscopic mass loadings. The computation results are in a very good agreement with physical experiments.

NSTI Nanotech 2003 Conference Technical Program Abstract