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
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
NSTI Nanotech 2003 Conference Technical Program Abstract