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Boundary element methods for viscous flow with applications in microcantilever array


Fluid-structure interactions at microscale are ubiquitous in biology and engineering. Understanding the complex micromechanical phenomena arises from the interplay between inertia, elastic and viscous forces on the microstructures are computationally formidable tasks but essential. At zero Reynold number asymptotic limit, fluids are dominated by viscosity, and the drag force changes linearly with local fluid speed, which exists analytical Green’s functions for the governing Stokes equations. In this thesis, the N-body hydrodynamic interactions of Euler-Bernoulli elastic beams immersed in viscous, incompressible fluids at zero Reynold number limit are solved computationally. A numerical recipe and program based on the symmetric Galerkin boundary element method are developed in Matlab for solving the boundary integral equations. In the end, up to one hundred hydrodynamically fully coupled elastic beams were able to be solved efficiently on a standard desktop personal computer. These microstructures simulation could serve as the numerical basis for understanding how the macroscopic transport and rheological property is modified at the vicinity of cantilever arrays, and also as viscosity and flow sensors for various engineering applications.

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