Optimization Of Lab-on-chip Flow Distribution Channel With Level Set Method

Micro fluidic chip design mainly includes the design of the micro-valve, micro pumps and micro flow channels. Based on the fluid incompressible Navier-Stokes equations and the level set method, this thesis focuses on the optimization of micro-flow channel to meet the flow distribution requirement.Level set surface evolution was first proposed by Osher and Sethian in1988. As Level set function can quickly track a moving boundary, the method has been applied in the fields of image processing, calculate geometry, fluid mechanical, structural optimization and so on. Based on the previous work, this thesis improves the level set method applied in the optimization of the micro fluidic channel:(1) By adding grid nodes on the implicit boundary, a New Re-initialization method based on the geometric contours of the level set function is proposed. The method not only shortens the numerical calculation time of re-initializing the level set function, but also enhances the distance characteristic of the level set function. Therefore, this method can significantly improve the accuracy of the level set function’s numerical evolution.(2) Combination of the level set method and Distmesh method is proposed to improve the precision of the numerical solution of physical field during the optimization process. The Distmesh method can quickly generate high-quality unstructured implicit boundary-fitted grid, which is conducive to ensure the accuracy of flow velocity’s derivatives on the boundary.(3) By reconstruction of explicit design domain with the help of explicit boundary level set method, the formed physical problem can be solved accurately. The explicit boundary level set method not only can greatly improve the numerical solution of physical field as the moving mesh method using real boundary condition to solve physical field, but also maintains the level set method’s characteristics of topology change during optimization process.(4) In order to maintain the mesh quality and accelerate optimization process, the small holes are deleted when the implicit boundary is transformed into explicit boundary.Based on the aforementioned theoretical works, the explicit boundary level set method is extended to optimize the micro fluidic channels. Firstly, two kinds of mathematical optimization models of flow distribution are proposed. Secondly, the sensitivity of models is implemented based on the finite difference method and adjoint equation. Finally, numerical examples illustrate the effectiveness of the proposed optimization model under the flow-rate or body-force drive flows.