應用沉浸有限元素法於具複雜幾何微流體元件之固液耦合計算力學研究

Abstract

本論文探討複雜微流道內之流固耦合現象，利用計算流體力學 (Computational fluid dynamics) 結合沉浸有限元素法 (Immersed finite element method)，建構了一套高效且準確的數值模擬平台。首先，採用Navier-Stokes方程式與連續方程式描述流體行為，透過有限差分法 (Finite difference method) 以及交錯網格進行數值離散，並透過虛擬網格以及邊界條件提高模擬的穩定性與精確度。此外，沉浸有限元素法之應用使固體自由移動於流體網格中，並透過形狀函數以及高斯積分等有限元素技術，精確計算固液交互作用產生的耦合力。 本研究更進一步應用直接強制法處理微流道中的複雜幾何邊界問題，並採用自適應積分法以提升模擬精度與效率。為了驗證模擬平台之正確性，本研究透過與商用軟體SimLab的結果進行比對，確認其模擬準確性與穩定性。在應用層面上，本研究設計並模擬多種具代表性的微流道幾何，包含十字、漸擴、曲線與螺旋流道，且針對紅血球、細菌與癌細胞等不同生物粒子，分析其運動軌跡、變形行為與耦合力的變化。透過與實驗文獻數據比較，成功驗證了此方法之準確性，並進一步提出依據細胞尺寸與彈性差異的無標記式 (Label-free) 分離策略，顯示此數值方法對於生醫診斷與細胞篩選等應用具有高度的潛力。

This thesis investigates fluid-structure interaction (FSI) phenomena within complex microfluidic channels by developing an efficient and accurate numerical simulation platform based on computational fluid dynamics (CFD) and the immersed finite element method (IFEM). The fluid behavior is described using the Navier-Stokes equations and the continuity equation, which are discretized via the finite difference method (FDM) on a staggered grid. Virtual grids and boundary conditions are further applied to enhance the stability and accuracy of the simulation. The application of IFEM allows solid structures to move freely within the fluid mesh, and the interaction forces between fluid and solid are accurately computed using finite element techniques such as shape functions and Gaussian quadrature. Moreover, the study employs the direct forcing method to handle complex geometric boundaries in microchannels and adopts an adaptive integration scheme to improve simulation precision and efficiency. To validate the correctness of the simulation platform, results are compared with those obtained from the commercial software SimLab, confirming its accuracy and stability. On the application level, several representative microchannel geometries, including cross, expansion, curved, and spiral channels, are designed and simulated. The behavior of various biological particles such as red blood cells, bacteria, and cancer cells is analyzed in terms of motion trajectory, deformation, and interaction forces. By comparing the results with experimental data from the literature, the proposed method is shown to be accurate. Furthermore, a label-free separation strategy based on differences in cell size and elasticity is proposed, demonstrating the high potential of this numerical method in biomedical diagnostics and cell sorting applications.