Due to the limits of computational time and computer memory, topology optimization problems involving fluidic flow frequently use simplified 2D models. Extruded versions of the 2D optimized results typically comprise the 3D designs to be fabricated. In practice, the depth of the fabricated flow channels is finite; the limited flow depth together with the no-slip condition potentially make the fluidic performance of the 3D model very different from that of the simplified 2D model. This discrepancy significantly limits the usefulness of performing topology optimization involving fluidic flow in 2D—at least if special care is not taken. Inspired by the electric circuit analogy method, we limit the widths of the microchannels in the 2D optimization process. To reduce the difference of fluidic performance between the 2D model and its 3D counterpart, we propose an applicable 2D optimization model, and ensure the manufacturability of the obtained layout, combinations of several morphology-mimicking filters impose maximum or minimum length scales on the solid phase or the fluidic phase. Two typical Lab-on-chip functional units, Tesla valve and fluidic channel splitter, are used to illustrate the validity of the proposed application of length scale control.

中文翻译：

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使用具有长度比例约束的2D拓扑优化设计适用的3D微流体功能单元。

由于计算时间和计算机内存的限制，涉及流体流动的拓扑优化问题经常使用简化的2D模型。2D优化结果的拉伸版本通常包括要制造的3D设计。实际上，所制造的流道的深度是有限的。有限的流动深度以及防滑条件可能使3D模型的流体性能与简化2D模型的流体性能大不相同。这种差异极大地限制了执行涉及2D流体流动的拓扑优化的有用性-至少在没有特别注意的情况下。受电路模拟方法的启发，我们在2D优化过程中限制了微通道的宽度。为了减少2D模型与其3D模型之间的流体性能差异，我们提出了一个适用的2D优化模型，并确保了所获得布局的可制造性，几种形态模拟滤镜的组合在固相或流体相上施加了最大或最小长度尺度。两个典型的芯片实验室功能单元，特斯拉阀和流体通道分配器，用于说明所建议的长度比例控制应用的有效性。