Research On Topology Optimization Method For Centrifugal Microfluidic Chip

This thesis is focused on the design of microfluidic devices on microfluidic chips usingthe topology optimization, to utilize and overcome the microscale effect of microflows.Microfluidic chip is the hotspot in the area of biochemical-analysis instrument, andthe carrier of microfluidic techniques. As the decreasing of the size scale, microflowspresents different characteristics comparing to macroflows. And these characteristicsmainly include the low Reynolds number and high surface-volume ratio. Low Reynoldsnumber results in the laminar flow, where the distribution of the streamlines is regularand incrossed, the convection of the flow is less important, diffusion becomes the mainfactor for the mass transfer in the flows. Meanwhile, high surface-volume ratio makesthe surface force become the important factor loaded on the fluid, and the volumetricforce (e.g. the gravity) can be ignored. Therefore, the main problem in the designof microfluidic devices is on how to utilize or overcome the microscale effect of themicroflow and what design method can be used to implement the design to ensure thereliability and stability of the microfluidic devices. Currently, the design method in-cludes the size and shape optimization and the traditional trial and error method. Sizeand shape optimization is performed based on the design obtained by the trial and errormethod. Then the size and shape optimization method can not change the topologyof the given design. And the size and shape optimization method has relative strongdependence on the experience of the designer and can not enhance the performance ofthe devices as best as possible. On the other hand, the topology optimization methodcan achieve not only the design of the size and shape but also the optimal topology.And topology optimization method has low dependence on the experience of the de-signer. This is helpful to propose creative design with stable performance. Therefore,the topology optimization method is used to perform the design of microfluidic devicesin this thesis.The topology optimization of steady flow without physical body force has beenmature, and has been used to implement the design of micromixer, microreactor andelectroosmosis micropump. However, the unsteady and body force driven flows existswidespread on microfluidic chips. Then this thesis extends the theory of topology opti-mization to the area of unsteady and body force driven flow before using the topology optimization method to design microfluidic devices. Based on the density model pro-posed by Borrvall and Petersson for the topology optimization of steady flow withoutphysical body force, the topology optimization problem is constructed and analyzedusing the continuous adjoint method. The continuous adjoint method overcomes thecomplexity of the analysis of the topology optimization problem for unsteady flow us-ing the discrete adjoint method, where the analysis is independent on the discretizationof the time domain. Then the topology optimization problem is solved using the finiteelement method and evolving the design variable using the method of moving asymp-totes. Based on the topology optimization method of the unsteady flow, the influenceof the dynamic effect of the unsteady flow on the optimal topology is analyzed. Forthe body force driven flow, the gray area will appear in the optimal topology if thedensity model is used directly. Therefore, the power-law method is adopted to penalizethe body force, where the body force is eliminated in the solid phase and maintainedin the fluid phase. Then the topology optimization problem for the body force drivenflow is constructed, analyzed and solved for the gravity, centrifugal and Coriolis forcedriven flows. In view of the level set method has the virtue on expressing the contin-uously moving interface, ensuring the smooth boundary and abstracting the geometrycorresponding to the optimal topology, this thesis proposes the topology optimizationof flows using the level set method furthermore. The conventional level set methodcan not nucleate new level set, which results in the suboptimal topology and strongdependence of the initial value. To overcome this drawback, the topology sensitivity isconsidered in the topology optimization of body force driven flow using the level setmethod. Then the level set method based topology optimization is extended to the areaof Navier-Stokes flows with body forces.Based on the above theory of topology optimization method, the microfluidic de-vices with unsteady and body force driven flows can be designed. In this thesis, thetopology optimization of microvalve, micropump and micromixer are implemented.In microfluidics, the no moving part microvalve and valveless micropump are usedwidespread. However, the reported micro Tesla valve mainly focused on the flow withReynolds number lower than100, and the design of the micronozzle/diffuser still adoptsthe shape optimization method, where the diodicity can not be enhanced effectively; thedesign of the main channel of the valveless micropump is mainly based on the trial anderror method and shape optimization, where the net flux can not be increased effec-tively; the reported micromixers has the drawback on low mixing efficiency and longmixing length, and the size and shape optimization method can not change the topologyof the micromixer to strengthen the convection of of the flow and improve the mixingperformance effectively. Therefore, the topology optimization method is used to in-vestigate the design of the micro Tesla valve, valveless micropump and micromixer toachieve the optimal topology design with acceptable performance and manufacturabil-ity. Based on the topology optimization method, the optimal topology design of the main channel of the valveless micropump is implemented for the first time; the diod-icity of the micro Tesla valve and micronozzle/diffuer are enhanced16%and19%,respectively; the mixing efficiency of the micromixer is enhanced40.4%.