压电无阀薄膜微泵多场耦合建模与仿真研究
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摘要
随着微加工技术的飞速发展，微型化、自动化、集成化、智能化、批量化微流控系统已成为各国学术界和工业界所瞩目并研究的一个热点，并公认将会给21世纪的生命科学、医学研究和化学分析带来一场革命。作为核心部件的驱动子系统，对微流控系统的输出性能有着决定性的影响。驱动子系统的高效高稳定性工作是微流控系统实现长期可靠应用的前提和基础。但是目前关于驱动子系统研究仍偏重于驱动机理设计和加工方法的讨论，而对于微尺度下基础理论的研究仍处在初步探索阶段。这给驱动子系统的分析和设计提出了极大的挑战，严重地限制了微流控系统的发展速度，并阻碍从实验模型向商业化产品的转化过程。
本文以微流控系统中常用的驱动子系统—压电无阀薄膜微泵为研究对象，研究无阀薄膜微泵及相关组件（压电驱动器和微型收缩管/扩张管）的工作特性。压电无阀薄膜微泵服役机理十分复杂，基础理论研究还存在不少争议。影响无阀薄膜微泵基础理论发展的几个关键因素在于：①微型器件集成度的提高，导致服役过程中多学科、多过程和多变量强耦合效应增强，难于从单一学科推演出有效的分析方法和实用的设计准则；②实际的力学行为十分复杂，连续介质模型是否适用、建立何种模型、适用范围如何仍然需要进一步讨论；③微型器件特征尺寸的减小，增加了微观流体动力学现象仿真分析和实验观测的难度，建立合适的模拟技术是十分必要的。
本文围绕多过程和多变量强耦合作用下压电无阀薄膜微泵系统设计研究所迫切需要解决的有关理论和技术问题，通过理论分析、有限元仿真和物理实验相结合的方法，对薄膜微泵强耦合建模理论（主要涉及电-固域内耦合以及流-固边界耦合等）展开了系统深入的研究，提出了压电无阀薄膜微泵及相关组件的跨物理域耦合模型和数字化行为仿真方法，并初步探索采用集成数字化仿真的UML设计平台实现微流控系统和压电无阀薄膜微泵快速设计的关键理论，上述研究为压电无阀薄膜微泵的设计和加工提供理论指导和设计参考。主要研究内容和创新点包括：
1.改进了压电驱动器电-固耦合建模理论中的若干细节问题，使该理论在逐步改进中趋于实用化：①基于等效多层薄板模型假设和压电耦合理论，提出了适用于积层式圆形压电驱动器和单压电晶片驱动器的电-固耦合通用模型，将等效多层薄板模型的研究范围从宏观结构对称型压电驱动器的性能分析扩展到微观非对称型压电驱动器的状态预测；②为了简化非对称型压电驱动器的理论分析过程，基于电-固耦合通用模型相关假设以及能量变分原理，提出了单压电晶片驱动器电-固耦合变分模型，提高了现有耦合变分模型的预测精度。
2.基于数值模拟实验和物理实验，分析了压电驱动器的耦合特性，提出了压电驱动器优化设计思路：利用数值模拟实验和物理实验分析了压电驱动器的静态特性和动态特性，论证了电-固耦合通用模型和电-固耦合变分模型的有效性以及适用范围，揭示了压电驱动器的结构参数对于器件横向弯曲的影响，证实压电驱动器存在最佳的尺寸参数使工作性能最优。
3.综合考虑电场、机械场和微流场的耦合作用，提出了压电薄膜微泵电-固-流耦合变分模型：基于压电驱动器电-固耦合变分模型、流体雷诺输运定律和能量损失理论，提出了压电无阀薄膜微泵的电-固-液强耦合变分模型，推导出压电无阀薄膜微泵的谐振频率和输出特性方程；定性地研究泵腔结构变化对于无阀微泵输出特性的影响。上述耦合变分模型比现有的简化模型能够更加全面地反映薄膜微泵的工作特性，为薄膜微泵耦合建模理论的发展提供了新的思路。
4.基于有限元数值模拟，分析了收缩管/扩张管的微扩散特性，并提出了压电无阀薄膜微泵耦合行为仿真分析方法：利用商业有限元软件ANSYS建立了微型收缩管/扩张管有限元模型，对管内微流场特性进行了深入的仿真分析，确定了结构参数和流态变化对于收缩管/扩张管扩散性能的影响；建立了压电无阀薄膜微泵的电-固-液耦合仿真模型，更加直观地、系统地揭示了结构参数对微泵输出性能的影响，为实现微泵性能的优化设计提高了有效的思路。上述有限元耦合仿真方法的建立弥补了压电无阀薄膜微泵仿真实验缺乏的现状。
5.探索性地提出压电无阀薄膜微泵在药物传输中的应用思路，初步建立了融合行为仿真分析和UML的微流控系统/器件的设计策略和理论：比较完整地提出了压电无阀薄膜微泵在糖尿病患者药物治疗系统中的应用思路；为了表达设计思想并实现微流控系统快速设计，探索性地提出了基于有限元仿真分析及统一建模语言（UML）的微系统设计策略和建模方法；建立了微流控药物传输系统的静态、动态模型和需求模型，全面地反映系统器件/子系统间的拓扑关系、信息传递和系统功能；开发了压电无阀薄膜微泵设计软件，验证了上述设计理论的有效性。上述设计理论融合微流控元件的设计建模、耦合场分析和数值仿真于一体，对于建立微流控系统的实用性设计准则提供了重要理论支撑。
With rapid development of micromachining technologies, microfluidiccontrol systems, with properties of miniaturization, automation, integration,intelligence and batch-processing, have been widely studied and used inacademia and industry. It is believed that the new technology (e.g. BioMEMS)will lead to a revolution in the fields of life science, medical research andchemical analysis. As an important element, the driving sub-system of amicrofluidic control system determines its functionality of the entire system.The long-term and highly reliable applications of a microfluidic controlsystem depend on the highly efficient and stable performance of its drivingsub-system (e.g. micropump). Currently, the study on the driving sub-systemsof microfluidic control systems is mostly focused on the working principlesand their micromachining processes, but the research on fundamental theoriesof modeling and analysis of micro devices are still at the primary stage. Thesefactors bring a great challenge for the design and analysis of drivingsub-systems, limit the development of microfluidic control systems, and mayeven delay the transfer between the experimental models and the practicalproducts.
In this thesis, a piezoelectric valveless micropump commonly used inthe microfluidic control system is studied. To understand the behaviors of thepiezoelectric valveless micropump and its components (mainly including piezoelectric actuator and microdiffuser/micronozzle), the multi-physicalfield coupling modeling and digital simulation method is presented.
Because of various, complicated mechanical behaviors of thepiezoelectric valveless micropump, there are a lot of debates on the researchof fundamental theories for its modeling and analysis. Some key open issueson the theory development include:①Because of the improvement of themicrodevices integration, and the coupling effects with multiple disciplines,multiple processes and multiple variables are strengthened, it is difficult touse the analysis methods and design standards from one single discipline forthe analysis of microsystems.②The applicability and available scope of thecontinuum model should be discussed further.③Due to the reduction of thecharacteristic sizes, it is difficult to exactly observe the output properties ofthe driving sub-system and its microflow phenomena, and to predict itsbehavior during the initial stage of the system design In this case, it isimportant to develop the simulation technology.
In this thesis, some theoretical and technological problems about thedesign of piezoelectric valveless micropumps with the multi-disciplinary andmulti-variable coupling effects are studied. The coupling model (mainlyincluding electro-solid and fluid-solid coupling) of the valveless micropumpis systemically discussed by using the combined methods of theoreticalanalysis, finite element simulation and physical experiment. Furthermore, themulti-field coupling model and its digital simulation are presented. Thedesign environment based on the UML and digital simulation is also explored.The research results can provide the theoretical reference or instruction forthe design and fabrication of the piezoelectric valveless micropump. Themain contents and contributions of this research work include:
1. Improvement on the electro-solid coupling model which enhances the integrity of the modeling theory.①Based on thepiezoelectric coupling theory and the assumption of the equivalent laminatedplate model, the general coupling model for the piezoelectric actuators,including the stacked circular piezoelectric actuator and circular unimorphactuator, is presented. This extends the application of the equivalentlaminated plate model from the symmetrical piezoelectric actuator tounsymmetrical piezoelectric actuator.②For simplifying the analysis of thecoupling model, the coupling variation model of the unimorph actuator ispresented based on the energy variation principle and piezoelectric couplingtheory, which improves the accuracy of the current variation model.
2. Analysis and its optimal design of the coupling performances ofthe piezoelectric actuator based on numerical simulations and physicalexperiments. The static and dynamic properties of the piezoelectric actuatorare analyzed by numerical simulations and physical experiments, and theavailable range for the general coupling model and variation coupling modelabove are discussed. The results show the effect of the structure parameters ofthe piezoelectric actuator on the deflection. It is found that there is an optimalsize parameter for the piezoelectric actuator to achieve the largest deflection.
3. Establishment of the electro-solid-fluid coupling variation modelsuitable for the problem with the combined effect of the electrical,mechanical and fluid fields. The electro-solid-fluid coupling variationmodel is presented based on the variation coupling model of the piezoelectricactuator, Reynolds transportation equation and energy loss theory. Moreover,the equation of output properties and the first natural frequency for thepiezoelectric valveless micropump are derived, and the effect of the changeof the pump chamber on the properties of the piezoelectric valvelessmicropump is discussed. Compared with the current, simplified model for the valveless micropump, the new coupling model can represent the entireperformance of the micropump, which provides a new method for theanalysis of the piezoelectric valveless micropump.
4. The numerical analysis and simulation method for themicrodiffusion characteristics of the diffuser/nozzle element and thepiezoelectric valveless micropump. The finite element model of themicrodiffuser/micronozzle is modeled by ANSYS software. The flowproperties in fluid field are simulated, and the results show that the structuralparameters and flow status for the diffuser/nozzle element have effect on themicrodiffusion. The simulation model of the piezoelectric valvelessmicropump is built. By simulation the output characteristics of thepiezoelectric valveless micropump are systematically analyzed, and theoptimal designs are determined. The simulation method for the piezoelectricvalveless micropump can be used for solving the problems resulted from theabsence of the electro-solid-fluid coupling simulation.
5. Exploration of the application design of the piezoelectricvalveless micropump in the drug delivery, and the design method andtheory combining the numerical simulation and UML for the designenvironment of the microfluidic control system. The application design ofthe piezoelectric valveless micropump for treatment of the diabete patient isstudied. To model the system design and achieve a quick design ofmicrofluidic control system, a systematic modeling and design method basedon the finite element simulation and Unified Modeling Language (UML) ispresented. The static and dynamic models for the microfluidic control systemare built, which represents the topological relations, informationtransmissions, and system functions among the devices/sub-systems in themicrosystem. The design software of the piezoelectric valveless micropump is developed, and then the validation of the design theory is verified. Thedesign method combining the design model, coupling analysis and numericalsimulation provides a way for the study on the design standard of themicrofluidic control system.
本文以微流控系统中常用的驱动子系统—压电无阀薄膜微泵为研究对象，研究无阀薄膜微泵及相关组件（压电驱动器和微型收缩管/扩张管）的工作特性。压电无阀薄膜微泵服役机理十分复杂，基础理论研究还存在不少争议。影响无阀薄膜微泵基础理论发展的几个关键因素在于：①微型器件集成度的提高，导致服役过程中多学科、多过程和多变量强耦合效应增强，难于从单一学科推演出有效的分析方法和实用的设计准则；②实际的力学行为十分复杂，连续介质模型是否适用、建立何种模型、适用范围如何仍然需要进一步讨论；③微型器件特征尺寸的减小，增加了微观流体动力学现象仿真分析和实验观测的难度，建立合适的模拟技术是十分必要的。
本文围绕多过程和多变量强耦合作用下压电无阀薄膜微泵系统设计研究所迫切需要解决的有关理论和技术问题，通过理论分析、有限元仿真和物理实验相结合的方法，对薄膜微泵强耦合建模理论（主要涉及电-固域内耦合以及流-固边界耦合等）展开了系统深入的研究，提出了压电无阀薄膜微泵及相关组件的跨物理域耦合模型和数字化行为仿真方法，并初步探索采用集成数字化仿真的UML设计平台实现微流控系统和压电无阀薄膜微泵快速设计的关键理论，上述研究为压电无阀薄膜微泵的设计和加工提供理论指导和设计参考。主要研究内容和创新点包括：
1.改进了压电驱动器电-固耦合建模理论中的若干细节问题，使该理论在逐步改进中趋于实用化：①基于等效多层薄板模型假设和压电耦合理论，提出了适用于积层式圆形压电驱动器和单压电晶片驱动器的电-固耦合通用模型，将等效多层薄板模型的研究范围从宏观结构对称型压电驱动器的性能分析扩展到微观非对称型压电驱动器的状态预测；②为了简化非对称型压电驱动器的理论分析过程，基于电-固耦合通用模型相关假设以及能量变分原理，提出了单压电晶片驱动器电-固耦合变分模型，提高了现有耦合变分模型的预测精度。
2.基于数值模拟实验和物理实验，分析了压电驱动器的耦合特性，提出了压电驱动器优化设计思路：利用数值模拟实验和物理实验分析了压电驱动器的静态特性和动态特性，论证了电-固耦合通用模型和电-固耦合变分模型的有效性以及适用范围，揭示了压电驱动器的结构参数对于器件横向弯曲的影响，证实压电驱动器存在最佳的尺寸参数使工作性能最优。
3.综合考虑电场、机械场和微流场的耦合作用，提出了压电薄膜微泵电-固-流耦合变分模型：基于压电驱动器电-固耦合变分模型、流体雷诺输运定律和能量损失理论，提出了压电无阀薄膜微泵的电-固-液强耦合变分模型，推导出压电无阀薄膜微泵的谐振频率和输出特性方程；定性地研究泵腔结构变化对于无阀微泵输出特性的影响。上述耦合变分模型比现有的简化模型能够更加全面地反映薄膜微泵的工作特性，为薄膜微泵耦合建模理论的发展提供了新的思路。
4.基于有限元数值模拟，分析了收缩管/扩张管的微扩散特性，并提出了压电无阀薄膜微泵耦合行为仿真分析方法：利用商业有限元软件ANSYS建立了微型收缩管/扩张管有限元模型，对管内微流场特性进行了深入的仿真分析，确定了结构参数和流态变化对于收缩管/扩张管扩散性能的影响；建立了压电无阀薄膜微泵的电-固-液耦合仿真模型，更加直观地、系统地揭示了结构参数对微泵输出性能的影响，为实现微泵性能的优化设计提高了有效的思路。上述有限元耦合仿真方法的建立弥补了压电无阀薄膜微泵仿真实验缺乏的现状。
5.探索性地提出压电无阀薄膜微泵在药物传输中的应用思路，初步建立了融合行为仿真分析和UML的微流控系统/器件的设计策略和理论：比较完整地提出了压电无阀薄膜微泵在糖尿病患者药物治疗系统中的应用思路；为了表达设计思想并实现微流控系统快速设计，探索性地提出了基于有限元仿真分析及统一建模语言（UML）的微系统设计策略和建模方法；建立了微流控药物传输系统的静态、动态模型和需求模型，全面地反映系统器件/子系统间的拓扑关系、信息传递和系统功能；开发了压电无阀薄膜微泵设计软件，验证了上述设计理论的有效性。上述设计理论融合微流控元件的设计建模、耦合场分析和数值仿真于一体，对于建立微流控系统的实用性设计准则提供了重要理论支撑。
With rapid development of micromachining technologies, microfluidiccontrol systems, with properties of miniaturization, automation, integration,intelligence and batch-processing, have been widely studied and used inacademia and industry. It is believed that the new technology (e.g. BioMEMS)will lead to a revolution in the fields of life science, medical research andchemical analysis. As an important element, the driving sub-system of amicrofluidic control system determines its functionality of the entire system.The long-term and highly reliable applications of a microfluidic controlsystem depend on the highly efficient and stable performance of its drivingsub-system (e.g. micropump). Currently, the study on the driving sub-systemsof microfluidic control systems is mostly focused on the working principlesand their micromachining processes, but the research on fundamental theoriesof modeling and analysis of micro devices are still at the primary stage. Thesefactors bring a great challenge for the design and analysis of drivingsub-systems, limit the development of microfluidic control systems, and mayeven delay the transfer between the experimental models and the practicalproducts.
In this thesis, a piezoelectric valveless micropump commonly used inthe microfluidic control system is studied. To understand the behaviors of thepiezoelectric valveless micropump and its components (mainly including piezoelectric actuator and microdiffuser/micronozzle), the multi-physicalfield coupling modeling and digital simulation method is presented.
Because of various, complicated mechanical behaviors of thepiezoelectric valveless micropump, there are a lot of debates on the researchof fundamental theories for its modeling and analysis. Some key open issueson the theory development include:①Because of the improvement of themicrodevices integration, and the coupling effects with multiple disciplines,multiple processes and multiple variables are strengthened, it is difficult touse the analysis methods and design standards from one single discipline forthe analysis of microsystems.②The applicability and available scope of thecontinuum model should be discussed further.③Due to the reduction of thecharacteristic sizes, it is difficult to exactly observe the output properties ofthe driving sub-system and its microflow phenomena, and to predict itsbehavior during the initial stage of the system design In this case, it isimportant to develop the simulation technology.
In this thesis, some theoretical and technological problems about thedesign of piezoelectric valveless micropumps with the multi-disciplinary andmulti-variable coupling effects are studied. The coupling model (mainlyincluding electro-solid and fluid-solid coupling) of the valveless micropumpis systemically discussed by using the combined methods of theoreticalanalysis, finite element simulation and physical experiment. Furthermore, themulti-field coupling model and its digital simulation are presented. Thedesign environment based on the UML and digital simulation is also explored.The research results can provide the theoretical reference or instruction forthe design and fabrication of the piezoelectric valveless micropump. Themain contents and contributions of this research work include:
1. Improvement on the electro-solid coupling model which enhances the integrity of the modeling theory.①Based on thepiezoelectric coupling theory and the assumption of the equivalent laminatedplate model, the general coupling model for the piezoelectric actuators,including the stacked circular piezoelectric actuator and circular unimorphactuator, is presented. This extends the application of the equivalentlaminated plate model from the symmetrical piezoelectric actuator tounsymmetrical piezoelectric actuator.②For simplifying the analysis of thecoupling model, the coupling variation model of the unimorph actuator ispresented based on the energy variation principle and piezoelectric couplingtheory, which improves the accuracy of the current variation model.
2. Analysis and its optimal design of the coupling performances ofthe piezoelectric actuator based on numerical simulations and physicalexperiments. The static and dynamic properties of the piezoelectric actuatorare analyzed by numerical simulations and physical experiments, and theavailable range for the general coupling model and variation coupling modelabove are discussed. The results show the effect of the structure parameters ofthe piezoelectric actuator on the deflection. It is found that there is an optimalsize parameter for the piezoelectric actuator to achieve the largest deflection.
3. Establishment of the electro-solid-fluid coupling variation modelsuitable for the problem with the combined effect of the electrical,mechanical and fluid fields. The electro-solid-fluid coupling variationmodel is presented based on the variation coupling model of the piezoelectricactuator, Reynolds transportation equation and energy loss theory. Moreover,the equation of output properties and the first natural frequency for thepiezoelectric valveless micropump are derived, and the effect of the changeof the pump chamber on the properties of the piezoelectric valvelessmicropump is discussed. Compared with the current, simplified model for the valveless micropump, the new coupling model can represent the entireperformance of the micropump, which provides a new method for theanalysis of the piezoelectric valveless micropump.
4. The numerical analysis and simulation method for themicrodiffusion characteristics of the diffuser/nozzle element and thepiezoelectric valveless micropump. The finite element model of themicrodiffuser/micronozzle is modeled by ANSYS software. The flowproperties in fluid field are simulated, and the results show that the structuralparameters and flow status for the diffuser/nozzle element have effect on themicrodiffusion. The simulation model of the piezoelectric valvelessmicropump is built. By simulation the output characteristics of thepiezoelectric valveless micropump are systematically analyzed, and theoptimal designs are determined. The simulation method for the piezoelectricvalveless micropump can be used for solving the problems resulted from theabsence of the electro-solid-fluid coupling simulation.
5. Exploration of the application design of the piezoelectricvalveless micropump in the drug delivery, and the design method andtheory combining the numerical simulation and UML for the designenvironment of the microfluidic control system. The application design ofthe piezoelectric valveless micropump for treatment of the diabete patient isstudied. To model the system design and achieve a quick design ofmicrofluidic control system, a systematic modeling and design method basedon the finite element simulation and Unified Modeling Language (UML) ispresented. The static and dynamic models for the microfluidic control systemare built, which represents the topological relations, informationtransmissions, and system functions among the devices/sub-systems in themicrosystem. The design software of the piezoelectric valveless micropump is developed, and then the validation of the design theory is verified. Thedesign method combining the design model, coupling analysis and numericalsimulation provides a way for the study on the design standard of themicrofluidic control system.
引文
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