面向MEMS设计的微流体流动特性研究
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摘要
针对微流体器件内部流动规律的认识还相对落后的现状，开展对微尺度、微结构及微功能器件开展微流体机理研究，寻找合适的微流体力学建模方法，进而对微流体器件的结构及参数进行优化研究，是目前微流体研究中亟待解决的科学问题，将为新结构、新器件的设计提供重要的理论根据。
本文介绍了微流体力学领域的连续介质模型、分子模型和介观模拟方法三类主要的建模方法，并探讨了它们各自的适用场合，这对如何选择微流体器件的建模方法具有理论意义。
对滑流区的微流体流动阻力特性进行了较为系统地分析和研究。基于一阶滑流边界条件，对滑流区的压差流动、剪切流动等典型流动问题进行分析，并得到了几种典型问题的解析解；针对滑流区中典型截面的压差流动的等效粘度修正方法，推导并给出了多种截面流动的等效粘度修正系数及其相关参数，为工程计算提供了一种简便易行的方法。
针对MEMS微结构中的气体压膜问题，基于一阶滑流边界条件，提出了一种双动量协调系数的修正雷诺方程；并对新模型的误差进行了分析，指出采用该模型能够满足MEMS工程设计的精度需求。基于双动量协调系数的修正雷诺方程，对几种典型情况下的不可压缩和可压缩气体的挤压膜阻尼特性进行了详细分析，推导出了压强分布、阻尼力和阻尼系数等参数的解析表达式。完善了原有文献中关于矩形平板在平动和转动情况下可压缩气体压膜阻尼问题的解析解。
对滑流边界条件下Couette流、Stokes流和Poiseuille流三种模型的滑膜阻尼特性进行了研究，给出了三种模型的解析解，并指出了其适用场合。
基于稀薄气体物理学理论和滑流修正的雷诺方程，研究了平板电容式加速度计的气膜阻尼特性，得到阻尼力和阻尼系数的简化解析解；给出了几种减小气膜阻尼的方法，并指出动量协调系数对于气膜阻尼(尤其是压膜阻尼)的影响很大，有待进一步的理论和实验研究。
对中心开孔圆盘在微流体中所受到的阻尼特性进行了研究，得到了微流体压力和流速的分布函数，分析了压膜与滑膜合成阻尼与结构设计尺寸及滑移长度之间的关系，得到了方便于工程实用的解析解。对具有多孔平板的气膜阻尼特性的研究方法进行了综述；针对气体不可压缩情况下具有高通孔率厚板的气膜阻尼特性进行了研究，给出了圆形通孔情形下阻尼系数的解析解：完善了求解多孔平板气膜阻尼问题的有限元方法，将其应用扩展到具有方孔平板的场合。
采用有限差分方法，对微加速度计的动态阻尼特性进行了研究和分析，仿真分析结果与试验数据吻合较好。建立了静电致动式弹性挠曲微梁的动态耦合模型，采用解析方法对微梁挠度远小于气膜厚度的情况进行了分析，得到了气膜阻尼作用下微梁品质因子和谐振频率的表达式；在微梁最大挠度与气膜厚度相当的情况下，采用有限差分方法对系统动态耦合方程进行了离散，给出了方程及其初始条件和边界条件的差分格式，并对系统在常阻尼系数和气膜阻尼情况下的动态响应进行了求解。
对横向振动梳状谐振器的动态气膜阻尼特性进行了研究，理论分析结果与试验数据吻合较好；指出对于横向振动的微结构而言，拖曳力是影响系统动态特性的非常重要因素之一，尤其对系统品质因子影响很大。
针对超薄气膜的润滑问题，提出了一种具有三个可调参数的计算模型；依据线性波尔兹曼方程对Poiseuille流量的预测值，采用最小二乘法得到了三个可调参数的一组最优化值。与其它方法相比，在特征Kn数倒数D很宽的范围内(10~(-4)＜D＜10~2)，采用该模型方程计算得到的压强分布和承载力能更好与采用线性波尔兹曼方程所得到的预测结果相吻合，有利于更好的微流体器件设计。
Currently, there is a little knowledge for the flow rules in microfluidic devices basedon MEMS technology. Aiming at this research status for microfluidics, it is necessary tostudy the micro fluidic mechanisms in the domains of microscale, micro structures andmicro functional devices, and find a suitable modeling methodology for the study ofmicrofluidics, then investigate on the optimization of the structures and parameters forthe microfluidic devices. These studies are needed to be proceeded urgently. Theachievements will provide important theoretical basement for the design of newstructures, new devices.
Three main modeling methodologies such as continuum medium models, molecularmodels and mesoscale methods is systematically reviewed. The applicable domains forthese methods are investigated respectively, which is very significant to select propermodeling method for a special microfluidic device.
The flow resistance characteristics is systematically analyzed and researched formicrofluid in the slip-flow region. Based on the first order slip-flow boundary condition,the analytical solutions of some typical problems such as pressure-difference flows andshear flows in the slip-flow region are obtained after the corresponding detailed analysis.According to the amendment method named equivalent viscosity for pressuredifferential flow in slip-flow region, the modified coefficients of equivalent viscosityand relevant parameters are deduced for several typical crosssection flows, whichsupply a simple method for engineering computation.
Based on the first order slip-flow boundary condition, a modified ReynoldsEquation with double momentum compatibility coefficients is put forward for gas filmdamping problems in microstructures based on MEMS. The error analysis of the newmodel shows that the precision requirements of MEMS engineering design can befulfilled by utilizing this model. Based on the modified Reynolds equation brought outin this paper, the damping characteristics of squeezed film are analyzed for thenon-condensable and condensable gas. The analytical expressions of the parameterssuch as pressure distribution, damping force and damping coefficient are deduced then.The analytical solutions of the gas damping problems are well developed for rectangularplates in the conditions of parallel motion and turning motion.
Under the slip-flow boundary condition, the slide-film damping characteristics of Couette flow, Stokes flow and Poiseuille flow are researched, and the analyticalsolutions of the three models are presented. Meanwhile, their applications fields arepointed out.
Based on the rarefied gas dynamics and the slip-flow modified Reynolds equation,the gas film damping characteristic of the plate capacitive accelerometer is studied, andthe simplified analytical solutions of the damping force and the damping coefficient areobtained. Several methods decreasing the gas film damping are given in this dissertation.The fact is point out that the momentum compatibility coefficient has a significant effecton the gas film damping, especially the squeeze film damping, which is needed a furthertheoretical and experimental study.
The damping characteristic of the disk with a role in the center moving in the microfluid is studied. The distribution functions of the pressure and the flow velocity areobtained. The relationship among the compound damping brought by the squeezed-filmand the slide film, structure parameters and the slip length is analyzed, and thecorresponding analytical solution suitable for the engineering practice is obtained. Manystudies on gas film damping for plate structures with multi holes are summarized in thisdissertation. As the gas is non-condensable, the gas film damping characteristic of thethick plate with high via hole-density is studied, and with the above analysis, theanalytical solution of the damping coefficient is presented. The FEM methods forsolving the gas film damping of the multi-hole plate is pieced out, and is extended tocalculate the damping of the plate with rectangular holes.
By using the finite difference method, the dynamic damping characteristic of themicro accelerometer is analyzed and studied. The simulation results are in goodagreement with those by experiments. The dynamic coupling model is established forthe electrostatic actuated micro elastic beam. The analytical method is used to analyzethe deformation of the microbeam which is much smaller than the thickness of the gasfilm. Under the effect of the gas film damping, the expressions of the quality factor andthe resonance frequency of the microbeam are obtained. When the maximum deflectionof the microbeam is considerable to the thickness of the gas film, the discretization ofthe dynamic couple equations are proceeded and the differential formats of theequations, the initial conditions and boundary conditions, are obtained using the finitedifference method. Then the dynamic response of the system with constant dampingcoefficient and film damping is simulated.
The dynamic characteristic of film damping is studied for the transverse oscillatedresonator. The analytical results are consistent with those by available experiments. For the transverse oscillated microstructures the drag force is one of the most importantfactors to affect the dynamic characteristics of the system, especially to the systemquality factor.
A computation model with three adjustable parameters is proposed for thelubrication problems of the ultra-thin gas film. Based on the predicted value of thePoiseuille flow by the linear Boltzmann equation, a set of optimization values for thethree parameters can be conducted by using the least square method. Compared withother methods, in a large scale of 10~(-4)＜D＜10~2, the pressure distribution and the loadcapacity calculated by this model keep a better agreement with those predicted valuesby linear Boltzmann equation, which is very helpful for the design of microfluidicdevices.
本文介绍了微流体力学领域的连续介质模型、分子模型和介观模拟方法三类主要的建模方法，并探讨了它们各自的适用场合，这对如何选择微流体器件的建模方法具有理论意义。
对滑流区的微流体流动阻力特性进行了较为系统地分析和研究。基于一阶滑流边界条件，对滑流区的压差流动、剪切流动等典型流动问题进行分析，并得到了几种典型问题的解析解；针对滑流区中典型截面的压差流动的等效粘度修正方法，推导并给出了多种截面流动的等效粘度修正系数及其相关参数，为工程计算提供了一种简便易行的方法。
针对MEMS微结构中的气体压膜问题，基于一阶滑流边界条件，提出了一种双动量协调系数的修正雷诺方程；并对新模型的误差进行了分析，指出采用该模型能够满足MEMS工程设计的精度需求。基于双动量协调系数的修正雷诺方程，对几种典型情况下的不可压缩和可压缩气体的挤压膜阻尼特性进行了详细分析，推导出了压强分布、阻尼力和阻尼系数等参数的解析表达式。完善了原有文献中关于矩形平板在平动和转动情况下可压缩气体压膜阻尼问题的解析解。
对滑流边界条件下Couette流、Stokes流和Poiseuille流三种模型的滑膜阻尼特性进行了研究，给出了三种模型的解析解，并指出了其适用场合。
基于稀薄气体物理学理论和滑流修正的雷诺方程，研究了平板电容式加速度计的气膜阻尼特性，得到阻尼力和阻尼系数的简化解析解；给出了几种减小气膜阻尼的方法，并指出动量协调系数对于气膜阻尼(尤其是压膜阻尼)的影响很大，有待进一步的理论和实验研究。
对中心开孔圆盘在微流体中所受到的阻尼特性进行了研究，得到了微流体压力和流速的分布函数，分析了压膜与滑膜合成阻尼与结构设计尺寸及滑移长度之间的关系，得到了方便于工程实用的解析解。对具有多孔平板的气膜阻尼特性的研究方法进行了综述；针对气体不可压缩情况下具有高通孔率厚板的气膜阻尼特性进行了研究，给出了圆形通孔情形下阻尼系数的解析解：完善了求解多孔平板气膜阻尼问题的有限元方法，将其应用扩展到具有方孔平板的场合。
采用有限差分方法，对微加速度计的动态阻尼特性进行了研究和分析，仿真分析结果与试验数据吻合较好。建立了静电致动式弹性挠曲微梁的动态耦合模型，采用解析方法对微梁挠度远小于气膜厚度的情况进行了分析，得到了气膜阻尼作用下微梁品质因子和谐振频率的表达式；在微梁最大挠度与气膜厚度相当的情况下，采用有限差分方法对系统动态耦合方程进行了离散，给出了方程及其初始条件和边界条件的差分格式，并对系统在常阻尼系数和气膜阻尼情况下的动态响应进行了求解。
对横向振动梳状谐振器的动态气膜阻尼特性进行了研究，理论分析结果与试验数据吻合较好；指出对于横向振动的微结构而言，拖曳力是影响系统动态特性的非常重要因素之一，尤其对系统品质因子影响很大。
针对超薄气膜的润滑问题，提出了一种具有三个可调参数的计算模型；依据线性波尔兹曼方程对Poiseuille流量的预测值，采用最小二乘法得到了三个可调参数的一组最优化值。与其它方法相比，在特征Kn数倒数D很宽的范围内(10~(-4)＜D＜10~2)，采用该模型方程计算得到的压强分布和承载力能更好与采用线性波尔兹曼方程所得到的预测结果相吻合，有利于更好的微流体器件设计。
Currently, there is a little knowledge for the flow rules in microfluidic devices basedon MEMS technology. Aiming at this research status for microfluidics, it is necessary tostudy the micro fluidic mechanisms in the domains of microscale, micro structures andmicro functional devices, and find a suitable modeling methodology for the study ofmicrofluidics, then investigate on the optimization of the structures and parameters forthe microfluidic devices. These studies are needed to be proceeded urgently. Theachievements will provide important theoretical basement for the design of newstructures, new devices.
Three main modeling methodologies such as continuum medium models, molecularmodels and mesoscale methods is systematically reviewed. The applicable domains forthese methods are investigated respectively, which is very significant to select propermodeling method for a special microfluidic device.
The flow resistance characteristics is systematically analyzed and researched formicrofluid in the slip-flow region. Based on the first order slip-flow boundary condition,the analytical solutions of some typical problems such as pressure-difference flows andshear flows in the slip-flow region are obtained after the corresponding detailed analysis.According to the amendment method named equivalent viscosity for pressuredifferential flow in slip-flow region, the modified coefficients of equivalent viscosityand relevant parameters are deduced for several typical crosssection flows, whichsupply a simple method for engineering computation.
Based on the first order slip-flow boundary condition, a modified ReynoldsEquation with double momentum compatibility coefficients is put forward for gas filmdamping problems in microstructures based on MEMS. The error analysis of the newmodel shows that the precision requirements of MEMS engineering design can befulfilled by utilizing this model. Based on the modified Reynolds equation brought outin this paper, the damping characteristics of squeezed film are analyzed for thenon-condensable and condensable gas. The analytical expressions of the parameterssuch as pressure distribution, damping force and damping coefficient are deduced then.The analytical solutions of the gas damping problems are well developed for rectangularplates in the conditions of parallel motion and turning motion.
Under the slip-flow boundary condition, the slide-film damping characteristics of Couette flow, Stokes flow and Poiseuille flow are researched, and the analyticalsolutions of the three models are presented. Meanwhile, their applications fields arepointed out.
Based on the rarefied gas dynamics and the slip-flow modified Reynolds equation,the gas film damping characteristic of the plate capacitive accelerometer is studied, andthe simplified analytical solutions of the damping force and the damping coefficient areobtained. Several methods decreasing the gas film damping are given in this dissertation.The fact is point out that the momentum compatibility coefficient has a significant effecton the gas film damping, especially the squeeze film damping, which is needed a furthertheoretical and experimental study.
The damping characteristic of the disk with a role in the center moving in the microfluid is studied. The distribution functions of the pressure and the flow velocity areobtained. The relationship among the compound damping brought by the squeezed-filmand the slide film, structure parameters and the slip length is analyzed, and thecorresponding analytical solution suitable for the engineering practice is obtained. Manystudies on gas film damping for plate structures with multi holes are summarized in thisdissertation. As the gas is non-condensable, the gas film damping characteristic of thethick plate with high via hole-density is studied, and with the above analysis, theanalytical solution of the damping coefficient is presented. The FEM methods forsolving the gas film damping of the multi-hole plate is pieced out, and is extended tocalculate the damping of the plate with rectangular holes.
By using the finite difference method, the dynamic damping characteristic of themicro accelerometer is analyzed and studied. The simulation results are in goodagreement with those by experiments. The dynamic coupling model is established forthe electrostatic actuated micro elastic beam. The analytical method is used to analyzethe deformation of the microbeam which is much smaller than the thickness of the gasfilm. Under the effect of the gas film damping, the expressions of the quality factor andthe resonance frequency of the microbeam are obtained. When the maximum deflectionof the microbeam is considerable to the thickness of the gas film, the discretization ofthe dynamic couple equations are proceeded and the differential formats of theequations, the initial conditions and boundary conditions, are obtained using the finitedifference method. Then the dynamic response of the system with constant dampingcoefficient and film damping is simulated.
The dynamic characteristic of film damping is studied for the transverse oscillatedresonator. The analytical results are consistent with those by available experiments. For the transverse oscillated microstructures the drag force is one of the most importantfactors to affect the dynamic characteristics of the system, especially to the systemquality factor.
A computation model with three adjustable parameters is proposed for thelubrication problems of the ultra-thin gas film. Based on the predicted value of thePoiseuille flow by the linear Boltzmann equation, a set of optimization values for thethree parameters can be conducted by using the least square method. Compared withother methods, in a large scale of 10~(-4)＜D＜10~2, the pressure distribution and the loadcapacity calculated by this model keep a better agreement with those predicted valuesby linear Boltzmann equation, which is very helpful for the design of microfluidicdevices.
引文
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