Research On Topology Optimization Method Of Electroosmotic Flow In Microfluidic Chip

Microfluidics is a high-tech developed in the past 30 years.It has been widely used in medicine,biology and environment,and has the characteristics of high efficiency,portable and micro-scale.Microfluidic chip is the carrier of microfluidics,mainly including micro-valve,micro-pump,and micro-mixer and pipeline network.Therefore,the design and optimization of these functional components in microfluidic chip determines the reliability,stability and integration of the microfluidic chip.Topology optimization method is an important tool in engineering structure design.The size and shape optimization is only carried out on the existing topology,which is not only dependent on the designer's experience,but also has a limited effect on the performance of the structure.The topology optimization method can find the optimal topology of the structure in the absence of the experience of the designer,and can also optimize the size and shape to a certain extent.This helps to achieve innovative design,while ensuring the realization of structural functions while maximizing performance.Therefore,in this paper,the topology optimization method is used to optimize the structure of microfluidic chip.The pressure-and electroosmotic driven are the two most widely used driving methods in microfluidics,and the pressure driven fluid flow topology optimization method has been very mature,including traditional density method and level set method.However,the development of electroosmotic driven fluid flow topology optimization is slow.On the one hand,the relatively single flow field problem becomes a coupling problem of flow field,electric field and ion concentration field,which greatly increases the complexity of the optimization model;on the other hand,in general,the thickness of the double layer is less than two to three orders of magnitude with respect to the micro pipe.Therefore,the problem of electroosmotic driven fluid flow topology optimization is also a multi-scale optimization problem,which greatly improves the difficulty of calculation.In this paper,we solve these problems from two aspects: the improved topology optimization method and the simplified physical model.The density method and the level set method are the two most common topology optimization methods,which have their own advantages and disadvantages.In order to overcome these shortcomings and make full use of their advantages,in recent years there have been topology description function method and parametric level set method.Since the driving force of electroosmotic driven is along the tangential direction of the pipe wall.In this paper,we adopt and extend the parametric level set method which can describe the boundary evolution.Compared with the traditional density method,the proposed method can effectively reduce the number of design variables and has a clear evolutionary boundary.Compared with the traditional level set method,the proposed method has less number of iterations,without re-initialization,and a mature optimization algorithm can be applied.In this paper,we first apply the extended parametric level set method to the optimization of the stiffness of the cantilever beam to verify the effectiveness and robustness of the algorithm.We also apply the extended parametric level set method to the optimization of steady flow without physical body force,the continuous adjoint equation and adjoint sensitivity are derived,and a large number of numerical examples are given to show that the topology optimization has different characteristics under different polishing parameters.Based on the above theory and design experience of extended parametric level set method,in this paper,the topology optimization of the induced electroosmotic flow micropump is carried out by using the extended parametric level set method.Compared with the traditional density method,the final structure boundary is clearer,and the intermediate density is less,making the results more convincing.Compared with the traditional level set method,the induced electroosmotic flow at different alternating voltage frequencies is larger.In order to apply the topology optimization method to the electroosmotic flow in the case of large pipe size,in this paper,we use the Helmholtz-Smoluchowski slip boundary condition to replace the electric double layer in the electroosmotic flow model,which simplifies the physical model.Then,by using the penalty term similar to the Brinaman penalty model,the slip boundary condition on the implicit boundary is added to the Navier-Stokes equation,the continuous adjoint equation and adjoint sensitivity of the problem are derived.Then the extended parametric level set method is used to optimize.Finally,based on topology optimization results of previous mixers,a new DC(Direct Current)electroosmotic micromixer is proposed.The EOF mixer can effectively reduce the number of electrodes and the voltage,which reduces the difficulty and cost of manufacturing.