Research On Multi-physics Coupling Lattice Boltzmann Method And Its Applications In Electrokinetic Mixing And Chemotaxis

The microfluidic chip is based on analytical chemistry and biotechnology, which has a wide range of applications in many fields, such as disease diagnosis, drug screening, envi-ronment monitoring, food security, judicial identification, counter-terrorism, aerospace and so on. Thus, the studies of the mechanism of the fluid control and the applications of mi-crofluidic chip have an important theoretical significance and far-reaching application value.Many fundamental problems in microfluidic chip including the electrokinetic mixing and chemotaxis problems, which are the researching focus in this paper, are involved in multi-physics coupling problems. However, in the multi-physics coupling problems, the macro-scale of the different physical fields has a great distinction, and the coupling always behave nonlinear character. Besides, due to the small scale of the microfluidic chip, it is very difficult to observe the complex fluid flow in the microfluidic chip, and it costs a lot to make experimentation. So, the experimental study of microfluidic chip is very difficult. In recent years, the lattice Boltzmann method (LBM) is developed rapidly due to its microscopic nature and mesoscopic characteristic. The relationship of the mulit-physics fields can be exactly described by LBM, and due to the locality principle of the LBM, it is quite suitable for large-scale parallel computing.The numerical study of the multi-physics coupling problem requires a high stability of the numerical method. However, the stability of the present LBM must be improved to study the the multi-physics coupling problem. In addition, it is also have to establish high-efficiency LBM to investigate the electrokinetic phenomenon in the microfluidic chip and chemotaxis. Hence, from the aspects of the stability improvement of LBM, the establish-ment of LBM and the application research, the main work of this paper have been carried out as follows:First of all, in terms of the theory related to multi-physics coupling LBM:(1) To improve the stability of LBM, two modified LBMs for incompressible Navier-Stokes equations and convection-diffusion equation are proposed via the addition of correc-tion terms in the evolution equations. Utilizing this modification, the value of the dimen-sionless relaxation time in the LBM can be kept in a proper range, and thus the stability of the LBM can be improved. Most of all, the proposed modified LBM can be extended to any other LBM, especially for the multi-physics coupling problems. The results of the sim-ulation of the natural convection in a square cavity show that a very high Rayleigh number (Ra) can be achieved (Ra=1012) by the modified LBM, which demonstrate that the stability of LBM has been improved significantly. The development of the modified LBM provides the basis for the following investigation of the multi-physics coupling problems.(2) Aimed at the highly nonlinear coupled Nernst-Planck model, we proposed the cor-responding multi-physics coupling LBM. Especially for the Nernst-Planck equation, a novel and efficient LBM is proposed. In addition, according to the complex coupling characteristic of Nernst-Planck model and the scale difference of the multi-physics, a reasonable iterative sequence and evolution number for each LBM are proposed.(3) A coupled LBM is proposed for the nonlinear coupled Keller-Segel (K-S) chemo-taxis model. Through the Chapman-Enskog analysis, the proposed LBM can correctly recover to the K-S model. Meanwhile, a local computational scheme for the gradient op-erator, which is included in the evolution equation, is developed, making the proposed LBM be implemented locally. Hence, both2D and3D problems with arbitrary geometries can be processed easily. In the numerical experiments, several representative chemotaxis problems are studied, including the blow up problem in square domain, chemotactic bacteria pattern formation in semi-solid medium in circle domain,3D pattern formation in liquid medium, and the tumor invasion into surrounding healthy tissue. The numerical results demonstrate the high efficiency, stability and robustness of the proposed LBM. Furthermore, the capa-bility of the proposed LBM in handling both2D and3D problems with complex domain is also illustrated.Next, in the applications of the electrokinetic mixing in microchannel and chemotaxis:(1) A comparison of the difference between Nernst-Planck model and Pois-son-Boltzmann model for the electro-osmotic flow in the microchannel with non-uniform surface potential is make. The comparison results show that Nernst-Planck model can exact-ly describe the interaction between the flow field and the ion concentration field, wherever, Poisson-Boltzmann model can not. After that, the mixing of non-Newtonian fluid in the micro-channel is studied. We mainly considered the influence of the pipeline flux when the non-Newtonian fluid is mixing. The results show that one should not simply focus on mixing and neglect liquid transport, especially for the shear thickening fluid.(2) A detailed investigation is performed for the single species and two species chemo-taxis blow up problems. For the single species chemotaxis blow up problem, the effects of the initial value, the bacterial diffusion coefficient and the chemotactic coefficient on the blow up problem are consider. Wherever, for the two species chemotaxis blow up prob-lem, the effects of the chemotactic coefficient for the first and second species are mainly considered.In summary, this paper take the micro fluid flow in the microfluidic chip and chemo-taxis as study background. Aimed at the multi-physics coupling characteristic, an efficient and stable coupled LBM has been developed. Moreover, a detailed numerical study of the electrokinetic mixing and chemotaxis is performed by the proposed coupled LBM. This work have broadened out the LBM study of the multi-physics coupling problems, and also provide a necessary basis for future studies.