PNP Model For Numerical Simulation Of Non-newtonian Power-law Electroosmotic Flow In Plate Microchannels

The biochemical processes such as separation, mixing, reaction, testing of liquid samples can be achieved in microfluidic chips. Most of these processes are carried out in the microchannel. Blood, protein solution and other non-Newtonian power-law fluids are often used as analysis samples of biological fluid in the microchannel. So the studies of non-Newtonian power-law fluid in microchannels have great significance. This paper uses the finite element method(FEM) to simulate numerically the non-Newtonian power-law fluids in the microchannel electroosmotic flow(EOF) based on the Poisson-Nernst-Planck(PNP) model. The main research contents and results are as follows:The mathematical model of the PNP model of power-law EOF in 2D plate microchannel is studied and the FEM discrete model of multi-physics coupling is built, on the basis of the formation mechanism of the electrical double layer. The numerical solutions of PNP model is analyzed comparative with an exact solution of linear Poisson-Boltzmann model for power-law EOF, which has been verified to be correct under some assumptions. The results show the correctness and universality of PNP model for power-law EOF.Combining with dimensional analysis, the thin EDL of PNP model of power-law EOF in plate microchannel is simulated. The law of influence on the electrical double layer potential and the velocity in microchannel by many different parameters are also received. The studies show that for the electric double layer ζ potential affects the magnitude and positive/negative valence affects the thickness. For EOF velocity, the magnitude is affected by the viscosity coefficient, the external electric field and the ζ potential, while the distance from the wall where the velocity is zero to the position where the velocity is maximum value only affected by the power-law index. There are a power function relationship between the EOF flow rate and the external electric field, the viscosity coefficient and the ζ potential, where the index of viscosity coefficient is the negative derivative of the power law exponent index. Also, the microchannel height and the diffusion coefficient does have no affect on the electric double layer EOF. These results will enhance the understanding of the power-law EOF and can give a guide in improvement of operation technique on the electroosmotic flow.The EOF of power-law flow in the rectangular, triangular, sinusoidal, fractal roughness microchannel are simulated based on the PNP model. The impact of relative roughness and other parameters on the electrical double layer potential, velocity near the walls as well as the flow flux in the whole microchannel are studied. The studies display the influence law of roughness elements on EOF, and have a reference value to the theoretical development of microfluidic chip electroosmotic driven and practical application.