Numerical Simulation Based On Finite Element Theory Of Pres-sure-Driven Flow In Circular Microchannels

The structural characteristic of microfluidic chips is microchannels network, themicrofluidic chips rely on fluid flow to achieve the transport of the sample and theprocess of the mixing and separation and reaction or detection, the key problem is toachieve the precise control of microfluidic. In this paper, considering the boundaryslip effects and the electrokinetic effects of micro-scale fluid flow, starting from thebasic equations of hydromechanics, a multiphysics coupled electrodynamics mathe-matical model of microfluidic was established, and numerical simulation of streamingpotential and flow characteristics of pressure-driven flow in circular microchannelsbased on the finite element method was studied. The main research task of this paperis as follows:Firstly, using the Nernst-Planck equation coupled the Poisson equation and theNavier-Stokes (NS) equations to described electric double layer potential and ion dis-tribution in smooth circular microchannels, and established the Pois-son-Nernst-Planck (PNP) model, using the finite element software COMSOL to solveequations, numerical solution of electric double layer potential in microchannels wasobtained, comparative analysis of the electric double layer potential of the PNP modeland the traditional Poisson-Boltzmann (PB) model. The results show, when the cha-racteristic length of the microchannel is small or ionic concentration is low, theBoltzmann distribution assumption is not satisfied, the electric double layer potentialof the two model is different, compared with the PB model, the PNP model can moreaccurately description of the electric double layer microchannel potential and ion dis-tribution.Secondly, in the smooth circular microchannel, based on the PNP model simu-lated the pressure-driven flow in microchannels, and analyzed streaming potential inmicrochannels and fluid flow rate. The results showed, the electrokinetic effects havea blocking effect on the flow and the boundary slip effects have a promoting effect.With the pressure gradient increasing or ion concentration decreasing, streaming po-tential increases. With the characteristic length of the microchannel increasing, thestreaming potential increases rapidly at first and then slowly decreases. When cha-racteristic length is very small or ionic concentration is very low, the flow rate isgreater deviates from the theoretical value, and the impact of electrokinetic effects on the flow is obviously. The phenomenon of the partial reflowing in the small characte-ristic length channel occurs for the low ion concentration solution, and the funda-mental reason is that the direction of the fluid shear stress changed, considered thevelocity slip, the boundary slip effects exacerbated the reflux of fluid near the wall ofthe microchannel, and reduced the streaming potential, at the same time, the flow vo-lume increases. When there is no reflow phenomenon, streaming potential and flowvelocity increases with slip coefficient increasing, and when the ion concentration islow, the impact of boundary slip effects on the flow rate and streaming potential is notobviously. These results enrich the basic theory of pressure-driven flow in circularmicrochannels.Thirdly, the pressure-driven flow in the circular micro-diffusion tube was studied.The results show, the streaming potential along the flow direction is non-linear in-creasing, and the streaming potential of the diffusion direction is greater than theshrink direction. With the ion concentration or the diffusion angle increasing, thestreaming potential decreases, but increases with the pressure differential increasing.At the same pressure differential, the flow volume rate of the diffusion direction isgreater than the shrink direction, considered the electrokinetic effects, the flow vo-lume has been reduced, especially when ion concentration is very low, considered theboundary slip effects, the flow volume increases. With the ion concentration or slipcoefficient increasing, flow efficiency slight increases. The length and spread angle ofmicro-diffusion tube too big or too small is disadvantage for flow efficiency. Theseresults provide references to improve the flow volume and the flow efficiency of mi-cro-diffusion tubes.Finally, a physical model of rough circular microchannel was established bytypical roughness elements and random roughness, the numerical simulation of pres-sure-driven flow in rough microchannels was studied. The results show, with thenumber of roughness elements and the height and the width of roughness elementsincreasing, the streaming potential decrease, but increase with the slip coefficient in-creasing. The friction coefficient increase with the number of roughness elements andthe height and the width of roughness element increasing, but decrease with the slipcoefficient increasing.