Analysis And Hydrodynamic Properties Of The Electroosmosis Flow In The Annular And Circular Microchannels

In this study,the electroosmotic flow(EOF)in the annular and circular microchannels were discussed by finding the analytical solution and combining some numerical simulation.The physical model in this study include the Poisson-Boltzmann(P-B)equations,Navier-Stokes(N-S)equation and Debye-Hiickel(D-H)approximation etc.The steady and starting EOF in the annular and circular microtubes were discussed base on D-H approximation and the the P-B equation.An analytical solution of the EOF were first obtained under the linearized Debye-Hiickel approximation(DHA),and then extended to the non-linear Poisson-Boltzmann equation(PBE)by the method of homotopy.The annular tube has different zeta potentials(denoted by ?,?,respectively)developed on the inner and outer channel walls.The EOF,influenced by five physical parameters,the pair of zeta potentials(?,?),b-the ratio of the inner to outer radii,K-the electrokinetic width as well as ? which measures the nonlinearity of the P-B equation,has been studied.The steady-state EO flow rate for any given pair of(?,?)were optimized with respect to the ratio b of inner to the outer radii,and the corresponding temporal developments of the optimal EO flow were given detailed investigation.The optimal EO flow rates QM(?,?)were presented on the ?-? plane for several electrokinetic widths(K)to illustrate their general trends versus the corresponding b(denoted by bmax),which serves as a useful guide for practical applications.Investigation were also given to the shifts of bmax and QM(?,?)with varying the parameter ?,which measures the nonlinearity of the PBE.In this study,the EOF in a circular tube with longitudinal uniform and non-uniform zeta potential were considered,and discussed the influences of different K and ? for the steady and unsteady starting EOF,For the uniform case,the variations of flow rate for small and large K and ? in the unsteady state were found,and the corresponding temporal development of the starting EOF have received detailed investigation.For longitudinal non-uniform case,the distributions of the steady velocity in a circular micro-tube with different K and ? have been investigated through an example that the Zeta potential has a small periodic perturbation in the tube,and the corresponding temporal development of the starting EOF have received detailed investigation.