Applications Of Electroosmotic Flows Of Non-Newtonian Fluids With Slip Boundary Condition

In this paper,we study the velocity distribution of electroosmotic flows of non-Newtonian fluids in different microchannels with slip boundary condition.The paper is divided into five chapters.In chapter 1,we briefly introduce the basic knowledge of non-Newtonian fluid,electroosmotic flow,fractional calculus,integral transformation and finite difference method.In chapter 2,we study electroosmotic slip flow of Eyring fluid in a slit microchannel under the electric field and pressure.The mechanical model of the Eyring fluid in the micro-parallel pipeline is established considering the micro-scale effect,the electric field effect,the non-Newtonian characteristic and the slip boundary condition.By solving the linear Possion-Boltzmann equation and the Cauchy momentum equation,we give the exact solution and approximate analytical solution of the velocity distribution,and we discuss the influence of the above factors on the electroosmotic flow.The influence of electric field and pressure on the velocity distribution is compared and analyzed,and meaningful results are obtained.In chapter 3,the electroosmotic flow of a fractional Oldroyd-B fluid in a circular microchannel is studied.The linear Navier slip velocity model is used as the chosen slip boundary condition.Exact solutions for the electric potential and transient velocity are established by means of Laplace and finite Hankel transforms.And the velocity was presented as a sum of the steady part and the unsteady one.The corresponding solutions for the fractional Maxwell fluid,fractional second grade fluid,and Newtonian fluid can also be obtained from our results.Finally,numerical results for the fluid flow are obtained and some useful conclusions are drawn.Our results may be useful for the prediction of the flow behavior of viscoelastic fluids in microchannels and can benefit the design of microfluidic devices.In chapter 4,we use the finite difference method to discretize the fractional Oldroyd-B fluid in the tube,and simulate the velocity distribution and compare it with the construct-ed analytical solution.An effective numerical method is proposed.Finally,in chapter 5,we summarize the main conclusions,and discuss the current research of electroosmotic flow and fractional calculus.