Unsteady Electroosmotic Flow Of Maxwell Fluids Through A Parallel Plate Micro-channel

Microfluid flow is the problem in the microscale pipeline, which is widely used in the area of physics, biology, chemistry and so on. Usually the ion in the electrolyte solution and micro in pipe wall are procuded by the interaction and eventually form electric double layer (EDL). By the influence of the extranal electric field, the free ions will move to nearby motion of fluid particles as the viscosity of the fluid, eventually the electroosmotic flow (EOF) forms. The study about EOF of Newtonian fluid has become a mature technology in theory and experiment.In this paper, we represent an analytical solution of transient velocity for unsteady electroosmotic flow of Maxwell fluids through micro-parallel channel using the method of Laplace transform. The constitutive relations of linear viscoelastic is simulated by the model of Maxwell fluids. We solve the problem including the linearized Poisson-Boltzmann equation, the Cauchy momentum equation and Maxwell constitutive equation. We analyze electroosmotic flow velocity by the influence of dimensionless Reynolds number, Relaxation time and electric width K. We get the semi-analytical solutions by inverse Laplace numerical calculation in parallel plate micro-channel. The results show that the velocity of Maxwell fluids strongly depends on relaxation time λ1and dimensionless timet driven by Direct Current (DC). With the increasing of relaxation time λ1the fluid tends to be steady and slow DC EOF. With the increasing of dimensionless time t, the velocity of electroosmotic flow tends to be steady DC EOF. The velocity of DC EOF is mainly concentrated in a slit area.The velocity of Maxwell fluids strongly depends on relaxation time λ1,Reynolds number and dimensionless timet driven by Alternating Current (AC). For the given Reynolds number,the velocity amplitude changes fast as the increasing of relaxation time λ1. For the given relaxation time λ1, the velocity amplitude changes fast as the increasing of Reynolds number. The velocity of AC EOF changes obvious in the given relaxation time λ1that the velocity amplitude increases with the dimensionless timet. The velocity of AC EOF is presented periodic change and the sharp fluctuation.The velocity of Maxwell fluids strongly depends on relaxation time λ1, pulse-width a and dimensionless time t driven by Pulse Current. For the given pulse-width a, the Pulse Current velocity amplitude changes fast as the increasing of relaxation time λ1. For the given relaxation timeA λ1, the Pulse Current velocity amplitude changes fast as the increasing of pulse-width a. It is obvious that the velocity amplitude of electroosmotic flow changes under the same relaxation time λ1with the increasing of dimensionless time t, and the change of EOF velocity amplitude mainly concentrated in the solid wall which is close to EDL. The velocity profile of frequency is different because of the different pulse width a. With the pluse width a increases, the different frequency of velocity profile changes slow, as meaning the long cycle time.