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Viscoelastic fluids have many applications in engineering, and studying the complex fluidity of viscoelastic fluids can improve their applicability. Based on the flow caused by the pressure or the moving plate with various velocities, the aim of this paper is to deeply study the significance of absorbing boundary condition for the flow mechanism analysis of the fractional Maxwell fluid, of which the constitutive relation is formulated by introducing the relaxation parameter and the fractional parameter with considering the memory characteristics. For treating the model in a semi-infinite boundary domain, the artificial boundary method is applied to transfer it to a problem in a bounded domain with absorbing boundary condition, which is solved numerically by the finite difference method combined with the L1 formula and verified by numerical examples. The difference of the flow characteristics is subject to the direct truncation boundary condition and the absorbing boundary condition is compared and the effectiveness and rationality are analyzed graphically, and the influences of the dynamic parameters on the velocity and the flow mechanism are also discussed. The main findings of this research are that the larger relaxation parameter plays a role in a stronger delay effect, a larger fractional parameter refers to the stronger memory characteristics of the delay effect, and the smaller Reynolds number leads to the larger viscous force, all of which lead to a slower flow process. [ABSTRACT FROM AUTHOR]

This work investigates unsteady electro-osmotic flow of a fractional second-order viscoelastic fluid in a micro-rectangle channel with considering depletion effects. Due to the existence of depletion, there are depletion layer near the plate and bulk flow adjacent to depletion layer for the flow in the whole domain. In order to express the boundary conditions at the interface, we introduce Maxwell stress to describe the interaction between Newtonian fluid and viscoelastic fluid with fractional derivative. To ensure the validity of the semi-analytical solution obtained by Laplace transform, the numerical solutions are acquired by finite difference method and Grünwald-Letnikov approximation and both of them have a better agreement. The increasing viscosity of viscoelastic fluid leads to the increasing driving difficulty of fluid in non-depleted layer and the decreasing velocity amplitude at steady state. Moreover, the increasing interfacial zeta potential difference can promote the fluid flow, and the change of interface charge density makes the velocity at the interface change dramatically. [ABSTRACT FROM AUTHOR]

The finite difference schemes for equations depicting the fluid flow, heat and mass transfer of viscoelastic fluid in porous media based on fractional constitutive model are analyzed, when Soret and Dufour effects are taken into account. Different from the conventional fractional partial differential equations, the governing momentum equation of this system not only contains convection terms, but also a term: D t β 0 (∂ 2 u / ∂ y 2) , which are great challenges when we do the stability analysis. In addition, the temperature equation and concentration equation are coupled with each other, which increases the difficulty of numerical analysis. By using the energy method, the stability and convergence of the finite difference schemes employed for the governing equations are obtained. The accuracy of the scheme for momentum equation is O (τ + h x 2 + h y 2) , while the one for temperature and concentration equations is O (τ 2 + h x 2 + h y). Finally, numerical examples are presented to verify methods and demonstrate the analysis effectiveness. [ABSTRACT FROM AUTHOR]

In order to study the mass separation or mixture of EOF for biological or chemical fluids with viscoelastic characteristics, the EOF of two layers consisting of Newtonian fluid and fractional second-order fluid in a rotating frame in parallel microchannel is investigated. The numerical solutions are obtained by finite difference method. Two interesting phenomena can be found. One of them is that reverse flow can be found near the interface as the rotation velocity is big enough. Another is that the streamwise velocity will increase firstly and decrease subsequently before the steady flow reaches on account of the existence of angular velocity. [ABSTRACT FROM AUTHOR]