We study the magnetohydrodynamic electro-osmotic flow of Maxwell fluids through two microparallel plates with patterned charged surfaces. The combined influences of two imposed time periodic electric fields (one along the lateral direction and the other along the axial direction) and an external vertical magnetic field are taken into account. The flow is driven by Lorentz force and electric field force and is 2D due to charge modulated surfaces. Upon the assumptions of the Debye-Hückel linearization, the analytical solutions of the stream function and velocity field are derived. The variations in velocity with the dimensionless relaxation time De, the Hartmann number Ha, and the oscillating Reynolds number Re are depicted graphically. Furthermore, the parameters that influence the generation of vortexes in the flow field are also discussed.
An innovative device transforming the active control of rotating rods to passive control with a pair of impellers is proposed and numerically examined in this paper. The coupling response of a vortex-induced vibrating (VIV) circular cylinder symmetrically equipped with two impellers that are free to rotate is analyzed based on the results of computations that carried out for a reduced velocity range of Ur = 2–14 at a low Reynolds number of 150. In comparison with the bare cylinder, both the in-line and cross-flow responses are significantly augmented in the VIV initial branch with the introduction of a pair of passively rotating impellers, which is mainly attributed to the unstable rotation response in both direction and speed and the wake adjustment including the reduction in vortex formation length and broadening of flow wake. In the VIV lower branch, although the response amplitude is close to that of a bare cylinder, the strong interaction between two directional responses occurs with the same dominant frequency locking on the natural one. Nevertheless, the coexistence of multiple vibration frequencies leads to irregular oscillation trajectories and irregular vortex shedding. Moreover, the secondary vortex street is observed in the whole Ur range, but the number of merged vortices for the formation of secondary vortex street varies with Ur, depending on the response amplitude and the interaction between the shear layers of the main cylinder and impellers. In terms of time-averaged rotation, the symmetrical inward counter-rotating pattern is achieved despite the intermittent alteration of rotation direction. Furthermore, the vibration–rotation coupling is demonstrated from the variation of time-averaged rotation speed that closely follows the variation of vibration amplitude against Ur.
In microfluidic electrokinetic flows, heterogeneous wall potentials are often required to fulfill some functions, such as increasing dispersion and mixing efficiency. In this paper, we study the pressure-driven electrokinetic flow through microannulus with heterogeneous wall potentials in circumferential direction. The streaming potential induced by the ions accumulating in downstream of the microannulus is considered and the electrokinetic energy conversion efficiency is further investigated. Interestingly, based on the method of Fourier expansion, the analytical solutions of fluid velocity, streaming potential and energy conversion efficiency are derived for arbitrary peripheral distribution of the small wall potential for the first time. Four specific patterned modes of the heterogeneous wall potential, i.e., constant, step, sinusoid with period 2π and sinusoid with period π/2 are represented. The distributions of the electric potential and the velocity for four different modes are depicted graphically. Furthermore, the variations of the streaming potential and the electrokinetic energy conversion efficiency with related parameters are also discussed. Results show that when these integral values from -π to π associated with the wall potentials are identical, the streaming potential and the electrokinetic energy conversion efficiency corresponding to different modes are the same. Additionally, the amplitude of fluid velocity peripherally reduces with the increase of the wavenumber of wall potential distribution in θ-direction.
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