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In this work, we study the unsteady electro‐osmotic flow of fractional viscoelastic fluids in micro‐parallel channels, where the velocity slip effect on the walls is also considered. The analytical solution is obtained through solving the Cauchy momentum equation, together with the linearized Poisson–Boltzmann equation and the fractional Maxwell constitutive equation. The influences of the normalized electrokinetic width K, Deborah number De, slip length L and fractional derivative α on the velocity and volume flow rate are discussed. The results demonstrate that the dimensionless parameters L, De and K all have a promoting effect on the electro‐osmotic flow and resonance behavior of fractional Maxwell fluids. In addition, compared with the classical Maxwell fluid, the microstructure of the fractional Maxwell fluid weakens the resonance behavior. [ABSTRACT FROM AUTHOR]

The present study provides analytical and numerical solutions for an electromagnetohydrodynamic (EMHD) flow using a Caputo time-fractional Maxwell model. The flow is a typical rectangular channel flow. When the scale of the cross-stream is much smaller than the streamwise and spanwise scales, the model is approximated as a two-dimensional slit parallel plate flow. Moreover, the influence of the electric double layer (EDL) at the solid–liquid interface is also considered. The electro-osmotic force generated by the interaction between the electric field and the EDL will induce a flow (i.e., electro-osmotic flow). Due to the application of the electric field at the streamwise and the vertical magnetic field, the flow is driven by Lorentz force along the spanwise direction. Simultaneously, under the action of the magnetic field, the electro-osmotic flow induces a reverse Lorentz force, which inhibits the electro-osmotic flow. The result shows that resonance behavior can be found in both directions in which the flow is generated. However, compared with the classical Maxwell fluid, the slip velocity and resonance behavior of fractional Maxwell fluid are suppressed. In the spanwise direction, increasing the strength of magnetic field first promotes the slip velocity and resonance behavior, and then suppresses them, while in the streamwise direction, both the electro-osmotic flow and resonance behavior are suppressed with the magnetic field. [ABSTRACT FROM AUTHOR]

This study investigates the electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids through a microchannel under the Navier slip boundary condition. The flow is driven by the pressure gradient and electromagnetic force where the electric field is applied horizontally, and the magnetic field is vertically (upward or downward). When the electric field direction is consistent with the pressure gradient direction, the changes of the steady flow rate and velocity with the Hartmann number Ha are irrelevant to the direction of the magnetic field (upward or downward). The steady flow rate decreases monotonically to zero with the increase in Ha. In contrast, when the direction of the electric field differs from the pressure gradient direction, the flow behavior depends on the direction of the magnetic field, i.e., symmetry breaking occurs. Specifically, when the magnetic field is vertically upward, the steady flow rate increases first and then decreases with Ha. When the magnetic field is reversed, the steady flow rate first reduces to zero as Ha increases from zero. As Ha continues to increase, the steady flow rate (velocity) increases in the opposite direction and then decreases, and finally drops to zero for larger Ha. The increase in the fractional calculus parameter α or Deborah number De makes it take longer for the flow rate (velocity) to reach the steady state. In addition, the increase in the strength of the magnetic field or electric field, or in the pressure gradient tends to accelerate the slip velocity at the walls. On the other hand, the increase in the thickness of the electric double-layer tends to reduce it. [ABSTRACT FROM AUTHOR]

Complex fluids always possess obvious non-Newtonian properties that facilitate the occurrence and development of vortex instability in porous media, which is of critical significance in many natural and industrial processes. It is widely known that this flow instability is regulated by both fluid flow and solid structure. However, the quantitative understanding of how structural characteristics of porous space affect the evolution of vortex instability is still nascent, especially in the case of fluids with varying rheological properties. Herein, the flow of polymer solutions with distinct non-Newtonian properties through microcavity arrays is experimentally studied, by which we systematically explore the effect of structural parameters of the cavity array on vortex instability. We find that, for both Newtonian and shear-thinning fluids with negligible elasticity, the vortex evolution behavior in each cavity of the cavity array is identical to those in an isolated cavity. In contrast, for viscoelastic fluids, the vortex instability is visibly affected by cavity number and cavity–cavity interval, and this effect exhibits different forms when the fluid shear-thinning participates or not. Multiplex vortex instabilities are observed under these tested conditions. By multiplex, we mean the vortex formation dynamics and evolution patterns are diversified. These unusual evolution phenomena are then interpreted in terms of the interplay between the elongation and relaxation of polymers as they navigate among neighboring cavities. These results can help us to further understand the flow instability of complex fluids in porous media and evoke new strategies for microfluidic applications of efficient mixing. [ABSTRACT FROM AUTHOR]

• Electroosmotic and pressure-driven slip flow of fractional viscoelastic fluids in microchannels is studied. • Analytical solutions are derived using the Laplace transform and residue theorem. • Numerical schemes are also provided based on the finite difference approximation. • The effects of relevant parameters on the velocity profiles and flow rates are investigated. This study investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate microchannel under the combined effect of electroosmotic and pressure gradient forcings. Analytical solutions for velocity and potential distributions are derived using the Debye–Hackel linearization, Laplace transform, and residue theorem. Numerical solutions are also provided based on the finite difference method. The process through which the velocity and flow rate attain a steady state is related to the governing groups, including the fractional calculus parameter α , slip coefficient L , Deborah number D e , normalized electrokinetic width K and ratio Π of the pressure to electroosmotic driving forces. Results show that an increase in α , D e , L or Π increases the time required to reach a steady state. The steady flow rate depends on L and K but is independent of α and D e. For the same slip coefficient, increases in α , D e or K increase the slip velocity at the wall. [ABSTRACT FROM AUTHOR]

Energy conversion in micro/nano-systems is a subject of current research, among which the electrokinetic energy conversion has attracted extensive attention. However, there exist two different definitions on the electrokinetic energy conversion efficiency in literature. A few researchers defined the efficiency using the pure pressure-driven flow rate, while other groups defined the efficiency based on the flow rate with the inclusion of the effect of the streaming potential field. In this work, both definitions are investigated for different fluid types under the periodic electrokinetic flow condition. For Newtonian fluids, the two definitions give similar results. However, for viscoelastic fluids, these two definitions lead to significant difference. The efficiency defined by the pure pressure-driven flow rate even exceeds 100% in a certain range of the parameters. The result shows that in the case of viscoelastic flow, it is incorrect to define the energy conversion efficiency by pure pressure-driven flow rate. At the same time, the reason for this problem is clarified through comprehensive analysis. [ABSTRACT FROM AUTHOR]