Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis

Ding, Zhaodong; Jian, Yongjun

doi:10.1017/jfm.2021.380

Cited by 31 publications

(9 citation statements)

References 75 publications

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“…The electrical potential Ψ( y ) and the local net charge density ρ e are described by the following Poisson–Boltzmann equations: 10,16

\begin{matrix} right \nabla^{2} Ψ (y) & left = - \frac{ρ_{e} (y)}{ϵ}, \\ right ρ_{e} (y) & left = z_{ν} e (n_{+} - n_{-}) = - 2 n_{0} z_{ν} e \sinh [(z_{ν} e Ψ) / (k_{b} T)], \end{matrix}

where

n_{\pm} = n_{0} \exp ([], \mp ((), e z_{ν} normalΨ) false/ ((), k_{b} T))

are the ionic number concentrations for the cations and anions in the liquid respectively, ϵ is the dielectric coefficient of the electrolyte liquid, e is the electron charge, z ν is the valence, k b is the Boltzmann constant, n 0 is the ion density of bulk liquid, and T is the absolute temperature. Assuming the electrical potential Ψ( y ) is low, the Debye–Hückel approximation can be applied to obtain the linearized equation 10,24

\frac{{normald}^{2} normalΨ}{normald y^{2}} = k^{2} normalΨ, with k^{2} = \frac{2 n_{0} z_{ν}^{2} e^{2}}{ϵ k_{B} T} .

…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Introduce a set of dimensionless parameters:

\overset{u}{true} = \frac{u}{U_{e o}}, \overset{y}{true} = \frac{y}{h}, \overset{t}{true} = \frac{t μ}{ρ h^{2}}, \overset{ω}{true} = \frac{ω ρ h^{2}}{μ}, K = k h, L = \frac{l}{h}, D e = λ \frac{μ}{ρ h^{2}}, U_{e o} = - \frac{ϵ E_{0} {normalΨ}_{0}}{μ},

where L is the dimensionless slip length, U eo is the steady Helmholtz–Smoluchowski velocity and De is the Deborah number characterizing the magnitude of the elastic effect. As De → 0, the fluid relaxes much faster than the typical time scale of the flow and the Newtonian flow behavior is recovered, and while De > 1, the relaxation time of the fluid is larger than the time scale of the flow and the fluid elasticity dominates the flow behavior 24 . Then, the dimensionless equation is given by

D_{\overset{t}{true}}^{1} \overset{u}{true} = - D e^{α} D_{\overset{t}{true}}^{α + 1} \overset{u}{true} + D e^{β - 1} D_{\overset{t}{true}}^{β - 1} ((), \frac{\partial^{2} \overset{u}{true}}{\partial {\overset{y}{true}}^{2}}) + ([], D e^{α} D_{\overset{t}{true}}^{α} \cos false(\overset{ω}{true} \overset{t}{true} false) + \cos false(\overset{ω}{true})

…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…As De → 0, the fluid relaxes much faster than the typical time scale of the flow and the Newtonian flow behavior is recovered, and while De > 1, the relaxation time of the fluid is larger than the time scale of the flow and the fluid elasticity dominates the flow behavior. 24 Then, the dimensionless equation is given by…”

Section: Theoretical Formulationmentioning

confidence: 99%

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Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

Tian

Ding

2022

Math Methods in App Sciences

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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.

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“…The electrical potential Ψ( y ) and the local net charge density ρ e are described by the following Poisson–Boltzmann equations: 10,16

\begin{matrix} right \nabla^{2} Ψ (y) & left = - \frac{ρ_{e} (y)}{ϵ}, \\ right ρ_{e} (y) & left = z_{ν} e (n_{+} - n_{-}) = - 2 n_{0} z_{ν} e \sinh [(z_{ν} e Ψ) / (k_{b} T)], \end{matrix}

where

n_{\pm} = n_{0} \exp ([], \mp ((), e z_{ν} normalΨ) false/ ((), k_{b} T))

\frac{{normald}^{2} normalΨ}{normald y^{2}} = k^{2} normalΨ, with k^{2} = \frac{2 n_{0} z_{ν}^{2} e^{2}}{ϵ k_{B} T} .

…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Introduce a set of dimensionless parameters:

\overset{u}{true} = \frac{u}{U_{e o}}, \overset{y}{true} = \frac{y}{h}, \overset{t}{true} = \frac{t μ}{ρ h^{2}}, \overset{ω}{true} = \frac{ω ρ h^{2}}{μ}, K = k h, L = \frac{l}{h}, D e = λ \frac{μ}{ρ h^{2}}, U_{e o} = - \frac{ϵ E_{0} {normalΨ}_{0}}{μ},

D_{\overset{t}{true}}^{1} \overset{u}{true} = - D e^{α} D_{\overset{t}{true}}^{α + 1} \overset{u}{true} + D e^{β - 1} D_{\overset{t}{true}}^{β - 1} ((), \frac{\partial^{2} \overset{u}{true}}{\partial {\overset{y}{true}}^{2}}) + ([], D e^{α} D_{\overset{t}{true}}^{α} \cos false(\overset{ω}{true} \overset{t}{true} false) + \cos false(\overset{ω}{true})

…”

Section: Theoretical Formulationmentioning

confidence: 99%

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Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

Tian

Ding

2022

Math Methods in App Sciences

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“…The streaming potential and EKEC have been investigated in various geometric shapes [38][39][40][41][42]. Based on the experimental study of Van der Heyden et al [43], wall zeta potential and surface charge density presented by Choi and Kim [44] were utilized to describe the electrokinetic flow-induced currents in nanofluidic channels.…”

Section: Introductionmentioning

confidence: 99%

Electrokinetic energy conversion through cylindrical microannulus with periodic heterogeneous wall potentials

Chu¹,

Jian²

2022

J. Phys. D: Appl. Phys.

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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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“…They summarized the effects of the dimensionless electrokinetic width and the rotational angular velocity on the streaming potential. Ding and Jian [32] studied the flow of viscoelastic fluid under an oscillating pressure gradient and concluded the resonances that are generated for the streaming potential field and for the flow rate. In many studies, the magnetic field is often applied based on the pressure gradient.…”

Section: Introductionmentioning

confidence: 99%

The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces

Bian

Jian

2021

Micromachines

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In this paper, the effects of asymmetrically modulated charged surfaces on streaming potential, velocity field and flow rate are investigated under the axial pressure gradient and vertical magnetic field. In a parallel-plate microchannel, modulated charged potentials on the walls are depicted by the cosine function. The flow of incompressible Newtonian fluid is two-dimensional due to the modulated charged surfaces. Considering the Debye–Hückel approximation, the Poisson–Boltzmann (PB) equation and the modified Navier–Stokes (N-S) equation are established. The analytical solutions of the potential and velocities (u and v) are obtained by means of the superposition principle and stream function. The unknown streaming potential is determined by the condition that the net ionic current is zero. Finally, the influences of pertinent dimensionless parameters (modulated potential parameters, Hartmann number and slip length) on the flow field, streaming potential, velocity field and flow rate are discussed graphically. During the flow process and under the impact of the charge-modulated potentials, the velocity profiles present an oscillating characteristic, and vortexes are generated. The results show that the charge-modulated potentials are beneficial for the enhancement of the streaming potential, velocity and flow rate, which also facilitate the mixing of fluids. Meanwhile, the flow rate can be controlled through the use of a low-amplitude magnetic field.

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Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis

Abstract: Abstract

Cited by 31 publications

References 75 publications

Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

Quasi‐periodic electro‐osmotic flow of fractional viscoelastic fluids

Electrokinetic energy conversion through cylindrical microannulus with periodic heterogeneous wall potentials

The Streaming Potential of Fluid through a Microchannel with Modulated Charged Surfaces

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