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Research Papers: Fundamental Issues and Canonical Flows

Time-Periodic Electro-Osmotic Flow With Nonuniform Surface Charges

[+] Author and Article Information
Hyunsung Kim

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164-2920
e-mail: hyunsung.kim@wsu.edu

Aminul Islam Khan

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164-2920
e-mail: aminulislam.khan@wsu.edu

Prashanta Dutta

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164-2920
e-mail: prashanta@wsu.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 5, 2018; final manuscript received January 2, 2019; published online January 30, 2019. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 141(8), 081201 (Jan 30, 2019) (10 pages) Paper No: FE-18-1591; doi: 10.1115/1.4042469 History: Received September 05, 2018; Revised January 02, 2019

Mixing in a microfluidic device is a major challenge due to creeping flow, which is a significant roadblock for development of lab-on-a-chip device. In this study, an analytical model is presented to study the fluid flow behavior in a microfluidic mixer using time-periodic electro-osmotic flow. To facilitate mixing through microvortices, nonuniform surface charge condition is considered. A generalized analytical solution is obtained for the time-periodic electro-osmotic flow using a stream function technique. The electro-osmotic body force term is accounted as a slip boundary condition on the channel wall, which is a function of time and space. To demonstrate the applicability of the analytical model, two different surface conditions are considered: sinusoidal and step change in zeta potential along the channel surface. Depending on the zeta potential distribution, we obtained diverse flow patterns and vortices. The flow circulation and its structures depend on channel size, charge distribution, and the applied electric field frequency. Our results indicate that the sinusoidal zeta potential distribution provides elliptical shaped vortices, whereas the step change zeta potential provides rectangular shaped vortices. This analytical model is expected to aid in the effective micromixer design.

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Figures

Grahic Jump Location
Fig. 1

Schematic of time-periodic electro-osmotic flow with variable surface charge distributions along the channel

Grahic Jump Location
Fig. 2

The u-velocity distribution at different axial locations for sinusoidal zeta potential distribution along the channel surface: (a) x = 0, (b) x = L/5, (c) x = 3L/5, and (d) x = 4L/5. A DC electric field (E = 10 KV/m) is used for both studies.

Grahic Jump Location
Fig. 3

The velocity vector field and u-velocity contours with sinusoidal zeta potential distribution at both top and bottom walls at various nondimensional times: (a) =(π/2), (b) Ωt=(3π/4), (c) Ωt=π, and (d) Ωt=(5π/4). Here f=100Hz,k=(2π/L),H=100μm,ζ0=−100mV,Eref=10(kV/m).

Grahic Jump Location
Fig. 4

The velocity vector field and u-velocity contours for asymmetric surface potential distribution on upper and lower surfaces: (a) upper surface: ζ1x=ζ0sinkx, lower surface: ζ2x=−ζ0sin(kx) and (b) upper surface: ζ1x=ζ0sinkx, lower surface: ζ2x=ζ0cos(kx). Here f=100Hz,Ωt=(π/2),k=(2π/L),H=100μm,ζ0=−100mV,Eref=10kV/m.

Grahic Jump Location
Fig. 5

The effect of periodicity of zeta potential distribution on velocity vector field and u-velocity contours: (a) upper surface: ζ1x=ζ0sinkx, lower surface: ζ2x=ζ0sinkx and (b) upper surface: ζ1x=ζ0sinkx, lower surface: ζ2x=−ζ0sin(kx). Here f=100Hz,k=(4π/L), Ωt=(π/2),H=100μm,ζ0=−100 mVandEref=10kV/m.

Grahic Jump Location
Fig. 6

The effect of external electric field frequency on velocity vector field and u-velocity contours for symmetric surface potential distribution: (a) f=100Hz, (b) f=1kHz, and (c) f=10kHz. Here k=(2π/L),Ωt=(π/2),H=100μm,ζ0=−100mV,Eref=10 kV/m.

Grahic Jump Location
Fig. 7

The effect of channel height on velocity vector field and u-velocity contours for symmetric sinusoidal zeta potential distribution: (a) H = 50μm, (b) H = 100μm, and (c) H = 200μm. Here, f=100Hz,k=(2π/L),Ωt=(π/2),ζ0=−100mV,Eref=10kV/m.

Grahic Jump Location
Fig. 8

Schematic of step change in zeta potential along the channel

Grahic Jump Location
Fig. 9

The velocity vector field and u-velocity contours for step change in zeta potential at various nondimensional time: (a) Ωt=(π/2), (b) Ωt=(3π/4), (c) Ωt=π and (d)Ωt=(5π/4). Here f=100Hz,k=(2π/L),H=100μm,ζ1=−100mV,Eref=10kV/m.

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