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An analytical model for flow rectification of a microdiffuser driven by an oscillating source

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Abstract

In this study, we employ the similarity transformation and the AC-circuit analogy to investigate the flow rectification property of a microdiffuser. Driven by an oscillating source, the transient two-dimensional radial flow of viscous fluid in a planar microdiffuser, which consists in a wedge-shaped domain bounded by two circular arcs, is solved. The ratio of flow impedances is determined to evaluate the performance of the flow rectification. By gauging the leverage between viscous and unsteady effects, we discuss the influences of the half angle, the Reynolds number, the excitation frequency, and the ratio of inlet to outlet radii in flow directing properties of the microdiffuser. We find that net flow in the expansion direction only occurs when the product of the half angle and the Reynolds number is small and the Womersley number is low. Moreover, the reversal Womersley number, at which preference of flowing direction switches, decreases with increasing the product of half angle and the Reynolds number or reducing the ratio of inlet to outlet radii. We find that a wider half angle, stronger oscillation, higher frequency, broader inlet, and longer microdiffuser all contribute to the augmentation of the transient inertia and lead to the promotion of converging flow. The specific goal of this study is to provide the means to manipulate the flow rectification effect of a microdiffuser by varying its geometry or the driving conditions.

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Abbreviations

f :

f(θ, t) = −[F(θ, t) + 1]/3

F :

Dimensionless velocity [F(θ, t) = ur/2ν]

h :

Radius of microdiffuser inlet (μm)

H f :

Hydraulic inductance (Pa s2 m−2)

p :

Pressure (Pa)

Δp :

Pressure drop across microdiffuser (Pa)

p 1 :

p 1(r, t) = p(r, θ, t) − 4rν2 F/r 2 (Pa)

℘(θ):

Weierstrassian elliptic function

Q :

Instantaneous flow rate per unit depth of microdiffuser (m2 s−1)

r :

Radial direction in the polar coordinate

R :

Radius of microdiffuser outlet (μm)

Re :

Reynolds number (Re = 2αF 0)

R f :

Flow resistance (Pa s m−2)

t :

Time (s)

u :

Velocity component in the radial direction

Wo :

Womersley number [Wo = αh(ω/ν)1/2]

Z f :

Flow impedance (Pa s m−2)

α :

Half angle of microdiffuser (°)

η :

Ratio of flow impedance (η = Z f,o/Z f,i)

ν :

Kinematic viscosity of fluid (m2 s−1)

θ :

Angular direction in the polar coordinate (°)

ρ :

Density of fluid (kg m−3)

ω :

Excitation frequency (rad s−1)

0:

Centerline of microdiffuser (θ = 0)

i:

Inflow/expansion flow

o:

Outflow/contraction flow

opt:

Optimal

r:

Reversal

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Acknowledgments

This work was supported by the Graduate Student Fellowship of the Department of Mechanical Engineering at National Taiwan University (Sung Tsang) and the Ministry of Science and Technology of Taiwan under Grant Number NSC 101-2221-E-002-064-MY3.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Taiwan University, 1 Sec. 4 Roosevelt Road, Taipei, 10617, Taiwan

    Chen-li Sun, Sung Tsang & Hung-Yen Huang

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  1. Chen-li Sun
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  2. Sung Tsang
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Correspondence to Chen-li Sun.

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Sun, Cl., Tsang, S. & Huang, HY. An analytical model for flow rectification of a microdiffuser driven by an oscillating source. Microfluid Nanofluid 18, 979–993 (2015). https://doi.org/10.1007/s10404-014-1487-7

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