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Research Papers: Fundamental Issues and Canonical Flows

Oscillatory Flow Between Two Hemispheres for Shearing Protein Solution

[+] Author and Article Information
Dejuan Kong

Department of Aerospace and
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: dejuanko@usc.edu

Anita Penkova

Mem. ASME
Department of Aerospace and
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: penkova@usc.edu

Satwindar Singh Sadhal

Professor
Fellow ASME
Department of Aerospace and
Mechanical Engineering,
University of Southern California,
400 G Olin Hall,
Los Angeles, CA 90089
e-mail: sadhal@usc.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 30, 2014; final manuscript received April 26, 2015; published online June 8, 2015. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 137(10), 101201 (Oct 01, 2015) (8 pages) Paper No: FE-14-1235; doi: 10.1115/1.4030484 History: Received April 30, 2014; Revised April 26, 2015; Online June 08, 2015

Protein aggregation, one of the common molecular mechanisms for neurodegenerative diseases, is affected by variety of physical factors, one of which is shear rate of protein solution. This paper provides theoretical background on the shear rate in the experimental system we have proposed to effectively apply and control shear. We carried out the mathematical analysis of the flow field resulted from torsional or transverse oscillation on the outer boundary between two concentric hemispheres by perturbation method. We have obtained analytical solutions for the velocity field, the shear rate, and the flow pattern of steady streaming created by the nonlinear interaction of the oscillatory flow.

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References

Figures

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Fig. 1

Schematic of the proposed experiment. The circular rod can be vibrated rotationally or laterally.

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Fig. 2

First-order dimensionless shear stress profiles on the equatorial plane over one time period for the torsional oscillation with β = 0.5. The dashed curve shows the time-average of absolute shear stress values over one period: (a) α = 1, (b) α = 5, and (c) α = 20.

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Fig. 3

First-order dimensionless shear stress profiles on the equatorial plane over one time period for the transverse oscillation with β = 0.5. The dashed curve shows the time-average of absolute shear stress values over one period: (a) α = 1, (b) α = 5, and (c) α = 20.

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Fig. 4

First-order dimensionless shear stress profiles on the equatorial plane over one time period for the torsional oscillation in a sphere. The dashed curve shows the time-average of absolute shear stress values over one period: (a) α = 1, (b) α = 5, and (c) α = 20.

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Fig. 5

The streaming flow pattern in the torsional oscillation case with β = 0.5: (a) α = 1 and (b) α = 20

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Fig. 6

The streaming flow pattern in the transverse oscillation case with β = 0.5: (a) α = 1 and (b) α = 20

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Fig. 7

Streaming intensity as a function of Womersley number α at various polar angles θ with β = 0.5 for (a) torsional and (b) transverse oscillations

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