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Pressure drop of single phase flow in microchannels and its application in characterizing the apparent rheological property of fluids

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Abstract

The aim of this work was to experimentally examine apparent rheological properties of fluids in microchannels based on pressure drop. Pressure drops of Newtonian and non-Newtonian fluids in microchannels were measured using pressure sensors. The effects of flow rate, Reynolds number, and viscosity of fluids on the pressure drop of single phase flow in microchannels were investigated, and the measurements of pressure drop were compared with prediction models. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 26/Re. The results show that the pressure drop of Newtonian fluid is in good agreement with the prediction formula proposed by Cornish. However, the pressure drop of non-Newtonian fluid deviates from the theoretical prediction. A power-law is proposed for the relationship between the apparent viscosity of non-Newtonian fluid and the characteristic shear rate in a microchannel based on the pressure drop measurement. This relationship between the apparent viscosity and the characteristic shear rate in a specific microchannel is completely different from the rheological curve measured by cone-and-plate rheometer, due to the heterogeneous distribution of shear rates at the radial direction for non-Newtonian fluids flowing in a microchannel.

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Abbreviations

Q :

Volumetric flow rate, m3 s−1

ρ :

Density of fluid, kg m−3

η :

Viscosity of fluid, Pa s

k :

Consistency coefficient of fluid, Pa s–n

n :

Flow characteristic index of fluid

f :

Friction factor

Re :

Reynolds number

Re* :

Generalized Reynolds number

ΔP :

Pressure drop, Pa

u :

Velocity of fluid, m s−1

D h :

Hydraulic diameter of microchannel, m

τ w :

Wall shear stress, N

\(\dot{\gamma }_{\text{w}}\) :

Apparent shear rate, s−1

W :

Width of microchannel, m

D :

Depth of microchannel, m

L :

Length of microchannel, m

w:

Wall of microchannel

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Acknowledgements

The financial supports for this project from the National Natural Science Foundation of China (No. 21878212, 91634105, 21776200, 21576186), and the Tianjin Natural Science Foundation (17JCQNJC05300) are gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300372, People’s Republic of China

    Xiaohan Yang, Netsanet Tesfaye Weldetsadik, Zafar Hayat, Taotao Fu, Chunying Zhu & Youguang Ma

  2. The 718th Research Institute of China Shipbuilding Industry Corporation, Handan, 056027, People’s Republic of China

    Shaokun Jiang

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  1. Xiaohan Yang
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  2. Netsanet Tesfaye Weldetsadik
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  3. Zafar Hayat
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Correspondence to Taotao Fu.

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Yang, X., Weldetsadik, N.T., Hayat, Z. et al. Pressure drop of single phase flow in microchannels and its application in characterizing the apparent rheological property of fluids. Microfluid Nanofluid 23, 75 (2019). https://doi.org/10.1007/s10404-019-2241-y

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