Abstract
Paper-like materials have found widespread applications in various fields, especially recently emerging applications in biomedicine as paper-based devices, where liquid wicking behavior plays a significant role. Although tremendous experimental evidence has indicated that fluid control is a key technology to improve the performance of these paper-based devices, the underlying mechanisms of liquid wicking behavior in paper-like materials remain unclear. Numerical and mathematical techniques provide effective strategy and great potential in understanding the liquid flowing process in the complex fibrous structure of paper-like materials. In this review, we first present the basic physical process and key factors of liquid wicking behavior in paper-like materials. Furthermore, we review various macroscopic and mesoscopic mathematical models on fluid flow in porous materials, focusing on each model’s advantages and challenges, and summarize their related biomedical applications. The aims are to better understand the underlying mechanisms of liquid wicking behavior in paper-like materials through mathematical models and to provide guidance in the design and optimization of paper-based biomedical devices.
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Abbreviations
- \(h\) :
-
The distance migrated by the liquid front (m)
- \(\sigma\) :
-
The vapor–liquid interfacial tension (N m−1)
- \(\theta\) :
-
The contact angle (rad)
- \(\mu\) :
-
The fluid dynamic viscosity (Pa s)
- \(t\) :
-
The liquid wicking time (s)
- \(\rho\) :
-
The liquid density (kg m−3)
- \(g\) :
-
The gravity acceleration (m s−2)
- \(R\) :
-
The effective pore radius (m)
- \(K\) :
-
The permeability (m2)
- \(\varepsilon\) :
-
The porosity
- \(\varphi\) :
-
The drainage coefficient
- \({\delta _{\text{g}}}\) :
-
The length of gap between flexible film and the paper surface (m)
- \(\delta\) :
-
The thickness of paper (m)
- \(\alpha\) :
-
The empirical coefficient considering the length of wetting lines contacted with the hydrophobic wax boundaries
- \(\beta\) :
-
The correction coefficient
- \({\theta _{\text{b}}}\) :
-
The contact angle on side boundaries (rad)
- \(\omega\) :
-
The fiber water content
- \({\dot {m}_{{\text{evp}}}}\) :
-
The evaporation rate of liquid weight per unit area per second (kg m−2 s−1)
- \({P_\omega }\) :
-
The water saturated pressure (Pa)
- \({P_{{\text{RH}}}}\) :
-
The partial pressure of water vapor (Pa)
- \(\gamma\) :
-
The heat of vaporization of water (W m−1 s−1)
- \({V_{{\text{air}}}}\) :
-
The air flow velocity in the environment (m s−1)
- \({q_0}\) :
-
The evaporation rate of liquid volume per unit area per second (m s−1)
- \(r_{{{\text{eff}}}}^{'}\) :
-
The empirical fitting parameter in Eq. 10
- \(b\) :
-
The empirical fitting parameter in Eq. 10
- \(\nabla p\) :
-
The pressure drop (Pa m−1)
- \(\vec {V}\) :
-
The liquid velocity (m s−1)
- \({\mu _{\text{e}}}\) :
-
The effective viscosity for Brinkman term (Pa s)
- \(W\) :
-
The channel width (m)
- \(H\) :
-
The channel thickness (m)
- \(L\) :
-
The channel length (m)
- \(Q\) :
-
The volumetric velocity (m3 s−1)
- \(U\) :
-
The voltage change (V)
- \(I\) :
-
The current (A)
- \({R_i}\) :
-
The resistance for each segment i (Ω)
- \({P_{{\text{ca}}}}\) :
-
The capillary force (Pa)
- \(S\) :
-
The local saturation of porous material
- \({\theta _i}\) :
-
The inclination angle of paper strip with respect to horizontal direction (rad)
- \({R_0}\) :
-
The initial load (Pa s m−3)
- \(A\) :
-
The cross-sectional area (m2)
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Acknowledgements
This work was financially sponsored by the National Natural Science Foundation of China (51676153), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (51721004), the National Program for Support of Top-Notch Young Professionals, the National Instrumentation Program of China (2013YQ190467), the Key Program for Science and Technology Innovative Research Team in Shaanxi Province of China (2017KCT-22), the Program for Innovative Research Team in Yulin Shaanxi Province of China (2017KJJH-02), the China Postdoctoral Science Foundation (2017M623167), the Initiative Postdocs Supporting Program (BX201700186) and the Fundamental Research Funds for the Central Universities (xjj2018256).
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This article is part of the topical collection “2018 International Conference of Microfluidics, Nanofluidics and Lab-on-a-Chip, Bei**g, China” guest edited by Guoqing Hu, Ting Si and Zhaomiao Liu.
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Liu, Z., He, X., Han, J. et al. Liquid wicking behavior in paper-like materials: mathematical models and their emerging biomedical applications. Microfluid Nanofluid 22, 132 (2018). https://doi.org/10.1007/s10404-018-2151-4
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DOI: https://doi.org/10.1007/s10404-018-2151-4