Abstract
Rapid advances in microfluidic devices have induced interest in the study of the microscale flow mechanism. However, the experimental results of microscale flow often deviate from the classical theory, and we attribute this deviation to the changing liquid viscosity in the microchannels. Because of the effect of the solid–liquid intermolecular force, the viscosity of the liquid near the walls is different from the bulk viscosity. Based on molecular theory and wetting theory, we propose a modified apparent viscosity model. The apparent viscosity of the liquid in microchannels increases with the increase in wettability and decreases with the increase in distance from the wall and the increase in drive pressure. The apparent viscosity near the hydrophilic wall is higher than the bulk viscosity, which increases the flow friction in the microchannels. To validate this model, we experimentally investigate the frictional characteristic of a deionized water flow in smooth parallel-plate microchannels with different wettabilities and heights of approximately 20 and 50 \(\upmu \hbox {m}\). The results indicate that the friction factor is higher than that predicted by the classical theory. Such a difference increases with increasing wettability and decreases with increasing hydraulic diameter and pressure drop, which is consistent with the results of theoretical analysis. The apparent viscosity calculated by the apparent viscosity model notably fit the experimental results, with a relative difference of less than ± 2.1%.
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Abbreviations
- \(A_{\mathrm{ch}}\) :
-
Cross-sectional area of the channel (\(\hbox {m}^{2}\))
- \(A_{\mathrm{p}}\) :
-
Cross-sectional area of the plenum (\(\hbox {m}^{2}\))
- \(D_{\mathrm{h}}\) :
-
Hydraulic diameter (\(\upmu \hbox {m}\))
- \(F_{\mathrm{LL}}\) :
-
Liquid–liquid intermolecular forces (\(\hbox {N}\))
- \(F_{\mathrm{LS}}\) :
-
Solid–liquid intermolecular forces (\(\hbox {N}\))
- f :
-
Darcy’s friction factor
- H :
-
Height of the microchannel (\(\upmu \hbox {m}\))
- \(K_{90}\) :
-
Bend loss coefficient
- \(K_{\mathrm{c}}\) :
-
Contraction loss coefficient
- \(K_{\mathrm{e}}\) :
-
Expansion loss coefficient
- k :
-
Coefficient in Eq. (3)
- L :
-
Length of the microchannel (\(\hbox {mm}\))
- n :
-
Coefficient in Eq. (3)
- \(\Delta P\) :
-
Frictional pressure drop (Pa)
- \(\Delta P_{\mathrm{H1}}\) :
-
Inlet hydrostatic pressure losses (Pa)
- \(\Delta P_{\mathrm{H2}}\) :
-
Outlet hydrostatic pressure losses (Pa)
- \(P_{\mathrm{in}}\) :
-
Inlet pressure (Pa)
- \(P_{\mathrm{out}}\) :
-
Outlet pressure (Pa)
- u :
-
Velocity in the x-direction (\(\hbox {m}/\hbox {s}\))
- \(u_{\mathrm{m}}\) :
-
Mean velocity (\(\hbox {m}/\hbox {s}\))
- Re :
-
Reynolds number
- W :
-
width of the microchannel (\(\hbox {mm}\))
- x, y :
-
Cartesian coordinates (\(\hbox {m}\))
- \(\delta \) :
-
Mean distance between two adjacent molecules (\(\hbox {nm}\))
- \(\mu _0\) :
-
Bulk viscosity [\({\hbox {kg}}/({{\hbox {m}\,\hbox {s}}})\)]
- \(\mu _{\mathrm{a}}\) :
-
Apparent viscosity [\({\hbox {kg}}/({\hbox {m}\,\hbox {s}})\)]
- \(\bar{{\mu }}_{\mathrm{a}}\) :
-
Average apparent viscosity [\(\hbox {kg}/(\hbox {m}\,\hbox {s})\)]
- \(\theta \) :
-
Contact angle (\(^{\circ }\))
- \(\rho \) :
-
Density (\({\hbox {kg}}/{\hbox {m}^{3}}\))
- \(\sigma _{\mathrm{L}}\) :
-
Surface tension of the liquid (N/m)
- \(\sigma _{\mathrm{L}}^0\) :
-
Internal surface force of the liquid (N/m)
- \(\sigma _{\mathrm{LS}}\) :
-
Interfacial tension of the liquid (N/m)
- \(\sigma _{\mathrm{LS}}^0\) :
-
External surface force of the liquid (N/m)
- \(\xi \) :
-
Parameter in Eq. (2)
- \(\exp \) :
-
Experimental value
- th:
-
Theoretical value
- 1:
-
Value of the top wall
- 2:
-
Value of the bottom wall
References
Ho, C.M., Tai, Y.C.: Micro-electro-mechanical-systems (MEMS) and fluid flows. Ann. Rev. Fluid Mech. 30, 579–612 (1998)
Stone, H.A., Stroock, A., Ajdari, A.: Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Ann. Rev. Fluid Mech. 36, 381–411 (2004)
Peng, X.F., Peterson, G.P., Wang, B.X.: Heat transfer characteristics of water flowing through microchannels. Exp. Heat Transf. 7, 265–283 (1994)
Qu, W.L., Mala, G.M., Li, D.Q.: Pressure-driven water flows in trapezoidal silicon microchannels. Int. J. Heat Mass Transf. 43, 353–364 (2000)
Zhigang, L., Ning, G., Chengwu, Z., Xiaobao, Z.: Experimental study on flow and heat transfer in a 19.6-\(\upmu \)m microtube. Exp. Heat Transf. 22, 178–197 (2009)
Li, Z.X., Du, D.X., Guo, Z.Y.: Experimental study on flow characteristics of liquid in circular microtubes. Microscale Thermophys. Eng. 7, 253–265 (2003)
Peng, X.F., Peterson, G.P., Wang, B.X.: Frictional flow characteristics of water flowing through microchannels. Exp. Heat Transf. 7, 249–264 (1994)
Mala, G.M., Li, D.Q.: Flow characteristics of water in microtubes. Int. J. Heat Fluid Flow 20, 142–148 (1999)
Liu, Y.P., Xu, G.Q., Sun, J.N., Li, H.W.: Investigation of the roughness effect on flow behavior and heat transfer characteristics in microchannels. Int. J. Heat Mass Transf. 83, 11–20 (2015)
Kandlikar, S.G., Joshi, S., Tian, S.: Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transf. Eng. 24, 4–16 (2003)
Choi, C.H., Westin, K.J.A., Breuer, K.S.: Apparent slip in hydrophilic and hydrophobic microchannels. Phys. Fluids 15, 2897–2902 (2003)
Nagayama, G., Matsumoto, T., Fukushima, K., Tsuruta, T.: Scale effect of slip boundary condition at solid–liquid interface. Sci. Rep. 7, 43125 (2017)
Wang, F., Yue, X.A., Xu, S.L., Zhang, L.J., Zhao, R.B., Hou, J.R.: Influence of wettability on flow characteristics of water through microtubes and cores. Chin. Sci. Bull. 54, 2256–2262 (2009)
Nagayama, G., Cheng, P.: Effects of interface wettability on microscale flow by molecular dynamics simulation. Int. J. Heat Mass Transf. 47, 501–513 (2004)
Mala, G.M., Li, D.Q., Werner, C., Jacobasch, H.J., Ning, Y.B.: Flow characteristics of water through a microchannel between two parallel plates with electrokinetic effects. Int. J. Heat Fluid Flow 18, 489–496 (1997)
Ren, L.Q., Qu, W.L., Li, D.Q.: Interfacial electrokinetic effects on liquid flow in microchannels. Int. J. Heat Mass Transf. 44, 3125–3134 (2001)
Xu, S.L., Yue, X.A., Hou, J.R.: Experimental investigation on flow characteristics of deionized water in microtubes. Chin. Sci. Bull. 52, 849–854 (2007)
You, X.Y., Zheng, J.R., Jing, Q.: Effects of boundary slip and apparent viscosity on the stability of microchannel flow. Forsch. Ing. Wes. 71, 99–106 (2007)
Mala, G.M., Li, D.Q., Dale, J.D.: Heat transfer and fluid flow in microchannels. Int. J. Heat Mass Transf. 40, 3079–3088 (1997)
Israelachvili, J.N.: Measurement of the viscosity of liquids in very thin films. J. Colloid Interface Sci. 110, 263–271 (1986)
Gee, M.L., Mcguiggan, P.M., Israelachvili, J.N., Homola, A.M.: Liquid to solidlike transitions of molecularly thin films under shear. J. Chem. Phys. 93, 1895–1906 (1990)
Lv, P., Yang, Z.H., Hua, Z., Li, M.Y., Lin, M.Q., Dong, Z.X.: Viscosity of water and hydrocarbon changes with micro-crevice thickness. Colloids Surf. A Physicochem. Eng. Asp. 504, 287–297 (2016)
Thomas, J.A., Mcgaughey, A.J.H.: Reassessing fast water transport through carbon nanotubes. Nano Lett. 8, 2788–2793 (2008)
Suk, M.E., Aluru, N.R.: Molecular and continuum hydrodynamics in graphene nanopores. RSC Adv. 3, 9365–9372 (2013)
Ghorbanian, J., Beskok, A.: Scale effects in nano-channel liquid flows. Microfluid. Nanofluid. 20, 121 (2016)
Blake, T.D., Coninck, J.D.: The influence of solid–liquid interactions on dynamic wetting. Adv. Colloid Interface Sci. 96, 21–36 (2002)
Zhang, F.T.: Interface layer model of physical interface. J. Colloid Interface Sci. 244, 271–281 (2001)
Tretheway, D.C., Meinhart, C.D.: Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14, 9–12 (2002)
Kandlikar, S.G., Garimella, S., Li, D.Q., Colin, S., King, M.R.: Heat Transfer and Fluid Flow in Minichannels and Microchannels. Elsevier Ltd, Oxford (2006)
Dey, R., Das, T., Chakraborty, S.: Frictional and heat transfer characteristics of single-phase microchannel liquid flows. Heat Transf. Eng. 33, 425–446 (2012)
Liu, Z.M., Pang, Y.: Effect of the size and pressure on the modified viscosity of water in microchannels. Acta Mech. Sin. 31, 45–52 (2015)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 11702320) and the Training Program of the Major Research Plan of the National Natural Science Foundation of China (No. 91741107).
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Li, X., Chen, X., Huang, Y. et al. Effect of interface wettability on the flow characteristics of liquid in smooth microchannels. Acta Mech 230, 2111–2123 (2019). https://doi.org/10.1007/s00707-019-2371-z
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DOI: https://doi.org/10.1007/s00707-019-2371-z