Abstract
Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The centrifugal force and Coriolis force, arising as a consequence of the microchannel rotation, change the flow pattern significantly from the symmetric profile of a non-rotating channel. Successful design of microfluidic devices in centrifugal microfluidics depends on effectively regulating these forces in rotating microchannels. In this work, we have numerically investigated the flow and heat transfer in rotating rectangular microchannel with continuum assumption. A pressure-based finite-volume technique with a staggered grid was applied to solve the steady incompressible Navier–Stokes and energy equations. It was observed that the effect of Coriolis force was determined by the value of the non-dimensional rotational Reynolds number (Re ω ). By comparing the root mean square deviation of the axial velocity profiles with the approximate analytical results of purely centrifugal flow for different aspect ratios (AR = width/height), a critical rotational Reynolds number (Re ω,cr) was computed. Above this value of (Re ω,cr), the effect of secondary flow becomes dominant. For aspect ratios of 0.25, 0.5, 1.0, 2.0, 4.0 and 9.09, this critical rotational Reynolds number (Re ω,cr) was found to be 14.0, 5.5, 3.8, 4.7, 6.5 and 10.0, respectively.
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Abbreviations
- a :
-
Width of the microchannel (m)
- AR:
-
Channel aspect ratio \( \left( { {=} \frac{a}{b}} \right) \)
- b :
-
Height of the microchannel (m)
- C p :
-
Specific heat at constant pressure (J/kg K)
- D h :
-
Hydraulic diameter of microchannel (m)
- d r :
-
Radial distance of inlet from the disk center (m)
- f app :
-
Apparent friction factor (m/s)
- f c :
-
Coriolis force (=2ωw)
- f ω :
-
Centrifugal force (=ω 2 d r)
- G :
-
Modified axial pressure gradient
- G * :
-
Reduced axial pressure gradient
- h :
-
Convective heat transfer coefficient (W/m2 K)
- k:
-
Thermal conductivity (W/m K)
- Kn :
-
Knudsen number
- L :
-
Length of the microchannel (m)
- Nu :
-
Nusselt number \( \left( { {=} \frac{{hD_{\text{h}} }}{k}} \right) \)
- p :
-
Pressure (Pa)
- Ra :
-
Rayleigh number
- Re ω :
-
Rotational Reynolds number \( \left( { {=} \frac{{\omega D_{\text{h}}^{2} \rho }}{\mu }} \right) \)
- Re ω,cr :
-
Critical rotational Reynolds number
- Re :
-
Reynolds number \( \left( { {=} \frac{{\rho W_{\text{avg}} D_{\text{h}} }}{\mu }} \right) \)
- Ro :
-
Rossby number \( \left( { {=} \frac{{Re_{\omega } }}{Re}} \right) \)
- RPM:
-
Revolution per minute
- S j :
-
Source term in j-direction
- T :
-
Temperature (°C)
- u, v, w :
-
Velocities in x, y and z directions (m/s)
- x i :
-
Co-ordinates in i-direction (x, y, z for i = 1, 2, 3)
- β :
-
Ratio of the Coriolis force to the centrifugal force
- \( \lambda ,\Gamma \) :
-
Eigen values
- ω :
-
Angular velocity (rad/s)
- μ :
-
Dynamic viscosity of fluid (Pa s)
- ρ :
-
Fluid density (kg/m3)
- v :
-
Kinematic viscosity (m2/s)
- app :
-
Apparent
- avg :
-
Average
- cr :
-
Critical
- i,j,k :
-
Array indices for tensor notation
- in :
-
Inlet
- max :
-
Maximum
- out :
-
Outlet
- w :
-
Wall
References
Amasia M, Madou M (2010) Large-volume centrifugal microfluidic device for blood plasma separation. Bioanalysis 2(10):1701–1710
Brenner T, Glatzel T, Zengerle R, Ducrée J (2004) Frequency-dependent transversal flow control in centrifugal microfluidics. Lab Chip 5(2):146–150
Chakraborty D, Chakraborty S (2010) Controlled microbubble generation on a compact disk. Appl Phys Lett 97(23):234103
Chakraborty D, Madou M, Chakraborty S (2011) Anomalous mixing behaviour in rotationally actuated microfluidic devices. Lab Chip 11(17):2823–2826
Chen JM, Huang PC, Lin MG (2008) Analysis and experiment of capillary valves for microfluidics on a rotating disk. Microfluid Nanofluid 4(5):427–437
Ducrée J, Brenner T, Haeberle S, Glatzel T, Zengerle R (2006a) Multilamination of flows in planar networks of rotating microchannels. Microfluid Nanofluid 2(1):78–84
Ducrée J, Haeberle S, Brenner T, Glatzel T, Zengerle R (2006b) Patterning of flow and mixing in rotating radial microchannels. Microfluid Nanofluid 2(2):97–105
Ducrée J, Haeberle S, Lutz S, Pausch S, von Stetten F, Zengerle R (2007) The centrifugal microfluidic Bio-Disk platform. J Micromechanics Microengineering 17:S103
Duffy DC, Gillis HL, Lin J, Sheppard NF Jr, Kellogg GJ (1999) Microfabricated centrifugal microfluidic systems: characterization and multiple enzymatic assays. Anal Chem 71(20):4669–4678
Garimella SV, Sobhan C (2003) Transport in microchannels—a critical review. Ann Rev Heat Transf 13:1–50
Gorkin R, Park J, Siegrist J, Amasia M, Lee BS, Park JM, Kim J, Kim H, Madou M, Cho YK (2010) Centrifugal microfluidics for biomedical applications. Lab Chip 10(14):1758–1773
Gorkin R, Soroori S, Southard W, Clime L, Veres T, Kido H, Kulinsky L, Madou M (2012) Suction-enhanced siphon valves for centrifugal microfluidic platforms. Microfluid Nanofluid 12(1):345–354
Grumann M, Geipel A, Riegger L, Zengerle R, Ducree J (2005) Batch-mode mixing on centrifugal microfluidic platforms. Lab Chip 5(5):560–565
Haeberle S, Brenner T, Zengerle R, Ducrée J (2006) Centrifugal extraction of plasma from whole blood on a rotating disk. Lab Chip 6(6):776–781
Haeberle S, Zengerle R, Ducrée J (2007) Centrifugal generation and manipulation of droplet emulsions. Microfluid Nanofluid 3(1):65–75
Hsieh SS, Hong YJ, Jeng SR (1994) Three-dimensional laminar forced convection in a rotating square duct with a rib on the leading wall. Int J Heat Mass Transf 37(15):2273–2285
Hwang G, Jen T (1990) Convective heat transfer in rotating isothermal ducts. Int J Heat Mass Transf 33(9):1817–1828
Johnson RD, Badr IHA, Barrett G, Lai S, Lu Y, Madou MJ, Bachas LG (2001) Development of a fully integrated analysis system for ions based on ion-selective optodes and centrifugal microfluidics. Anal Chem 73(16):3940–3946
Kawano K, Sekimura M, Minakami K, Iwasaki H, Ishizuka M (2001) Development of micro channel heat exchanging. JSME Int J Ser B 44(4):592–598
Kim J, Kido H, Rangel RH, Madou MJ (2008) Passive flow switching valves on a centrifugal microfluidic platform. Sens Actuators B Chem 128(2):613–621
Kong MCR, Salin ED (2011) Pneumatic flow switching on centrifugal microfluidic platforms in motion. Anal Chem 83(3):1148–1151
Lee PS, Garimella SV, Liu D (2005) Investigation of heat transfer in rectangular microchannels. Int J Heat Mass Trans 48(9):1688–1704
Lei U, Hsu C (1990) Flow through rotating straight pipes. Phys Fluids A 2:63
Liu M, Zhang J, Liu Y, Lau W, Yang J (2008) Modeling of flow burst, flow timing in Lab-on-a-CD systems and its application in digital chemical analysis. Chem Eng Technol 31(9):1328–1335
Madou M, Zoval J, Jia G, Kido H, Kim J, Kim N (2006) Lab on a CD. Annu Rev Biomed Eng 8:601–628
Mark D, Haeberle S, Roth G, Von Stetten F, Zengerle R (2010) Microfluidic lab-on-a-chip platforms: requirements, characteristics and applications. Chem Soc Rev 39(3):1153–1182
Mark D, Weber P, Lutz S, Focke M, Zengerle R, von Stetten F (2011) Aliquoting on the centrifugal microfluidic platform based on centrifugo-pneumatic valves. Microfluid Nanofluid 10(6):1279–1288
Mlcak JD, Anand NK, Rightley MJ (2008) Three-dimensional laminar flow and heat transfer in a parallel array of microchannels etched on a substrate. Int J Heat Mass Transf 51(21–22):5182–5191
Moore JL, McCuiston A, Mittendorf I, Ottway R, Johnson RD (2011) Behavior of capillary valves in centrifugal microfluidic devices prepared by three-dimensional printing. Microfluid Nanofluid 10(4):877–888
Morris WD (1981) Heat transfer and fluid flow in rotating coolant channels. Research Studies Press
Noroozi Z, Kido H, Micic M, Pan H, Bartolome C, Princevac M, Zoval J, Madou M (2009) Reciprocating flow-based centrifugal microfluidics mixer. Rev Sci Instrum 80(7):075102–075108
Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Pub
Patankar S, Liu C, Sparrow E (1977) Fully developed flow and heat transfer in ducts having streamwise-periodic variations of cross-sectional area. J Heat Transf 99:180
Qu W, Mudawar I (2002) Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. Int J Heat Mass Transf 45(12):2549–2565
Roy P, Anand NK, Banerjee D (2011) A numerical study of unsteady laminar flow and heat transfer through an array of rotating rectangular microchannels. In: ASME 2011 International mechanical engineering congress and exposition, Denver, CO, November 11–17, 2011
Shah R, London A (1974) Thermal boundary conditions and some solutions for laminar duct flow forced convection. J Heat Transf 96:159
Siegrist J, Amasia M, Singh N, Banerjee D, Madou M (2010a) Numerical modeling and experimental validation of uniform microchamber filling in centrifugal microfluidics. Lab Chip 10(7):876–886
Siegrist J, Gorkin R, Clime L, Roy E, Peytavi R, Kido H, Bergeron M, Veres T, Madou M (2010b) Serial siphon valving for centrifugal microfluidic platforms. Microfluid Nanofluid 9(1):55–63
Tien-Chien J, Lavine AS, Guang-Jyh H (1992) Simultaneously developing laminar convection in rotating isothermal square channels. Int J Heat Mass Transf 35(1):239–254
Zeng J, Banerjee D, Deshpande M, Gilbert JR, Duffy DC, Kellogg GJ (2000) Design analyses of capillary burst valves in centrifugal microfluidics. In: μTAS2000 symposium, Enschede, the Netherlands, May 14–18, 2000
Zhang J, Liu Y, Zhang J, Yang J (2009) Study of force-dependent and time-dependent transition of secondary flow in a rotating straight channel by the lattice Boltzmann method. Phys A 388(4):288–294
Acknowledgments
The authors gratefully acknowledge the Texas A&M Supercomputing Facility (http://sc.tamu.edu) for providing computing resources useful in conducting the research reported in this paper.
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Roy, P., Anand, N.K. & Banerjee, D. Numerical simulation of flow and heat transfer in radially rotating microchannels. Microfluid Nanofluid 15, 397–413 (2013). https://doi.org/10.1007/s10404-013-1159-z
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DOI: https://doi.org/10.1007/s10404-013-1159-z