Mixing in curved tubes

The mixing efficiency in a curved tube is a complex function of the Reynolds number, Schmidt number, curvature ratio and tube pitch, therefore, the relative effectiveness of a helical tube is quite complicated and challenging over a straight tube. A state of art review on mixing of two miscible liquids in curved tubes revealed that the mixing in coils of circular cross section has not been reported in the literature. In the present work a computational fluid dynamics study is performed in curved tubes of circular cross-section of finite pitch under laminar flow conditions to examine the scalar mixing of two miscible fluids using scalar transport technique. In the present study the phenomenon of mixing by convection and diffusion of two flow streams with inlet scalar concentrations of zero and unity in the two halves of a tube perpendicular to the plane of curvature has been reported. The mixing efficiency has been quantified with concentration distributions and unmixedness coefficient at different cross-sections and process conditions (Reynolds number, Schmidt number and curvature ratio) in the straight and curved tube of circular cross-section. The result shows that, in curved tube, for higher Schmidt number fluids, mixing is considerably improved at moderately low Reynolds numbers (Re ∼ 10), but is not affected for Reynolds number of the order of 0.1. It is also reported that mixing in the curved tube is higher at low values of curvature ratio as compared to the higher curvature ratio. 2006 Elsevier Ltd. All rights reserved.

[1]  BerndWerner,et al.  Mixers with Microstructured Foils for Chemical Production Purposes , 2005 .

[2]  R. A. Mashelkar,et al.  Advances in Transport Processes , 1982 .

[3]  Hassan Aref,et al.  Chaotic advection by laminar flow in a twisted pipe , 1989, Journal of Fluid Mechanics.

[4]  André Bakker,et al.  Laminar Flow in Static Mixers with Helical Elements , 2000 .

[5]  E. S. Szalai,et al.  Fundamental approach to the design and optimization of static mixers , 2003 .

[6]  Nakayama Wataru,et al.  Study on forced convective heat transfer in curved pipes: (1st report, laminar region) , 1965 .

[7]  F. Durst,et al.  The Development Lengths of Laminar Pipe and Channel Flows , 2005 .

[8]  J. Santiago,et al.  Electrokinetic instability micromixing. , 2001, Analytical chemistry.

[9]  W. R. Dean,et al.  Note on the motion of fluid in a curved pipe , 1959 .

[10]  Phil Paik,et al.  Rapid droplet mixers for digital microfluidic systems. , 2003, Lab on a chip.

[11]  Wolfgang Ehrfeld,et al.  Characterization of Mixing in Micromixers by a Test Reaction: Single Mixing Units and Mixer Arrays , 1999 .

[12]  Chun-Ping Jen,et al.  Design and simulation of the micromixer with chaotic advection in twisted microchannels. , 2003, Lab on a chip.

[13]  Robin H. Liu,et al.  Passive mixing in a three-dimensional serpentine microchannel , 2000, Journal of Microelectromechanical Systems.

[14]  Piet D. Iedema,et al.  CFD calculation of laminar striation thinning in static mixer reactors , 2001 .

[15]  D. B. Spalding,et al.  Prediction of laminar flow and heat transfer in helically coiled pipes , 1974, Journal of Fluid Mechanics.

[16]  Steffen Hardt,et al.  Simulation of helical flows in microchannels , 2004 .

[17]  Mahesh Madhukar Athavale,et al.  Plastic In-Line Chaotic Micromixer for Biological Applications , 2001 .

[18]  Alan Mathewson,et al.  Application of magnetohydrodynamic actuation to continuous flow chemistry. , 2002, Lab on a chip.

[19]  Yi-Kuen Lee,et al.  Efficient spatial-temporal chaotic mixing in microchannels , 2003 .

[20]  Krishna D.P. Nigam,et al.  Numerical simulation of steady flow fields in coiled flow inverter , 2005 .

[21]  W. R. Dean.  XVI. Note on the motion of fluid in a curved pipe , 1927 .

[22]  W. R. Dean.  LXXII. The stream-line motion of fluid in a curved pipe (Second paper) , 1928 .

[23]  Carl D. Meinhart,et al.  An Actively Controlled Micromixer , 1999, Micro-Electro-Mechanical Systems (MEMS).

[24]  A. Manz,et al.  Microstructure for efficient continuous flow mixing , 1999 .

[25]  V Hessel,et al.  An optimised split-and-recombine micro-mixer with uniform chaotic mixing. , 2004, Lab on a chip.

[26]  Klaus Drese,et al.  Optimization of interdigital micromixers via analytical modeling—exemplified with the SuperFocus mixer , 2004 .

[27]  Holger Löwe,et al.  Steering of Liquid Mixing Speed in Interdigital Micro Mixers – From Very Fast to Deliberately Slow Mixing , 2004 .

[28]  E. L. Paul,et al.  Handbook of Industrial Mixing: Science and Practice , 2003 .

[29]  Robin H. Liu,et al.  Bubble-induced acoustic micromixing. , 2002, Lab on a chip.

[30]  A. Berg,et al.  Micro Total Analysis Systems , 1995 .

[31]  Jin-Woo Choi,et al.  A Novel In-Plane Passive Micromixer Using Coanda Effect , 2001 .

[32]  Krishna D.P. Nigam,et al.  Coiled configuration for flow inversion and its effect on residence time distribution , 1984 .

[33]  Shizhi Qian,et al.  A chaotic electroosmotic stirrer. , 2002, Analytical chemistry.

[34]  C. Medaglia,et al.  A Numerical Study , 2005 .

[35]  I. N. Krivorotov,et al.  Uniform resonant chaotic mixing in fluid flows , 2022 .

[36]  S. Ehlers,et al.  Mixing in the offstream of a microchannel system , 2000 .

[37]  H. Peerhossaini,et al.  On the velocity field and tracer patterns in a twisted duct flow , 1995 .

[38]  Dorian Liepmann,et al.  PLANAR LAMINAR MIXER , 2000 .

[39]  Peter Woias,et al.  An Active Silicon Micromixer for μTAS Applications , 2000 .

[40]  Norbert Schwesinger,et al.  A modular microfluid system with an integrated micromixer , 1996 .

[41]  Armand Ajdari,et al.  Patterning flows using grooved surfaces. , 2002, Analytical chemistry.

[42]  Robin H. Liu,et al.  Hybridization enhancement using cavitation microstreaming. , 2003, Analytical chemistry.

[43]  F. Muzzio,et al.  Reynolds number effects on laminar mixing in the Kenics static mixer , 1998 .

[44]  Surya Pratap Vanka,et al.  Numerical study of scalar mixing in curved channels at low Reynolds numbers , 2004 .

[45]  Klavs F. Jensen,et al.  Novel Liquid Phase Microreactors for Safe Production of Hazardous Specialty Chemicals , 2000 .

[46]  I. Mezić,et al.  Chaotic Mixer for Microchannels , 2002, Science.

[47]  R. Miyake,et al.  Micro mixer with fast diffusion , 1993, [1993] Proceedings IEEE Micro Electro Mechanical Systems.

[48]  Hiroshi Goto,et al.  Ultrasonic micromixer for microfluidic systems , 2000, Proceedings IEEE Thirteenth Annual International Conference on Micro Electro Mechanical Systems (Cat. No.00CH36308).

[49]  Nadine Aubry,et al.  Enhancement of microfluidic mixing using time pulsing. , 2003, Lab on a chip.

[50]  V. Hessel,et al.  Laminar mixing in different interdigital micromixers: I. Experimental characterization , 2003 .

[51]  Steffen Hardt,et al.  Helical Flows and Chaotic Mixing in Curved Micro Channels , 2004 .

[52]  F. Schönfeld,et al.  Laminar mixing in interdigital micromixers with different mixing chambers – Part 2: Numerical simulations , 2003 .

[53]  Wolfgang Ehrfeld,et al.  Microreaction Technology: Industrial Prospects , 2000 .

[54]  P. Tabeling,et al.  Chaotic mixing in electrokinetically and pressure driven micro flows , 2001, Technical Digest. MEMS 2001. 14th IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.01CH37090).

[55]  Kee Suk Ryu,et al.  A NOVEL MICROSTIRRER AND ARRAYS FOR MICROFLUIDIC MIXING , 2001 .

[56]  Mark L. Sawley,et al.  Parallel computation and analysis of the flow in a static mixer , 1999 .

[57]  L. Talbot,et al.  Flow in Curved Pipes , 1983 .

[58]  Joel Voldman,et al.  Liquid Mixing Studies with an Integrated Mixer/Valve , 1998 .