Colored particle tracking method for mixing analysis of chaotic micromixers

Micromixers have a variety of applications in chemical and biological processes, becoming an important component in microfluidic systems. The present work aims at understanding detailed mixing behaviour of micromixers by developing a numerical analysis scheme, which ultimately facilitates efficient micromixer design. A systematic numerical method has been developed, enabling visualization of detailed mixing patterns and quantification of the mixing performance in chaotic micromixers. The overall numerical scheme is named 'colored particle tracking method' (CPTM), consisting of three steps: (i) a flow analysis to obtain a periodic velocity field of a periodic mixing protocol by the Galerkin/least-squares (GLS) method; (ii) a particle tracking step, particles being labeled by a specific color at the inlet according to fluid species, to obtain a distribution of colored particles at the end of the final period; (iii) a quantification of the degree of mixing from the obtained particle distribution. For the last step we propose a new mixing measure based on the information entropy. The CPTM has successfully been applied to three examples of micromixers with patterned grooves to evaluate their mixing performance both qualitatively and quantitatively. The CPTM seems promising as a practically attractive numerical scheme for mixing analysis of chaotic micromixers.

[1]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[2]  H. Aref.  Stirring by chaotic advection , 1984, Journal of Fluid Mechanics.

[3]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[4]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[5]  L. Franca,et al.  Stabilized finite element methods. II: The incompressible Navier-Stokes equations , 1992 .

[6]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[7]  T. H. Kwon,et al.  Enhancement of mixing performance of single‐screw extrusion processes via chaotic flows: Part I. Basic concepts and experimental study , 1996 .

[8]  Alan G. R. Evans,et al.  Two simple micromixers based on silicon , 1998 .

[9]  Mark L. Sawley,et al.  Optimization of a Kenics static mixer for non-creeping flow conditions , 1999 .

[10]  Dominique Pelletier,et al.  On stabilized finite element formulations for incompressible advective–diffusive transport and fluid flow problems , 2000 .

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

[12]  I. Manas‐Zloczower,et al.  Characterization of Distributive Mixing in Polymer Processing Equipment using Renyi Entropies , 2001, International Polymer Processing.

[13]  A Bertsch,et al.  Static micromixers based on large-scale industrial mixer geometry. , 2001, Lab on a chip.

[14]  J. Josserand,et al.  Mixing processes in a zigzag microchannel: finite element simulations and optical study. , 2002, Analytical chemistry.

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

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

[17]  Francis E. H. Tay.  Microfluidics and bioMEMS applications , 2002 .

[18]  T. Johnson,et al.  Rapid microfluidic mixing. , 2002, Analytical chemistry.

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

[20]  G. Whitesides,et al.  Controlling flows in microchannels with patterned surface charge and topography. , 2003, Accounts of chemical research.

[21]  Dong Sung Kim,et al.  Barrier embedded chaotic micromixer , 2003 .

[22]  T. Kwon,et al.  Chaotic Volumetric Transports in a Single-Screw Extrusion Process , 2003 .

[23]  Hengzi Wang,et al.  Numerical investigation of mixing in microchannels with patterned grooves , 2003 .

[24]  Wook Ryol Hwang,et al.  Direct simulation of particle suspensions in sliding bi-periodic frames , 2004 .