Simulation of miscible diffusive mixing in microchannels

Abstract The lattice Boltzmann (LB) method is used to simulate the flow field and subsequent analyte diffusion and convection of various analytes in a Y-shaped microchannel mixer, with a channel cross-section of 250 μm × 500 μm. This required a simulation code to be implemented that couples diffusive mass transfer with hydrodynamics, thus enabling a spatially varying viscosity that depends on a local analyte concentration. Where possible the simulation results were validated with 3D MRI experimental measurements of both the analyte concentration and the flow field in the microchannel; agreement is excellent. The simulation method is also able to quantify various expected physical observations, including the variation of diffusive dispersion due to the 3D velocity profile across the microchannel (butterfly effect), and the expected scaling laws for diffusive transport. The error resulting from employing a simplified 2D representation of the 3D microchannel for simulation purposes is also explored; typically this error is less than 3% of the maximum concentration.

[1]  P Yager,et al.  Theoretical analysis of molecular diffusion in pressure-driven laminar flow in microfluidic channels. , 2001, Biophysical journal.

[2]  P. Yager,et al.  Optical measurement of transverse molecular diffusion in a microchannel. , 2001, Biophysical journal.

[3]  G. Whitesides,et al.  Experimental and theoretical scaling laws for transverse diffusive broadening in two-phase laminar flows in microchannels , 2000 .

[4]  Lynn F. Gladden,et al.  Simulation of packed bed reactors using lattice Boltzmann methods , 2005 .

[5]  S. Quake,et al.  Microfluidics: Fluid physics at the nanoliter scale , 2005 .

[6]  J. Georgiadis,et al.  An Evaluation of the Bounce-Back Boundary Condition for Lattice Boltzmann Simulations , 1997 .

[7]  M. Schwarz,et al.  Recent developments in detection methods for microfabricated analytical devices. , 2001, Lab on a chip.

[8]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[9]  George M. Homsy,et al.  Viscous fingering in porous media , 1987 .

[10]  Don W. Green,et al.  Perry's Chemical Engineers' Handbook , 2007 .

[11]  Lynn F. Gladden,et al.  Single- and two-phase flow in fixed-bed reactors: MRI flow visualisation and lattice-Boltzmann simulations , 2001 .

[12]  Using MR techniques to probe permeability reduction in rock cores , 2003 .

[13]  B. Finlayson,et al.  Quantitative analysis of molecular interaction in a microfluidic channel: the T-sensor. , 1999, Analytical chemistry.

[14]  Robert S. Bernard,et al.  Simulation of flow through bead packs using the lattice Boltzmann method , 1998 .

[15]  Dominique Salin,et al.  Simulations of viscous flows of complex fluids with a Bhatnagar, Gross, and Krook lattice gas , 1996 .

[16]  Shan,et al.  Lattice Boltzmann model for simulating flows with multiple phases and components. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[18]  Flekkoy.  Lattice Bhatnagar-Gross-Krook models for miscible fluids. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Qisu Zou,et al.  A improved incompressible lattice Boltzmann model for time-independent flows , 1995 .

[20]  Nam-Trung Nguyen,et al.  Hydrodynamic focusing in microchannels under consideration of diffusive dispersion: theories and experiments , 2005 .

[21]  D. Salin,et al.  Miscible displacement between two parallel plates: BGK lattice gas simulations , 1997, Journal of Fluid Mechanics.

[22]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[23]  L. Luo,et al.  Lattice Boltzmann Model for the Incompressible Navier–Stokes Equation , 1997 .

[24]  Lynn F. Gladden,et al.  Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques , 2006 .

[25]  Edward L Cussler,et al.  Diffusion: Mass Transfer in Fluid Systems , 1984 .

[26]  Daniel L Marks,et al.  Structural and functional imaging of 3D microfluidic mixers using optical coherence tomography. , 2004, Proceedings of the National Academy of Sciences of the United States of America.