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On multi-objective optimization of geometry of staggered herringbone micromixer

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Abstract

A design methodology for micromixers is presented which systematically integrates computational fluid dynamics (CFD) with an optimization methodology based on the use of design of experiments (DOE), function approximation technique (FA) and multi-objective genetic algorithm (MOGA). The methodology allows the simultaneous investigation of the effect of geometric parameters on the mixing performance of micromixers whose design strategy is based fundamentally on the generation of chaotic advection. The methodology has been applied on a Staggered Herringbone Micromixer (SHM) at several Reynolds numbers. The geometric features of the SHM are optimized and their effects on mixing are evaluated. The degree of mixing and the pressure drop are the performance criteria to define the efficiency of the micromixer for different design requirements.

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Abbreviations

CFD:

Computational fluids dynamics

DOE:

Design of experiments

FA:

Function approximation technique

MEMS:

Micro-electromechanical systems

MOGA:

Multi-objective genetic algorithm

NSGA-II:

Non-dominated sorting genetic algorithm II

RBF:

Radial basis function

RBNN:

Radial basis neural network

RSM:

Response surface method

SHM:

Staggered Herringbone Mixer

SPEA2:

Strength pareto evolutionary algorithm 2

SQP:

Sequential Quadratic Programming

OA:

Orthogonal array

PF:

Pareto Front

M i :

mixing index

C :

local (area element) value of the concentration (mass fraction) of one fluid species

c i :

concentration distribution of one of the fluids species at the ith mesh cell on the outlet plane

c 0 :

local concentration at the inlet of the mixing channel

c ∞ :

concentration of complete mixing (mixing steady-state concentration)

A :

cross section plane in the mixing channel

A 0 :

inlet section or plane of the mixing channel

N :

number of cells defined by the mesh on the outlet plane

W :

width of the mixing channel (μm)

H :

height of the mixing channel plus half the depth of a groove (μm)

h m :

height of the mixing channel (μm)

w g :

width of the groove (μm)

d g :

depth of the groove (μm)

b :

asymmetry factor, b ≥ 0.5

N g :

number of grooves per half cycle

U :

upstream (inlet) channel width (μm)

Re :

Reynolds number

S/N :

signal-to-noise ratio

P :

gauge pressure (Pa)

P j :

performance parameter

X j :

design parameter

N :

number of designs parameters

M :

number of performance parameters

a 0 , a i , a ii , a ij :

coefficients of the polynomial function given by RSM

R 2, R 2adj :

accuracy factors of surface models

α :

groove depth ratio, d g /2h

α′:

ratio of groove depth to mixing channel height

γ :

acute angle formed by a groove and the channel axis (°)

θ :

groove intersection angle (°)

λ :

groove pitch (μm)

η :

signal-to-noise ratio

σ 2 :

square of Standard deviation

\( \mu_{{{\text{H}}_{2} {\text{O}}}} \) :

dynamic viscosity of water (kg m−1 s−1)

\( \rho_{{{\text{H}}_{2} {\text{O}}}} \) :

density of water (kg m−3)

\( \mu_{{{\text{C}}_{2} {\text{H}}_{60} }} \) :

dynamic viscosity of ethanol (kg m−1 s−1)

\( \rho_{{{\text{C}}_{2} {\text{H}}_{60} }} \) :

density of ethanol (kg m−3)

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Acknowledgments

This work was supported by a Dorothy Hodgkin Postgraduate Award (DHPA) of the United Kingdom and by Ebara Research Co. Ltd. of Japan.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University College London, London, UK

    Cesar Augusto Cortes-Quiroz & Mehrdad Zangeneh

  2. Ebara Research Co. Ltd, Fujisawa, Japan

    Akira Goto

Authors
  1. Cesar Augusto Cortes-Quiroz
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  2. Mehrdad Zangeneh
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  3. Akira Goto
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Correspondence to Cesar Augusto Cortes-Quiroz.

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Cortes-Quiroz, C.A., Zangeneh, M. & Goto, A. On multi-objective optimization of geometry of staggered herringbone micromixer. Microfluid Nanofluid 7, 29–43 (2009). https://doi.org/10.1007/s10404-008-0355-8

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