Chemical Engineering Journal 162 (2010) 730–737 Contents lists available at ScienceDirect Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej Shape optimization of a micromixer with staggered-herringbone grooves patterned on opposite walls Shakhawat Hossain, Afzal Husain, Kwang-Yong Kim ∗ Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong Nam-Gu, Incheon 402-751, Republic of Korea article info Article history: Received 24 November 2009 Received in revised form 21 May 2010 Accepted 28 May 2010 Keywords: Micromixer Herringbone grooves Optimization Navier–Stokes equations Mixing index Response surface method abstract The shape optimization of a micromixer with staggered-herringbone grooves at both the top and bottom walls has been performed through three-dimensional Navier–Stokes analysis. The mixing of two working fluids, viz., water and ethanol, is considered at Re = 1. The mixing index at the exit of the micromixer is selected as the objective function and four design variables, viz., the number of grooves per half cycle, angle of grooves, ratio of the groove depth to channel height, and ratio of the groove width to pitch are chosen out of the various geometric parameters that affect the performance of a micromixer with regard to shape optimization. The variance of the mass-fraction at various nodes on a plane is used to quantify the mixing performance in the micromixer. The design space is explored through some pre- liminary calculations and a Latin hypercube sampling method is used as the design of experiments to select design points in the design space. The objective function values are obtained at these design points by Navier–Stokes analysis, and a surrogate model, namely, the response surface approximation method, is used to construct a response surface for the objective function. Sequential quadratic programming is used to find out an optimal solution on the constructed response space. The optimization results show that the mixing is highly sensitive to the shape of the groove as well as the number of grooves per cycle, which can be used to control mixing in microfluidics. Through the optimization, the mixing index at the exit of the micromixer is enhanced by about 9% in comparison with the reference design. © 2010 Elsevier B.V. All rights reserved. 1. Introduction Rapid mixing is a fundamental requirement for any microflu- idic system that deals with chemical synthesis, drug delivery, high-throughput screening, and biochemistry. In microsystems, due to their small sizes, fluid mixing becomes very difficult, and conventional methods for stirring fluids are not applicable for carrying out the required mixing. Mixing in microchannels is pre- dominantly governed by molecular diffusion, which in itself is a very slow process; it can be improved by increasing the area of the contact interface between the fluids and decreasing the diffusion path. Microfluidic devices are used to perform many functions such as separation, mixing, reaction, and analysis on a single chip; therefore, mixing in microchannels plays an impor- tant role in realizing BioMEMS and micro total analysis systems [1,2]. Recently, a variety of active and passive micromixers have been developed to enhance fluid mixing in microchannels. Active micromixers depend on external effects to force fluids to mix together inside the microchannels [3,4]. To enhance the mixing ∗ Corresponding author. Tel.: +82 32 872 3096; fax: +82 32 868 1716. E-mail address: kykim@inha.ac.kr (K.-Y. Kim). performance in an active micromixer, the stirring effect can be achieved by using additional structures or external sources, includ- ing ultrasonic vibration, dielectrophoresis, electrohydrodynamics, electroosmosis, and magnetic-force techniques. Passive micromix- ers do not require any external energy other than the fluid drive: the mixing process is achieved by modifying the microchannel geometry with different shapes or microstructures. Due to vari- ous complications that are involved in active micromixers, passive micromixers are used in most microfluidic applications. The patterning of one or more surfaces of the micromixer by specially designed microstructures is one of the best procedures for enhancing the mixing performance of a passive micromixer. Stroock et al. [5] developed a novel type of T-shaped micromixer, which uses patterned grooves at the bottom of the channel; they reported that the groove shape could be very effective in mixing flu- ids. This micromixer creates a transverse flow pattern that stretches and folds the fluids, which increases the mixing performance. Wang et al. [6] investigated the mixing performance by using the com- putational fluid dynamics (CFD) method for a patterned-groove micromixer and reported that deeper grooves improved the mix- ing efficiency and reduced the channel length for complete mixing. The mixing of fluids in a herringbone-groove micromixer depends upon the geometric parameter of the herringbone grooves that represents their patterning, shape, and size. 1385-8947/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cej.2010.05.056