bilayer staggered herringbone micro-mixers with symmetric and asymmetric geometries

RESEARCH PAPER

Bilayer staggered herringbone micro-mixers with symmetricand asymmetric geometries

Rahul Choudhary • Tamalika Bhakat • Rajeev Kumar Singh • Anil Ghubade •

Swarnasri Mandal • Arnab Ghosh • Amritha Rammohan • Ashutosh Sharma •

Shantanu Bhattacharya

Received: 21 April 2010 / Accepted: 28 June 2010 / Published online: 16 July 2010

� Springer-Verlag 2010

Abstract Micro-mixing is an important research area for

various applications in sensing and diagnostics. In this

paper, we present a performance comparison of several

different passive micromixer designs based on the idea of

staggered herringbone mixers (SHM). The working princi-

ple in such designs includes the formation of centers of flow

rotation thus leading to multiple laminations with decreasing

sizes of the lamellae as the flow passes over staggered

structures. We have realized different layout designs of

staggered herringbones inside micro-channels and com-

pared their mixing performance. An overall reduction in

mixing time and length has been observed as the degree of

asymmetry within these structures is increased. The layouts

of these staggered structures are based on herringbone

bilayers wherein these layers are positioned on the top and

bottom walls of a micro-channel. Fluorescence microscopy

and computational fluid dynamics (CFD) based modeling

have been used to observe the extent of mixing and under-

stand the reasons behind the enhanced mixing effects. We

have further varied the degree of asymmetry of the her-

ringbone bilayers and investigated mixing as a function of

the asymmetry. We have developed a novel microfabrica-

tion strategy to realize these micro-devices using an

inexpensive non-photolithographic technique which we call

micro-replication by double inversion (MRDI). The paper

basically attempts to develop an overall understanding of the

mixing process by letting two fluids flow pass over a variety

of asymmetric structures.

Keywords Micromixer � Micromixing � Staggered

herringbones � Microfabrication � Micro-replication

by double inversion (MRDI) � Bilayer � Asymmetry

1 Introduction

Micro-fluidic devices are realized in the micrometer length

scales and they mostly involve flows with very small

Reynolds numbers (Re \ 1.0). The flow in such devices is

highly laminar. Thus, mixing becomes a great challenge

due to the streamlined nature of these flows and mostly

takes place through interlayer diffusion. Owing to this

reason bulk mixing is very slow and requires longer

interaction lengths for proper diffusion between the mixing

inter-layers (lamellae). Micro-mixer design and develop-

ment plays a vital role in a wide variety of fields like

environmental sensing (Vargas-Bernal 2006), clinical and

biochemical diagnostics (Knapp 2001; Auroux 2002),

protein labeling and separation (Kakuta et al. 2003a;

Kakuta et al. 2003b), chemical/biochemical micro-reactors

(de Mello and Wooton 2002; Wiles et al. 2001, 2002) etc.

Hence, to increase the efficiency and compactness of the

device, novel flow strategies and geometrical parameters

are estimated and designed to reduce the mixing channel

length and the mixing time.

Several mixer designs have been explored earlier for

promoting passive mixing at micro-scales. The first gen-

eration micro mixers were designs with T or Y shaped

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10404-010-0667-3) contains supplementarymaterial, which is available to authorized users.

R. Choudhary � T. Bhakat � R. K. Singh � A. Ghubade �S. Mandal � A. Ghosh � S. Bhattacharya (&)

Department of Mechanical Engineering, Indian Institute

of Technology Kanpur, Kanpur 208016, India

e-mail: [email protected]

A. Rammohan � A. Sharma

Department of Chemical Engineering, Indian Institute

of Technology Kanpur, Kanpur 208016, India

123

Microfluid Nanofluid (2011) 10:271–286

DOI 10.1007/s10404-010-0667-3

http://dx.doi.org/10.1007/s10404-010-0667-3

architectures followed by a meandering flow-path (Melin

et al. 2003), inter-digital flow distribution (Erbacher et al.

1999; Hardt and Schonfeld 2003) etc. Here the working

principle is to introduce a substantially higher residence

time for the mixing inter-layers for inter-layer diffusion to

occur. The second generation mixer designs introduced

multi-lamination effects by various techniques like split-

ting and recombining flows (Branebjerg et al. 1996; He

et al. 2001; Lee et al. 2006), nozzle based injection of one

fluid into the stream of other, use of techniques like super-

focusing (Hessel et al. 2005) etc. The basic working prin-

ciple in such designs is to reduce the inter-diffusion length

by creating mixing inter-layers or lamellae. It was, how-

ever, increasingly felt that shifting from 2 to 3 dimensional

geometries would give an opportunity to perform lamina-

tions in the bulk of fluid flow rather than just limiting to

effects on the surface and would promote mixing. Some

designs with these strategies that were reported were C

type (Michael et al. 2002), H-type (Yang et al. 2003),

zigzag (Mengeaud et al. 2002), rhombic (Chung and Shih

2008) and many more (Nguyen and Wu 2005). The second

generation designs, however, suffered from the limitations

of increasing fabrication complexities which plateaued the

rate of development and testing of such designs. Therefore,

researchers tried to evolve a paradigm in which these 3-D

effects could be realized without really going through the

3-D complexities (Stroock et al. 2002a, 2002b; Kim et al.

2004; Hessel and Zimmerman 2006; Kang et al. 2008;

Wang et al. 2003). The very first design which evolved was

the staggered herringbone micromixer (SHM) (Stroock

et al. 2002a), wherein although the fabrication was done

using 2 or 2 and 1/2 dimensional features on planar

substrates, the flow direction could be altered into the

3-dimensional bulk of mixing fluids. There were subse-

quently a lot of experimental and simulational works

exploring SHM designs. Li and Chen (2005) studied the

mixing performance of the chaotic mixer using lattice

Boltzmann method (LBM) based on particle mesoscopic

kinetic equations. They observed the simulated chaotic

mixing in the SHM using the LBM successfully, and got

the stream traces in the velocity field of the flow in the

micro-channel and the images of the concentration distri-

butions of the sample particles. They also investigated the

optimization of two geometrical parameters of the SHM

and found that the width fraction of about 0.6 of the

channel, as occupied by the wide arms of the herringbones,

was an optimal design. We also use around 0.65 as the

width fraction in our experiments. Ansari and Kim (2007)

optimized the ratio of the groove depth to channel height

which matches with the groove dimensions in our experi-

ments. They quantified mixing by first calculating the local

variance of the concentration with respect to the mean

concentration and then formulating ratio between the local

and the maximum variance at a different point within the

grooved micro-channel. A mathematical expression was

generated with this ratio which quantified the local mix-

ability. The asymmetry levels of herringbones on a single

plane were further optimized by Stroock and McGraw

(2004), who developed a lid-driven cavity flow model in

which they replaced fully the 3-dimensional flow with an

unperturbed longitudinal Poiseuille flow in the cross-sec-

tion. They calculated an optimal degree of asymmetry of

the herringbone-shaped grooves for the arm ratio value

between 7/12 and 3/4 for which the structure would gen-

erate the largest amount of chaos. In our designs, the arm

ratio used is 5/7 which definitely satisfies the optimization

criteria developed by Stroock et al. Yang et al. (2005)

found by comparing different geometric parameters that

the following is an order of influence of various factors on

the effectiveness of mixing (asymmetry index [ groove

intersection angle [ upstream to downstream channel

width ratio). We have also taken an asymmetry index value

which promotes maximum chaos and further patterned the

herringbones on both lower and upper channel walls in our

designs asymmetrically. Lynn and Dandy (2007) studied

the optimization of helical flow in micro-mixers with

oblique ridges (OR). The optimized geometries for SHM

were then derived from optimized geometries of OR. The

optimization strategy developed lead to an almost 50%

increase in the transverse flow. Kirtland et al. has presented

a detailed theoretical prediction of the mass transfer rates

across moving interfaces and across internal interfaces

between convectively disconnected sets in the flows. He

extended the modified Graetz behavior to low Reynold’s

number laminar flows (Kirtland et al. 2009).

The 2 and 1/2 dimensional features are so named

because in microsystems realizing feature thicknesses

above a certain critical value is challenging. One of the

fundamental principles which are used by these designs for

rapid mixing is chaotic advection which was first demon-

strated by Stroock et al. As indicated earlier, the SHM

design introduces centers of flow rotations over a helical

path by utilizing a set of staggered grooves laid out in the

flow direction on one of the surfaces enclosing the flows.

However, the effects that such staggered designs would

introduce to the flows on more than one surface enclosing

the flow path have been overlooked. It would also be very

interesting to find out the differences that may arise if the

herringbone features introduced on multiple surfaces con-

tains degree of asymmetry. In this paper, we have

attempted to study in detail the comparison of mixing

efficiency particularly by designing herringbone like fea-

tures in more than one surface enclosing the flow and also

by introducing a high degree of asymmetry between the

patterned surfaces. We have further varied this asymmetry

level and studied the impact on mixing length.

272 Microfluid Nanofluid (2011) 10:271–286

123

We have developed four independent designs, wherein

the arrangement of herringbone structures is altered to

investigate the changes in the center of rotations along both

the transverse and longitudinal directions to the flow path.

The designs are schematically represented in Fig. 1a–e. The

mixer design used to observe the mixing behavior experi-

mentally has three cycles of herringbone sets with 20 her-

ringbones in each set, with every alternate half cycle (10

herringbones) identical and every succeeding half cycle

asymmetric similar to that reported by Stroock et al. 2002(as

shown in Fig. 1b).The differences that we create in our

designs are the following: (1) herringbones are fabricated on

two surfaces (enclosing the flow) and are placed alternately

between these surfaces (as shown in Fig. 1c); (2) herring-

bones are fabricated on two surfaces (enclosing the flow) and

are symmetrically placed such that one is the mirror image of

the other (as shown in Fig. 1d); (3) herringbones are

fabricated on two surfaces asymmetrically on both planes

facing each other (as shown in Fig. 1e). The basic designs

discussed above have been named as alternate bilayer stag-

gered herringbone micromixer (ABHM), symmetric bilayer

staggered herringbone micromixer (SymBHM) and asym-

metric bilayer staggered herringbone micromixer (Asy-

BHM), respectively. We have used a photomultipler tube

mounted up on an inverted fluorescence microscope to

quantify the whole mixing process by change of fluorescence

intensity as we mix a high quantum yield fluorophore with

deionised industrial water (Millipore resistivity 18 MX cm).

We have further performed Fluent� simulations using

Gambit� models of these individual modules to develop an

understanding of the mechanism of mixing. All simulations

were carried out for the first two herringbone cycles which

are representative of the mixing mechanism in all the

designs. The asymmetry level in the design illustrated in

Fig. 1e is further varied by changing the arm lengths of the

herringbone. It is further quantified by looking at the

overlap of areas of the top and bottom herringbone arms.

We are able to find out the mixing length quantitatively

using COMSOL and get a nice correlation between mixing

length and the asymmetry index (AI).

The mixers were fabricated using soft polymeric material,

poly dimethyl siloxane (PDMS), by the MRDI process and

observed that the resolution of fabrication achieved by this

technique is comparable to traditional photolithography

process.

2 Theoretical fundamentals of chaotic micromixers

The main strategy of mixing in the above mentioned

designs is to produce the maximum amount of interfacial

area between two independent fluid streams to create rapid

inter-diffusion or mass–flux between the streams. The

fundamental methodology for mixing is based on stretch-

ing and folding of the twin streams in a lamellar manner so

as to create adjacent bands or striations of each other, thus

reducing the inter-diffusion length. Researchers have

demonstrated a reduction in mixing length of nearly 100

times through such schemes (Stroock et al. 2002a). Theo-

retically, a fluid element of length d(0) at time zero is

assumed to have a length d(t) at time ‘t’ due to stretching

and folding. This aspect is represented by the length stretch

factor defined as k = d(t)/d(0) (Ottino and Wiggins 2004).

The effectiveness of mixing is then simply determined by

looking at k which should ideally increase nearly every-

where (k[ 1), except some regions of compression where

k\ 1. Repeated folding and stretching actions of these

flow generate a lamellar structure consisting of striations

which quickly develop into a time evolving complex

morphology of poorly mixed regions of fluids (islands) andFig. 1 Schematic representation of the micromixer channel designs:

a Plain channel, b SHM, c ABHM, d SymBHM, e AsyBHM

Microfluid Nanofluid (2011) 10:271–286 273

123

well-mixed or chaotic region. Islands translate, stretch,

contract periodically and undergo a net rotation. Stretching

within islands on an average grows linearly and much

slower than in chaotic regions in which the stretching

increases exponentially with time. So, the overall goal in

designing of micromixer should really be to reduce the size

of these islands and increase the number of striations. We

believe that in our three dimensional designs, particularly

in the asyBHM case with varying degree of asymmetry

where we get the most efficient mixing, the flows develop

four asymmetric centers of rotations with different radii

(depending on the herringbone arm length and the asym-

metry index) thus achieving the fastest band formation.

Because of continuous interfacing of island/striation

structure with sequentially placed herringbones, the flow

lamination gets increasingly pronounced resulting in

reduction of striation thickness. Literature refers to an

appropriate relationship between k (length stretch factor)

and the mixing length (Dym) (Stroock et al. 2002a).

In stretching and folding chaotic flows of the above

type, a striation located at an axial length Dy from the inlet

of the flow-channel would have inter-diffusion length Dr

approximated by Eq. 1 (Stroock et al. 2002a).

Dr ¼ le�Dy

k ð1Þ

The residence time for these flows within the micro-

channel up to the axial length Dy is given by Eq. (2) by

assuming the mean flow velocity to be ‘U’. Similarly, the

diffusion time of the striation at Dy is given by Eq. (3).

Residence time; sr ¼Dy

Uð2Þ

Diffusion time; sD ¼Dr2

Dð3Þ

We know that the inter-diffusion time needs to be less than

or equal to the residence time for the flows to mix fully

which is the case at the mixing length Dym (Eq. 4).Thus,

srjDy¼Dym¼ sDjDy¼Dym

ð4Þ

Therefore, at Dym (Eqs. 5, 6 and 7):

Dym

U¼ Dr2

Dð5Þ

Dym

U¼ l2e

�2Dymk

Dð6Þ

Dym ¼Ul2

D� e�

2Dymk ð7Þ

where, U is the mean flow velocity, l is the characteristic

dimension of the channel, D is the coefficient of diffusivity,

Dym is the mixing length in the axial direction.

In this paper, we have determined the length stretch

factor (k) based on sectional views of flow simulations

performed using COMSOL and also calculated the mixing

lengths for geometries with different asymmetry indices

using Eq. 7. Detailed methodology of finding out k is given

in the supplementary figure 2. Table 1 lists the various

nomenclatures that have been used in this paper.

3 Experimental section

3.1 Device fabrication process

A novel, cost-effective fabrication strategy has been

developed for realizing the micro-mixer devices. The mold

for this process is realized on a cleaned and polished

(average roughness 0.01 lm) copper plate. We etch a CAD

defined pattern on this plate using a laser machining setup

(M/S LASER Lab India, Smartist� interface) followed by a

chemical planarizing operation wherein the machined

copper plate is dipped in a 2% ferric chloride solution. The

minimum spot size of the laser is around 10 lm and

multiple passes are executed to formulate the various fea-

tures. Also, the machining is carried out in two runs

wherein the first run is used to formulate just the channel

and the second run is used to machine the herringbone

features. The different steps of fabrication have been pre-

sented in Fig. 2. The planarized copper plate is surface

treated with a mold release agent hexamethyl disilazane

(HMDS) and PDMS is replicated over this. This is fol-

lowed by a heat curing step and the release of the PDMS

stamp from the mold. The stamp contains the negative of

the ablated features on the copper surface. This interme-

diate is used as a mold for creating the positive replica. The

negative is initially heat treated and passivated after release

from the copper mold.

The process is named micro-scale replication by double

inversion (MRDI). The principle advantages of MRDI are

the following: (1) a sturdy mold (made up of Copper), (2)

repeated use of the mold for replication, (3) process is

Table 1 Table for nomenclatures used

Symbol used Definition of the symbol

Dr Inter-diffusion length at Dy axial length

U Mean flow velocity

D Diffusion coefficient

sr Residence time of the flows within length Dy

sD Diffusion time

Dym Mixing length

l Characteristic dimension of the channel

k Length stretch factor

AI Assymetry index

Re Reynold’s number


123

inexpensive in comparison to other photolithography-dri-

ven processes, (4) PDMS replica mold can be used for

multiple reproductions without any feature change, (5) the

laser ablation process can be further replaced by any other

micromachining technique. Figure 3a–d shows optical

micrographs of the ablated copper plate and the doubly

inverted features in PDMS. We have also observed that the

surface roughness variation of the final surfaces of the

PDMS micro-channels is only around 1.7 lm, which is

around 1/30th of the minimum feature height of the her-

ringbones of around 50 lm. Also, the dimensional varia-

tion between the CAD (computer aided design) design and

that on the replicated piece of PDMS using the MRDI

technique is only around 2% (Chaudhury 2009). Literature

cites many ways and means of fabricating micro-scale

devices using direct laser ablation on polymer substrates or

CNC milling (Johnson et al. 2002; Howell et al. 2005).

These methods, however, needs the machining process on

each device. There are other approaches driven through

optical lithography which are used for obtaining a master

mold that is then replicated by soft polymer material.

While the light-directed processes (LDP) are very conve-

nient to layout complex geometry on a two-dimensional

plane, there are limitations especially in herringbone like

features where there is a height differential on the

machined surfaces. In these cases, particularly the LDP has

to use multi-layering and multiple exposures to realize the

thickness difference between channel and herringbones.

Our method being a combination of laser micromachining

and soft lithography offers the advantages of both these

methodologies. Although we have to do two passes for

imprinting the mixer designs on copper, once the master is

realized soft lithography can be carried out multiple times

to get many devices from the same master.

Fig. 2 Fabrication flow-chart for MRDI process. a Substrate plana-

rizing using FeCl3 (2% by weight), b laser ablation of planarized

substrate based on the CAD design, c surface pretreatment using

HMDS in a vacuum desiccator to make a mold releasing surface,

d replicating PDMS on the surface of Cu mold prepared in the earlier

step and obtaining the negative replica of the channel and herringbone

structures (as ridges), e heat treatment of negative at 250�C to make

the PDMS replica’s surface glassy and quick releasing, f treatment of

the glassy surface of PDMS replica with HMDS vapors, g replicating

PDMS on this glassy surface (with ridges) once again to obtain the

channels and herringbone features on PDMS


123

3.2 Assembly of the micromixer device

The mixer is assembled using two layers of PDMS with

each layer having suitably positioned herringbone struc-

tures corresponding to designs as illustrated in Fig. 1a–e.

Each layer made using MRDI was exposed to high pres-

sure, low power inductively coupled oxygen plasma. Prior

to this surface treatment, the top layer is perforated using a

syringe needle along the entry and exit ports. The post-

plasma exposed twin layers are aligned under an optical

microscope and irreversibly bonded over each other. The

upper and lower dies of replicated PDMS are equisized to

the internal dimensions of a hollow cuboidal cutter which

cuts over a predefined zone on the casted PDMS (this is

important for removing the thick PDMS edges from the

cast). Later on the same cutter is also used as an alignment

tool for guiding both halves of PDMS together on the stage

of a Nikon inverted fluorescence microscope. The final

device is connected to an off-chip syringe pump through

micro PEEK tubing � inch OD (outer diameter), 200 lm

ID (inner diameter) (M/S Upchurch Scientific�) press fitted

into the drilled inlet and outlet ports. The dimensions of

these mixer designs are illustrated in Table 1.

3.3 Instrumentation for quantitation of mixing and flow

control

As described earlier we perform a fluorescence-based

quantification of the mixing process using a Nikon� trin-

ocular fluorescence microscope (model Eclipse 80i)

mounted with a photo multiplier tube (PMT) module

(Hamamatsub� H5784-02). The PMT module is used to

transduce fluorescence intensity signals to an electrical

voltage with a suitable noise filtering. We use the acqui-

sition tool NI� PXI1042 which acquires and analyzes all

data through a Labview� interface. A dual syringe pump

(M/s Harvard� apparatus) is coupled to the various entry

ports and feed different lines with glycerine solution and an

aqueous solution of acridine orange (0.5 gm/ml) (Fluores-

cent dye). Figure 4 shows a scheme for the basic experi-

mental setup. We have used an Evolution� VF Peltier

cooled CCD camera (M/S Media Cybernatics) for captur-

ing the mixing images over the entire channel length in a

fully developed steady state flow condition. The images so

taken (corresponding to 250 lm of channel lengths) are

sequentially integrated using image analysis software to

have an idea of the overall mixing length.

(c)

(d)

(b)

(a)Fig. 3 a, b Optical micrographs

of the copper mold along the

entry port and the mixing

channel; c, d images of

corresponding doubly inverted

features in the PDMS


123

4 Simulation details

The flow simulations for different micromixer channels

were carried out with FLUENT�5. The micromixer

geometries were designed using the GAMBIT� prepro-

cessor with the specifications presented in Table 2. The

meshing was carried out using GAMBIT� and then was

subsequently imported to FLUENT�5. The governing

equations are Navier–Stokes conservation of mass and

momentum equations. The boundary conditions used at the

system inlet was uniform velocity perpendicular to the inlet

face with velocity magnitude equal to 0.001 m/s. A con-

stant outlet pressure and ‘no-slip’ boundary condition were

used at all solid/liquid interfaces. The solutions of

numerical simulations were then used to obtain y and

z velocities, x vorticity and helicity values at the mesh

nodes. The flow over first two cycles of herringbone

structures for all the micromixer designs was simulated and

compared.

The mixing characteristics and the residence time dis-

tribution of a bilayered SHM have been investigated

numerically with COMSOL Multiphysics 3.5a tool. All

simulations have been performed using a HP Compaq

dx2480 Business PC with 8 GB RAM and Intel(R) Cor-

e(TM)2 Quad CPU Q8200 @ 2.33 Ghz 2.33 GHz proces-

sor running on Windows 964 platform. The device was

modeled using incompressible Navier–Stokes equation in

the convection and diffusion application mode. The fol-

lowing are the governing equations that the solver

executes.

qðu:rÞu ¼ r �PI þ g ruþ ðruÞsð Þ½ � þ F ð8Þr:u ¼ 0 ð9Þ

q is the fluid density (kg/m3), u represents the velocity

vector (m/s), P equals the pressure (Pa), g denotes the

dynamic viscosity (Pa/s), F is the body force term (N/m3),

I is the identity matrix, T is the stress tensor. Equations 8

and 9 are solved in the convection and diffusion application

mode which has the following governing equation.

r � ð�DrCÞ ¼ R� u � rC ð10Þ

where, D is the diffusion coefficient, C is a transported

scalar, R is a source term and u is a convective velocity

vector. The finite element discretization is done using

Galerkin method and hence during the discretization of

Eq. 10 the numerical solutions are unstable for Peclet

number (Pe) larger than 1 as shown in Eq. 11.

Pe ¼ jjujjh2D

[ 1 ð11Þ

h = mesh element size

A large ‘Pe’ indicates that the convective effects dom-

inate over the diffusive effects. As long as diffusion is

present, there is a certain mesh resolution beyond which

the discretization is stable. This means that the spurious

oscillations of the results can be removed by refining the

mesh which sometimes lacks feasibility because of the

need for a very dense mesh. Thus, a stabilization method

Fig. 4 Schematic of the

experimental setup

Table 2 Generalized dimensions for all the micromixer layouts

Channel length 3 cm

Channel width 200 lm

Channel depth 200 lm

Herringbone depth 50 lm on each side of the

channel

Herringbone arm lengths:major arm

minor arm

280 and 200 lm

Herringbone angle 45�Inter herringbone spacing 50 lm

Herringbone width 200 lm


123

that adds an isotropic diffusion coefficient to Eq. 10 is

preferred [See supplementary Paragraph (1) for details].

This added diffusion coefficient dampens the effects of

oscillations and provides stability to the solutions. We have

presented the simulations of the bilayered SHM design

which contains asymmetric herringbone structures at both

the walls of the mixing channel (top and bottom). The

SHM geometry was simulated for different asymmetry

indices on two herringbone cycles. Each herringbone

consists of a major and minor arm. One cycle of herring-

bones corresponds to two packs of herringbone structures

with one of the packs having an interchanged major and

minor arm (Fig. 5). The grooves separating adjacent her-

ringbone structures are placed at 45� angles with respect to

the axial direction. The asymmetry of the design is char-

acterized by an index which is defined as an area ratio

between one major arm of the top wall and the minor arm

on the corresponding herringbone structure on the bottom

wall. The herringbones placed at the bottom wall of the

micro-channels have the same periodicity than the top one,

although they are geometrically inverted as described in

Fig. 1e earlier. The optimization strategies for one her-

ringbone layer have been carried out earlier by Lynn and

Dandy (2007) and in this work we use an identical strategy

to optimize bilayer designs. Furthermore, the asymmetry

index of the layout is varied between 1.0 (perfect sym-

metric case) and 2.0 and mixing lengths are calculated

from COMSOL simulations. We observe a reduction in

mixing length with a corresponding increase in asymmetry.

Input parameters that were used for the generating the

simulations are illustrated in Table 3. The simulations

show the striations and islands within the micro-channel as

we move away from the entry port.

5 Results and discussions

5.1 Optical micrographs of mixing process:

comparison of mixing lengths

The different designs were evaluated under an optical

microscope with glycerine solution and writer’s ink. The

microscope acquired the snapshots at 109 magnification,

which corresponded to a field of view 250 9 250 lm2. The

snapshots thus taken were stitched to formulate a complete

image of the micromixing process. Figure 6a–c show

snapshots of the plane channel, SHM and AsyBHM,

respectively. We provide a comparison of all these differ-

ent designs to have an idea about the advantage of bilay-

ered micromixers in terms of mixing lengths over the

earlier reported designs. As can be seen from the images in

the plane micromixer design, the ink stream enters the

main mixing channel jacketed with water layers and

remains confined to a thin streak for almost the entire

channel (3 cm length) and towards the end shows some

interlayer diffusion. Also in the SHM case, ink stream

starts to mix rapidly as soon as it meets the first set of

herringbones placed at around 3,000 lm from the entry

port. This mixing length is around 1/10th of the plane

channel as has been reported earlier. It is also interesting to

observe that the water jacket which is like a sheath

enclosing the ink stain at the entry rotates and comes in

between the ink stream (Fig. 6b; Sect. 3).

In the asyBHM design, mixing starts as soon as the two

streams meet the first set of herringbones and very quickly

we observe the diffusion of the ink stream in the water

jacket. We have also in a later module studied the fluo-

rescence intensity of a mixing fluorophore with a water

stream and found that for Re = 0.1, 80% mixing occurs at

15,000 lm in this case as opposed to the other two cases

wherein these are at 25,000–30,000 lm as illustrated in

Fig. 7a. The fluorescence data is captured by traveling

downstream by means of the micrometer resolution x–y

stage attached to our microscope. The length data thus

obtained is plotted with the relative fluorescence values for

a variety of Reynolds Number (0.1, 1, 10, and 100). For an

increased Re value, we should get a greater mixing length

as the two flows are now faster and cover a greater distance

in the same time that they would need to interdiffuse.

Figure 7b shows the experimental comparison at Re = 10

of 80% mixing which occur in the AsyBHM case at

26,000 lm. So this presents a quantitative comparison

Fig. 5 Simulation geometry of the micro-channel with herringbones

on the top and bottom walls. (Dimensions: W = 185 lm,

h = 100 lm, d = 50 lm, h = 45�, PW = 107 lm, Wd = 50 lm)

Table 3 Simulation parameters

Mixer properties Fluid properties

Channel width, w (lm) = 200 Density, q (kg/m3) = 998

Channel depth, h (lm) = 100 Dynamic Viscosity, l(Pa/s) = 8.90 9 10-4

Number of herringbones per

cycle = 20

Molecular Diffusivity,

D (m2/s) = 10-9

Relative groove depth, a = 0.3 Flow velocity, v (m/s) = 0.001

Herringbone asymmetry, p = 2/3

Herringbone angle, h (�) = 45


123

indicating a substantial decrease in mixing length because

of introduction of stretching and folding which gets further

enhanced for the bilayer designs, particularly for asyBHM

case.

5.2 Simulation results

5.2.1 Helicity and vorticity calculations using Fluent�5

By definition, helicity and axial vorticity (x-vorticity in our

case) depict mass transfer in a direction transverse to the

flow path. These two factors coupled together are respon-

sible for speeding up the diffusive mixing in SHM and

BSHMs through formation of centers of rotation. So,

helicity and vorticity magnitudes (averaged over the entire

channel length) are expected to be very good indicators of

the mixing performance. We have numerically calculated

these values in all designs and derived a performance

comparison between the different designs. The spatial

values of helicity and x-vorticity at every node or cell

center can be directly imported from Fluent�5. The aver-

aged values of x-vorticity and helicity were computed at

every node point. The results obtained from the simulations

carried out for plain channel, SHM, ABHM, symBHM and

asyBHM, have been tabulated in Table 4.

Through the numerical simulations we have been able to

successfully predict the outcomes of delving into the bulk

of fluid flowing through the bilayer designs. The data

(a)

(b)

(c)

Fig. 6 a Stitched micrographs

of plane channel micromixer,

b stitched micrographs of SHM,

c stitched micrographs of

asyBHM (all experiments

correspond to Re = 0.1)

(Optical micrographs)


123

shows a steep increase in vorticity from the plane channel

case to the SHM/ABHM designs. It gets further enhanced

as we evaluate symBHM. This is owing to the fact that the

centers of rotation formulated transverse to the flow

direction change from zero in the plain channel case to two

in SHM/ABHM case, and four in symBHM/Asy BHM

cases. Also, experimentally we have seen a shorter mixing

length qualitatively and quantitatively as bilayer designs

are explored. Mixing, therefore, can be attributed to

designs which can produce counter vortices of different

sizes with changing centers of rotations as in SHM or BHM

cases. In the BHM design, however as discussed earlier, the

flow centers not only change positions in the transverse

direction but also in the longitudinal directions to the flow

path. In summary, the average x-vorticity is arranged in

order of its numerical value in the following manner:

asyBHM [ symBHM [ SHM * ABHM � Plain chan-

nel (Table 3).

The increase in asymmetry in the channel and the

increase in surface patterns causing an increase in centers

of rotation are responsible for this trend. On the basis of

data obtained in the above mentioned designs, we can

safely predict that for the asyBHM case which heavily

involves the development of rotation centers asymmetri-

cally, both values would peak in the trend.

We hypothesize that the herringbone arms act as rotation

generators thus rotating, stretching and folding the

streamlines and laminating them. The phenomenon should

repeat every half cycle by virtue of the geometric layout

wherein the spatial position of rotation center should vary

longitudinally. In SHM design, this is the only variation of

the rotation center. The difference in mixing of fluids

flowing through SHM and ABHM designs originates

because in ABHM the the rotation centers also vary

transversely along with the longitudinal variations. Also,

the direction of the flow rotation introduced by one half

cycle of the surfaces is clockwise and that introduced by

the very next half cycle is anticlockwise. This increases the

lamination rate in the ABHM design by a higher level of

twisting and stretching of the flows In the SHM, however,

the flow rotation direction is always fixed as the flows

originate primarily at the bottom walls. For the bilayer

designs, the structures on both surfaces lead to an imme-

diate formation of two pairs of rotation centers which are

counter directional causing an increased stretching of

flows.

In order to get some idea of the different centers of

rotation, we have further plotted the y-velocity and

z-velocity components at mesh nodes (spatial points) using

OriginPro�8. These plots provide a cross-sectional view of

the flow and the center of rotations can be observed. Fig-

ure 8a, b shows a center of rotation getting generated after

half a cycle and complete cycle in the AHM case. We have

also provided the herringbone structures with these vector

plots. As one full cycle ends, wherein the flow meets a new

set of herringbones on the top surface, the centers of

rotation are found to shift and originate from the top

surface. The rotation centers rhyme very well with the

physical centers of both the major and minor arms of the

herringbones. Another very important factor to be observed

Fig. 7 Comparison of performance between Plain channel, SHM,

ABHM, symBHM and asyBHM at a Re equal to 0.1 and b Re equal to

10 (experimental data)

Table 4 Average helicity and x-vorticity magnitudes for five of the

mixer channel surface designs

Micromixer type Average helicity

magnitude

Average x-vorticity

magnitude

Plain channel 6.22E-06 1.22E-06

SHM 0.0110 10.9408

ABHM 0.0107 10.4460

symBHM 0.0168 14.4397

asyBHM 0.0210 14.6834


123

Fig. 8 Transverse velocity

vectors for ABHM a after first

half cycle, b after first full cycle


123

is the velocity scale in Fig. 8a, b, which falls with tra-

versing of flow downstream that is attributed to factors like

increasing chaos and fluid friction.

The simulations done in case of the symBHM and

AsyBHM show four centers of rotation analogous to our

expectation. To approximate the flow behavior in a

volume a vector plot has been prepared by coupling

views of cross-sectional planes over a small sectional

volume, 100 lm along the channel length (Fig. 9a, b).

The presence of 4 rotation centers with unequal radii

synchronous with the herringbone arm lengths is evident

through these plots in both cases. For a better under-

standing, the directions of average local rotation have

been schematically added to these plots as circular

arrows. Hence, because of the asymmetry and pairing up

of a bigger and a smaller radius of counter rotations

along both horizontal and vertical directions, we expect

the rate of stretching dk/dt to increase significantly,

which is further investigated in the next section using the

COMSOL tool.

Fig. 9 Transverse velocity

vectors over a span of 100 lm

of channel length in

a symBHM, b assyBHM–added

direction of movement (velocity

magnitude in m/s) (Simulation

data)


123

5.2.2 Calculations for mixing length for different

asymmetry indices using COMSOL 3.5a

We have also used the COMSOL tool to trace the striations

within our mixer design using a concentration plot. The

concentration traces are determined using the conservation

of mass principle in a convective and diffusive flow field in

an incompressible system. We assume water like properties

of the mixing fluids for solving the flow (density of

water, q = 1,000 kg/m3; dynamic viscosity of water,

g = 0.001 Pa/s; isotropic diffusion coefficient, D = 1 9

10-10 m2/s). An inlet velocity of 0.001 m/s is used at the

entrance and we assume a pressure boundary condition at

the outlet (Output pressure = p0 = 10 Pa). An input con-

centration of one of the two mixing fluids is assumed as

c0 = 50 mol/m3 and no slip boundary conditions are used

along all the walls of the mixing channel.

The geometry described in Fig. 5 is meshed into an

optimized number of mesh elements and mixing length

is calculated by finding out the k value numerically

(as detailed in Sect. 2 earlier). Mesh optimization is per-

formed by varying the number of mesh elements between

2.13E05 and 1.28E05 mesh elements, respectively. The

mixing length Dym is calculated in each case and plotted

with the mesh elements as illustrated in Fig. 10. We find

changes in mixing length after the number of mesh ele-

ments reach 1.8E05 value. The total number of degrees of

freedom in this case comes as 1.21E05. We observe the

mixing lengths to be in the range of 7.0–7.5 mm for the

optimized mesh design. All ‘Dym’ values are calculated

based on an asymmetry index of 2.0 as detailed in the next

few lines. Figure 11a–j show the slice plots describing the

striations and islands formulated in the concentration plots

(COMSOL simulations). The striations are shown by the

mixed regions in-between the twin flows and the islands are

the unicolored regions which rapidly decrease in sizes along

the length of the channel and finally vanish totally in the fully

mixed sample (image corresponding to L = 11,000 lm).

From these plots, it is apparent that with increasing length

L the islands become smaller and the striations or mixed

region increases. The slice plots towards the entry of the

channel and at a length where the islands are smallest yetFig. 10 Plot of mixing length versus number of mesh elements (for

asymmetry index = 1.4)

(a)

(f) (g) (h) (i) (j)

(b) (c) (d) (e)

Fig. 11 Slice plots of COMSOL simulations at different lengths from the entrance


123

distinguishable (referred to as Point P) are compared using

the pixel count option in Image J. The k value is obtained as

a ratio between the perimeter of the striation at the point P

with respect to that at the entry. [See supplementary figure 2]

The mixing lengths (Dym) based on the observed k values are

calculated from Eq. 7 in Sect. 2. We observe a reduction in

the mixing length from 9.7 to 6.0 mm for a corresponding

increase in asymmetry index from 1.0 to 2.0 (Fig. 12). These

lengths are lower than that observed experimentally in the

asymmetric herringbone design (13.7 mm approximately

corresponding to the 20% mixing level) as the velocity that

has been used at the flow entry is lower than the attainable

experimental value using the off-chip syringe pump. The

reduction in mixing lengths in the simulated case is well

expected as lower entry velocity of the flow would corre-

spond to an increased residence time where diffusional

mixing is enhanced and the effective length of the mixing

reduces.

5.3 Fluorescence microscopy results

The quantitative analysis of mixing for all the micromixer

designs was done by means of fluorescence microscopy.

Along the channel, the fluorescence intensity was trans-

duced by means of a PMT module to voltage signals. The

relative fluorescence intensity is a ratio between inlet

fluorescence intensity and the fluorescence intensity at

different points along the mixing length. This ratio was

plotted against the mixing length for all designs over a

range of Reynolds number (See Supplementary fig-

ure 1a–d). We have assumed in all cases that 80% decay in

fluorescence intensity corresponded to the value of the

mixing lengths. The performance of all designs is com-

pared on basis of the mixing lengths corresponding to this

drop in fluorescence intensity. In the fluorescence plots the

x axis ‘0’ corresponds to the point just before the onset of

herringbones or surface structures in all the micromixer

devices. Thus, the net mixing is an outcome of the mixing

caused by herringbone structures. The fluorescence value

decreases at a slower rate near the inlet and changes rapidly

after the flow has traversed a length of 5,000 lm. This can

be attributed to the fact that fluorescence intensity will

change because of the stretching and folding of the two

flows. However, the length after which the slope of the

relative fluorescence suddenly decreases varies with the

different Reynolds numbers. As maximum mixing would

occur for flows with a longer residence time, therefore the

minimum mixing length would be attained by flows having

low Reynolds number. Therefore, we compare the fluo-

rescence intensity drop in all the designs in a single plot

corresponding to Re = 0.1(Fig. 7a). The corresponding

fluorescence intensity drop at Re = 10 is indicated in

Fig. 7b. As can be seen, clearly the asyBHM design has the

shortest mixing length corresponding to 1.5 cm which is

half way down the channel. At a higher value of Re = 10

this length increases to 2.6 cm. This difference in the

mixing length is obvious as at a higher Re value the

velocities of the two mixing fluids are high and they cover

more path length in the time that is needed for the striations

developed to diffusively merge with one another. This in

comparison to the SHM design is significantly faster in

both cases. In the plane channel mixing begins to occur

after the flow traverses a huge length corresponding to both

Re = 01 and 10. The difference in the mixing lengths at

Re = 0.1 and 10 becomes prominent in all the other

designs. The plain channel probably has a very high mixing

length for this difference to be observed in both cases. The

comparison between the SHM and ABHM designs show

that the fluorescence intensity drop in ABHM case is

higher at Re = 0.1. At Re = 10, the mixing effects are

equal in both cases which can be due to the flow velocity

and less residence time. The time for the development of

the centers of rotation in Re = 0.1 is certainly more due to

an overall slow fluid transport. Thus, centers generated

from both top and bottom walls alternately are able to

develop fully in the bulk of the flow owing to a greater

residence time. The SymBHM shows similar trends in both

Reynolds numbers, although the overall mixing length for

Re = 10 is much higher (30,000 lm) in comparison to

Re = 0.1 where it is 23,500 lm approximately. Identical

differences in both SHM and ABHM cases have been

observed and hypothesized while explaining the vorticity

and helicity trends. From the comparative plots (Fig. 7a,

b), it is evident that for both Reynolds number values

the asyBHM possesses maximum mixing efficiency and

the comparative performance can be sequenced as

asyBHM > symBHM [ ABHM [ SHM [ plain channel.

1.0 1.2 1.4 1.6 1.8 2.0

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0Δ

y m (

mm

)

Area Index

Fig. 12 Mixing length versus asymmetry index for an entrance flow

velocity 0.001 m/s


123

Therefore, our mixer designs work substantially better at

Re = 0.1 or lower. This trend can be explained on the basis

of increased asymmetricity offered to the uniaxial pressure

driven flow by the topology of the micromixer channel.

The higher x-vorticity and helicity generated by these

asymmetric features is the factor responsible for inducing

such large chaos leading to multi-lamination and faster

interdiffusion.

6 Conclusions

We have studied a variety of bilayer herringbone designs

with different degree of asymmetry numerically represented

by a ratio AI. It was observed through numerical simulations

and fluorescence microscopy that mixing increases by

changing to bilayer designs and also by increasing the

asymmetry of the bilayered structure. If the area ratio of the

overlapping faces on the bilayered herringbone structure is

varied from 1 (perfect symmetric case) to 2 (highly asym-

metric case) the mixing length varies almost from 9.7 to

6 mm. Our simulations further indicate formation of four

centers of rotations which show parity with the individual

herringbone arm lengths. The centers of rotation thus gen-

erated are responsible for rapidly laminating the two flows as

they traverse over the herringbones and cause diffusive inter-

laminae mass transport. As the laminae sizes are reduced

along the length of the channel, the time of diffusion also

reduces which is favorable for rapid mixing. The mixing

length obtained for an asymmetry index of 1.4 in our case is

around 13.7 mm for a Reynold’s number of 10 which is

lesser in comparison to what has been experimentally

reported (15 mm) by Stroock et al. (2002a) We also show

physical snapshots of a stream of ink and water which mix in

plain channels as well as channels with herringbones and

bilayer herringbones. The snapshots indicate rapidity of the

mixing and shortened mixing lengths as the flow traverses

over all these three designs individually. The comparative

performance between the various designs that have been

explored follow the sequence asyBHM > symBHM [ABHM [ SHM [ plain channel. The micromixer designs

are fabricated using an easy microfabrication technique

called MRDI which has several advantages over the photo-

lithography-based approaches. We conclude that BHMs

with increasing degrees of asymmetry reduces the mixing

length and enhances mixing efficiency than monolayer

designs.

Acknowledgment The authors gratefully acknowledge the financial

support from the Department of biotechnology, Government of India

and the Dean of Research and Development, Indian Institute of

Technology, Kanpur for supporting this work. They also gratefully

acknowledge Professor Shubhra Gangopadhyay and Professor Keshab

Gangopadhyay; University of Missouri, Columbia, Professor Rashid

Bashir; University of Illinois at Urbana Champaign, Professor P K

Panigrahi, Professor Gautam Biswas and Professor S K Choudhary at

Department of Mechanical Engineering, IIT, Kanpur for their help,

advice and valuable suggestions.

References

Ansari MA, Kim KY (2007) Shape optimization of a micromixer with

staggered herringbone groove. Chem Eng Sci 62:6687–6695

Auroux PA (2002) Micro total analysis systems. 2. Analytical

standard operations and applications. Anal Chem 74:2637–2652

Branebjerg J, Gravesen P, Krog JP (1996) Fast mixing by lamination.

In: Proceedings of the IEEE micro electro mechanical systems,

San Diego, USA 441–446

Chaudhury R (2009) Bilayared staggered herringbone micromixers,

Master’s thesis. Department of Mechanical Engineering Faculty,

Indian Institute of Technology, Kanpur

Chung CK, Shih TR (2008) Effect of geometry on fluid mixing of the

rhombic micromixers. Microfluid Nanofluidics 4:419–425

de Mello A, Wooton R (2002) But what is it good for? Applications of

microreactor technology for the fine chemical industry. Lab chip

2:7N–13N

Erbacher C, Bessoth FG, Busch M, Verpoorte E, Manz A (1999)

Towards integrated continuous-flow chemical reactors. Mikro-

chim Acta 131:19–24

Hardt S, Schonfeld F (2003) Laminar mixing in interdigital micro-

mixers with different mixing chambers—Part 2: Numerical

simulations. AIChE J 49:578–584

He B, Burke BJ, Zhang X, Zhang R, Regnier FE (2001) A picoliter-

volume mixer for microfluidic analytical systems. Anal Chem

73:1942–1947

Hessel V, Zimmerman WB (2006) Investigation of the convective

motion through a staggered herringbone micro-mixer at low

Reynolds number flow. Chem Eng Sci 61:2977–2985

Hessel V, Lowe H, Schonfeld F (2005) Micromixers: a review on passive

and active mixing principles. Chem Eng Sci 60:2479–2501

Howell PB, Mott DR, Fertig S, Kaplan CR, Golden JP, Ran ES, Ligler

FS (2005) Microfluidic mixer with grooves placed on top and

bottom of the channel. Lab chip 5:524–530

Johnson TJ, Ross D, Locascio LE (2002) Rapid microfluidic mixing.

Anal Chem 75:45–51

Kakuta M, Hinsmann P, Manz A, Lendl B (2003a) Time-resolved

Fourier transform infrared spectrometry using a microfabricated

continuous flow mixer: application to protein conformation study

on the example of ubiquitin. Lab chip 3:82–85

Kakuta M, Jayawickrama DA, Wolters AM, Manz A, Jonathan V,

Sweedler JV (2003b) Micromixer-based time-resolved NMR:

applications to ubiquitin protein conformation. Anal Chem

75:956–960

Kang TG, Singh MK, Kwon TH, Anderson PD (2008) Chaotic mixing

using periodic and aperiodic sequences of mixing protocols in a

micromixer. Microfluid Nanofluidics 4:589–599

Kim DS, Lee SW, Kwon TH, Lee SS (2004) A barrier embedded

chaotic micromixer. J Micromech Microeng 14:798–805

Kirtland JD, Siegel CR, Stroock AD (2009) Interfacial mass transport

in steady three-dimensional flows in microchannels. New J Phys

11:075028

Knapp MR (2001) Commercialized and emerging Lab-on-a-Chip

applications in micro total analysis systems. Kluwer Academic

Publishers, Dordrecht, pp 7–9

Lee SW, Kim DS, Lee SS, Kwon TH (2006) A split and

recombination micromixer fabricated in a PDMS three-dimen-

sional structure. J Micromech Microeng 16:1067–1072


123

Li C, Chen T (2005) Simulation and optimization of chaotic

micromixer using lattice Boltzmann method. Sens Actuators B

Chem 106:871–877

Lynn NS, Dandy DS (2007) Geometrical optimization of helical flow

in grooved micromixers. Lab Chip 7:580–587

Melin J, Gimenez G, Roxhed NW, van der Wijngaart W, Stemme

G (2003) In: Proceedings of the 7th International conference

on micro total analysis systems, Lake Tahoe, California,

167–170

Mengeaud V, Josserand J, Girault HH (2002) Mixing processes in a

zigzag microchannel: finite element simulation and optical study.

Anal Chem 74:4279–4286

Michael GO, Juan GS, Ronald JA, Hassan A, Beebe DJ (2002)

Passive mixing in a three-dimensional serpentine microchannel.

J Microelectromech Syst 9:190–197

Nguyen NT, Wu ZG (2005) Micromixers: a review. J Micromech

Microeng 15:R1–R16

Ottino JM, Wiggins S (2004) Introduction: mixing in microfluidics.

Philos Trans R Soc Lond A 362:923–935

Stroock AD, McGraw GJ (2004) Investigation of the staggered

herringbone mixer with a simple analytical model. Philos Trans

R Soc Lond A 362:971–986

Stroock AD, Dertinger SK, Ajdari A, Mezic I, Stone HA, Whitesides

GM (2002a) Chaotic mixer for microchannels. Science

295:647–651

Stroock AD, Dertinger SK, Whitesides GM, Ajdari A (2002b)

Patterning flows using grooved surfaces. Anal Chem

74:5306–5312

Vargas-Bernal R (2006) In: Proceedings of robotics and automotive

mechanics conference 2:176–181

Wang H, Iovenitti P, Harvey E, Masood S (2003) Numerical

investigation of mixing in micro-channels with patterned

grooves. J Micromech Microeng 13:801–808

Wiles C, Watts P, Haswell SJ, Pombo-Villar E (2001) The aldol

reaction of silanol ethers within a micro reactor. Lab chip

1:100–101

Wiles C, Watts P, Haswell SJ, Pombo-Villar E (2002) 1, 4-Addition

of enolates to a, b-unsaturated ketones within a micro reactor.

Lab chip 2:62–64

Yang ID, Chen YF, Hsu HT, Tseng FG, Chieng CC (2003)

International conference on miniaturized chemical and biochem-

ical analysis systems, Squaw Valley, CA, US, 1005–1009

Yang JT, Huang KJ, Lin YC (2005) Geometric effects on fluid mixing

in passive grooved micromixers. Lab Chip 5:1140–1147


123

bilayer staggered herringbone micro-mixers with symmetric and asymmetric geometries

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