SHORT COMMUNICATION
Rapid measurement of fluid viscosity using co-flowing in a co-axial
microfluidic device
W. J. Lan • S. W. Li • J. H. Xu • G. S. Luo
Received: 21 September 2009 / Accepted: 16 November 2009 / Published online: 27 November 2009

Springer-Verlag 2009
Abstract This article presents a simple microfluidic
method to measure the Newtonian fluid viscosity. This
method is carried out in a co-axial microfluidic device. A
stable liquid/liquid annular co-laminar flow in the co-axial
microfluidic device has been realized, which can be
described by Navier–Stokes equations. The viscosity of
either fluid can be measured based on the equations when
the viscosities of another fluid is known. Proper conditions
to form stable annular co-laminar flow for the viscosity
measurement were investigated. Several fluids were tested
with viscosity ranging from 0.6 to 40 mPa s. The measured
results fit very well with those measured by a commercial
spinning digital viscometer. The novel method is highly
controllable and reliable, and has the advantage of less time
and material consumption, as well as easy fabrication of
the device.
Keywords Microfluidic device
Co-axial
Viscosity

Annular co-laminar flow
Navier–Stokes equations
1 Introduction
Viscosity is a main parameter of fluids, since it significantly
influences the flow and transfer properties. The knowledge
about the viscosity of liquids is of great importance in many
industrial and scientific fields (Zafarani-Moattar and
Khoshsima 2008; Zhang et al. 2008; Curtin et al. 2006;
Buiochi et al. 2006). According to different measuring
principles, traditional viscometry can be defined as follows:
capillary viscometry, rotating viscometry, falling ball, or
needle viscometry, etc. Although there are many measure-
ment methods, new methods with less time and material
consumption, more reliable and much easier operation
ability are still required.
In the past decade, microfluidic devices have been the
focus of numerous studies due to their high efficiency,
safety, repeatability, and facile controllability (Ehrfeld
et al. 2000). They have been widely used for emulsions
(Kobayashi et al. 2009; Li et al. 2009), chemical reaction
(Burns and Ramshaw 2001, 2002), liquid–liquid extraction
(Dittrich et al. 2006; Xu et al. 2005; Kumemura and
Korenaga 2006), biological analysis (Grodrian et al. 2004),
crystallization (Zheng et al. 2004), nanoparticle synthesis
(Yen et al. 2005; Li et al. 2008; Sotowa et al. 2007), and
structural material preparation (Shestopalov et al. 2004;
Zourob et al. 2006; Nie et al. 2005; Quevedo et al. 2005;
Dendukuri et al. 2005, 2006; Khan et al. 2004). One main
characteristic of microfluidic devices is that the surface and
viscous forces become dominant, while the inertial and
buoyancy forces become negligible. This characteristic
makes it possible to measure the viscosity using micro-
fluidic devices. Guillot et al. (2006) measured the fluid
viscosity using liquid/liquid co-laminar parallel flows in a
T-shape microchannel. The fluid flows to be studied side-
by-side with a reference viscosity. The shape of the liquid/
liquid interface was determined by using optical micros-
copy. Knowing the flow rates of the two liquids and the
geometrical features of the channel, they could calculate
the mean shear rate and its viscosity. However, the flow in
the T-shape microchannel has a two-dimensional structure
in the cross section, and the shape of the interface is
W. J. Lan
S. W. Li
J. H. Xu (&)
G. S. Luo (&)
The State Key Lab of Chemical Engineering, Department
of Chemical Engineering, Tsinghua University,
100084 Beijing, China
e-mail: xujianhong@tsinghua.edu.cn
G. S. Luo
e-mail: gsluo@tsinghua.edu.cn
123
Microfluid Nanofluid (2010) 8:687–693
DOI 10.1007/s10404-009-0540-4

variable. Therefore, the flow will be influenced by a
number of factors, which makes the physical analysis and
the functions for viscosity computation quite complicated.
It can also be mentioned that a stable liquid/liquid co-
laminar flow in a T-shape microchannel requires accurate
control ability. If one-dimension structure at the cross-
section of a liquid/liquid co-laminar flow in a microfluidic
device is realized, the process for measurement of viscosity
will be more controllable and reliable. The mathematical
model will be much simpler and easier to be solved.
Stable annular co-laminar flow in a capillary tube has a
one-dimensional structure at the cross-section. The flow
field can be easily described by Navier–Stokes equations
and the boundary conditions can be defined clearly. In this
study, we attempted to realize a stable liquid/liquid annular
co-laminar flow in a co-axial microfluidic device and
develop a simple method for the measurement of Newto-
nian fluid viscosity. A set of equations were suggested for
the calculation in the liquid/liquid annular co-laminar flow
field which contains the information of viscosity. Seven
liquid systems were selected, and the viscosities of the
fluids were measured. The results were compared with the
values measured by a commercial spinning digital
viscometer.
2 Microfluidic device and materials
The flow chart of the experiment and the microfluidic
device used are shown in Fig. 1a and b. The device was
fabricated on a 40 mm 9 20 mm 9 3 mm PMMA plate
using micromachining technology. A Teflon tube with
0.5 mm inner diameter was inserted as the main channel
for the multiphase flow, while a stainless steel microneedle
was inserted into the tube for inner phase flow. The outer
and inner diameter of the microneedle was 0.34 and
0.16 mm, respectively. The microfluidic device was sealed
using another 40 mm 9 20 mm 9 1 mm PMMA plate
with ultrasonic assisted sealing technique (Li et al. 2009).
Three microsyringe pumps and three gastight microsy-
ringes were used to pump the fluids into the microfluidic
device. As shown in Fig. 1a, a microscope coupled with a
high-speed CCD video camera was used to observe the
flow pattern in the microfluidic device.
Several systems were used as the model systems to
measure the viscosity of fluids. The tested systems included
(1) 1-octanol/silicone oil, (2) butyl acetate/silicone oil, (3)
liquid paraffin/silicone oil, (4) 1,2-propanediol/silicone oil,
(5) water/1,4-butanediol, (6) 70 wt% phosphoric acid in
water/1,4-butanediol, and (7) 85 wt% phosphoric acid in
water/1,4-butanediol. In all of the systems, the former
liquid was served as the inner phase, and the latter one was
served as the outer phase. The viscosities were all mea-
sured at 25C.
3 Measurement principle and mathematical model
Various liquid/liquid flow patterns, including dripping,
jetting, and co-laminar flow can be formed in the micro-
fluidic device. In this study, we would like to measure the
fluid viscosity in the co-laminar flow regime. For an exact
and easy measurement, the co-laminar flow should be
annular. However, the buoyancy effect may destroy this
idea flow state. In order to estimate this effect, the
dimensionless numbers, Bond number and Capillary
number, which are usually used in microchannels, are
calculated. The definition equations are as follows:
Bo ¼ ðqo  qiÞgd
2
f
c
ð1Þ
Ca ¼ louo
c
: ð2Þ
Here, df is the diameter of the inner phase flow, lo and uo
are viscosity and velocity for the outer phase fluid. Take
system (1) as an example in our experiment, Bond number
is in the range of 110
5
c  110
4
c and Capillary number is in
the range of 110
4
c  110
3
c : The ratio of Bo and Ca char-
acterizes the comparison between the buoyancy effect and
the shear effect of the outer flow on the inner phase flow.
Because BoCa  0:1; buoyancy affect little on the flow state.
However, the ratio is not small enough. We are not sure the
buoyancy effect can be ignored or not. Therefore, weFig. 1 The experimental setup
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