Extended Abstracts of the Ninth JSME-KSME Thermal and Fluids Engineering Conference
October 28-30, 2017, Okinawa, Japan

TFEC9-1420

FLUID VISCOSITY MEASUREMENT IN MICROCHANNELSUSING FLUORESCENCE POLARIZATION IMAGING
R. Kuriyama*, T. Nakagawa, K. Tatsumi and K. Nakabe
Department of Mechanical Engineering and Science, Kyoto University,
Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan

ABSTRACTThis study describes the development of a non-contact and two-dimensional fluid viscosity measurement
technique using fluorescence polarization microscopy. When fluorescent molecules dissolved in liquid are
excited by a linearly-polarized light, they experience rotational Brownian motion during the period fromexcitation to emission. Since fluorescence depolarization is observed with the degree influenced by the extent
of their rotation which is related to the fluid temperature, viscosity, and molecular size, fluid viscosity can be
determined under a fixed temperature condition by measuring steady-state fluorescence polarization degree(P). Concerning the viscosity dependences of P, three different fluorescent molecules were compared in apreliminary experiment and casein molecule labeled with fluorescein isothiocyanate (casein-FITC) was chosen
among them as a suitable probe. A calibration experiment was then carried out using casein-FITC in a straight
microchannel at a constant temperature of 30 °C. The calibration result showed a relationship that thereciprocal of P linearly increased with the reciprocal of viscosity, which qualitatively agreed with thetheoretical prediction. By applying this calibration result, a viscosity gradient was clearly visualized in a
microchannel in which co-flowing two solutions of different viscosities interdiffused. These results indicate
the potential of the present technique for contributing to microscale analyses of chemical and biological fluids.

KEYWORDS: Fluorescence polarization, Fluid viscosity measurement, Microchannel, Casein-FITC
1. INTRODUCTION
Determination of local viscosity in microscopic scale is of key importance especially for biological samples,such as blood plasma [1] and living cells [2] since it is directly linked with composition change and mass transportof biomolecules. It can provide useful information to understand various reactions and kinetics of biologicalprocesses; blood clotting and cell signaling, for instance. Local viscosity measurement also offers an aid todevelop diagnostic and therapeutic approaches as the viscosity can be an indicator of some diseases [1].
However, the wide-spread mechanical viscometers, such as capillary viscometer and rotational viscometer,
measure bulk viscosity of liquid, i.e., viscosity averaged over the whole sample. To obtain the microscopic
viscosity of samples in low volume, various measurement techniques based on optical sensing have been
proposed in recent years, including fluorescence imaging of molecular rotors [2], Brownian microscopy [3],steady-state or time-resolved fluorescence polarization [2,4,5], fluorescence lifetime imaging [5] and so forth.
Among these techniques, the present study employs steady-state fluorescence polarization which exploits
depolarization due to rational Brownian motion of fluorophores. The main advantage of the technique is thatplanar distributions of fluid viscosity can be visualized with relatively simple experimental arrangementcompared to time-resolved measurements. Moreover, unlike the techniques using molecular rotors, any
fluorescent molecule can be used as a probe if the molecular size and fluorescence lifetime are suitable for theintended viscosity range. In the present study, we focus on a development of a visualization method for*Corresponding Author: kuriyama@me.kyoto-u.ac.jp
Copyright © 2017 by The Author(s). Distributed by JSME and KSME, with permission.

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viscosity distributions in microscale based on fluorescence polarization and demonstrate a two-dimensional
measurement in microchannel flow to validate the feasibility of this method.

2. MEASUREMENT PRINCIPLE
When randomly oriented fluorophores are irradiated by a linearly-polarized excitation light, only those withthe absorption moments appropriately aligned to the excitation polarization direction can absorb the light.
Specifically, the probability of the absorption is proportional to the value cos2θ, where θ is the angle between
the directions of excitation polarization and absorption moment. If the excited fluorophores are at stationary
condition, they emit the fluorescence polarized in the same direction with the absorption moment (Fig. 1(a)).
On the other hand, if the excited fluorophores are suspended in fluid and thus free to rotate, they experiencerotational Brownian motion during the period from excitation to emission (Fig. 1(b)). Consequently, theemission moments, which are initially oriented along the absorption moments, are randomized according to
the extent of their rotation. Depolarization of fluorescence is therefore observed with the degree which isrelated to the fluid temperature, viscosity, and the molecular size.
Polarization degree, P, is defined as a function of I|| and I⊥, which are the fluorescence intensities of thecomponents that are parallel and perpendicular to the polarization direction of the excitation light, respectively:
P=

I || − I ⊥I || + I ⊥.

(1)

Perrin [6] theoretically derived the equation which relates this P value to the fluorescence lifetime and therotational diffusion of fluorescent molecules as

(

1 1
1 1
kBT
τ)
− ) = ( − )(1 +
µV
P 3
P0 3

(2)

where P0 is the intrinsic polarization defined as the polarization degree of the molecule at stationary condition(in absent of rotation), kB is the Boltzmann constant, V is the hydrodynamic volume of the rotating unit, and τ
is the fluorescence lifetime. T and µ are the absolute temperature and viscosity of the fluid, respectively.
Clearly seen from Eq. (2), the reciprocal of P shows a linear relation with T/µ. Therefore, if V and τ remains
constant during the measurement, the fluid viscosity, µ, can be determined by measuring P under fixed
temperature condition.
Absorption moment(a)

Excitation light
Polarization
direction

Fluorescence
Brownian motion

Fluorescentmolecule(b)

FluorescenceFig. 1 Polarization direction of the fluorescence emitted from (a) a molecule in stationary condition and (b)that suspended in fluid.

3. EXPERIMENTAL SECTION
3.1 Measurement System Figure 2(a) shows a schematic of the optical measurement system using an uprightmicroscope (Olympus, BX51). Polarization measurements can be performed by either transmission or epifluorescence observation. A light from LED was linearly-polarized by a polarized light condenser or a polarization
plate, filtered by an excitation filter and focused to the sample on the microscope stage. The fluorescence collected2

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by an objective lens (Olympus, LMPlanFLN10x) was filtered by a fluorescence filter and captured by aphotomultiplier (Hamamatsu Photonics, H5783-03) or a sCOMS camera (Andor, Zyla 4.2 plus) through a second
polarization plate mounted on a rotation stage. Only for epi-fluorescence observation, a dichroic mirror was placedin the optical path. Note that the LED light source and the set of filters were appropriately selected withconsideration of the fluorescence characteristics of the fluorophore used as a probe in the polarization measurement.
The temperature of the microscope stage was controlled by circulating water from an isothermal bath so that thetemperature of sample solution was maintained at 30 °C.

3.2 Microchannel Sample solution was enclosed in a prepared slide (consisting of bottom and upper coverglasses spaced by two strips of 120-µm thick parafilm), or introduced into a microchannel at a constant flow rateusing a syringe pump. Figure 2(b) shows a schematic of a Y-shaped microchannel used for two-dimensional
viscosity measurement. The microchannel was comprised of a PDMS chip and a cover glass, which were bondedby oxygen-plasma treatment. K-type thermocouples were inserted in 1-mm diameter holes made by biopsy punch
and the channel temperature was logged during the polarization measurement.

3.3 Chemicals The present study employed fluorescein (diameter = 1.0 nm[7], molecular weight = 332, Nacalai

Tesque, #16106-82), rhodamine B (dia.= 1.6 nm[8], MW = 479, Kishida Chemical, #000-68232), and casein
molecules labeled with fluorescein isothiocyanate (casein-FITC, dia.= 30 nm, MW = 26000, AAT Bioquest,#13440) as fluorescent probes. In anticipation of the future application to biological samples with relatively low
viscosity, such as human blood plasma, the viscosity of sample solution was controlled in the range 0.8−2.8 mPa⋅s
by adjusting glycerol concentration to 0−40 wt%.
(b)(a)
Light detector

Polarizer
Fluorescence filter
Dichroic mirror
Objective lensPolarizer

Top view
LED

Z
X

Polarizer
Y

Measurement area
500 µmy
Excitation filter
SampleCondenser

Inlet A

Thermocouples

Temperature
controlling stage

Inlet Bx1213 µm

Cross-sectional view

Thermocouples

Inlet

OutletLED

Mirror

35 µm

PDMS chip
Cover glass(120−170 µm in thickness)

Fig. 2 (a) Schematic of the optical system for fluorescence polarization measurement and (b) top and crosssectional views of a Y-shaped microchannel used for two-dimensional viscosity measurement.

4. RESULTS AND DISCUSSIONS
4.1 Selection of Fluorescent Probe In Eq. (2), 1/P theoretically shows linear increase with 1/µ and the slopechanges with τ and V. Therefore, the sensitivity and precision of the present technique highly depend on thecharacteristic properties of the fluorescent probe. In order to select an appropriate probe, polarization
measurements were carried out using fluorescein, rhodamine B, and casein-FITC. A prepared slide filled withsample solution was set on the microscope stage and fluorescence intensities, I|| and I⊥, were successively
measured with transmission observation. The fluorescence intensity was detected by the photomultiplier at 5 Hz
and accumulated for 2 s. Figure 3(a) shows the measurement result. 1/P increases with 1/μ in all cases, however,linear correlation is not obtained in fluorescein case. In rhodamine B and casein-FITC cases, 1/P shows
proportional increase with 1/μ and the slopes are nearly the same: measurement sensitivities for viscosity

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measurement are equivalent in the two cases. On the other hand, measurement precision is expected to behigher in casein-FITC case since the absolute value of P is larger compared with rhodamine B. Casein-FITC
was selected as a probe in the present study according to these discussions.

4.2 Calibration Experiment Prior to a two-dimensional viscosity measurement, a calibration experiment was
conducted using 0.1 wt% casein-FITC solutions in a straight microchannel with height of 35 µm and width of 500µm. The epi-fluorescence configuration and the sCOMS camera were used for the experiment. The exposure time
was set at 1 s and 10 fluorescent images were captured for each intensity component. P was then calculated byaveraging 10 polarization distributions temporally and spatially. Figure 3(b) shows the calibration result, where
each plot indicates the averaged value of four measurement data and the error bar shows the uncertainty at 95%
confidence level. It is clearly seen that 1/P linearly increases with 1/μ, which agrees well with the theoreticalprediction shown in Eq. (2). The dashed line shown in Fig. 3(b) was derived by linear least-square regression andused as a calibration line for viscosity measurement in the following section.
4.3 Viscosity Distribution Measurement Based on the calibration result, two-dimensional viscosity

measurement was performed in the Y-shaped microchannel (Fig. 2(b)). 40 wt% glycerol solution (2.8 mPa⋅s) andpure water (0.8 mPa⋅s) were injected from inlets A and B, respectively, at the same flow rate of 0.28 µL/min.
Polarization measurement was carried out with the same optical configuration and exposure time as the calibration
experiment. Figure 4(a) shows the two-dimensional viscosity distribution visualized at a spatial resolution of 1.4
× 1.4 µm2 by averaging over 2 × 2 pixels2. The measured viscosity was about ~2.7 mPa⋅s in the upper side of the
distribution and was ~0.7 mPa⋅s in the lower side. These results roughly match the viscosities of the two fluids
introduced from the corresponding inlets. Moreover, the viscosity gradually changed with y position near theinterface of the two fluids by interdiffusion. To obtain further insight into the measurement result, the spanwise
distributions at x = 144.4 µm and 1210.1µm were plotted (solid lines) and compared with the result of numericalcalculation (dashed lines) in Fig. 4(b). The vertical axis indicates the value normalized between 0−1 by theviscosity averaged over y = 20−120 µm and that over y = 400−500 µm. In numerical calculation, two-dimensional
diffusion equation was solved using the diffusion coefficient of glycerol solution (4.0 × 10-10 m2/s at 40 wt%[9]).
Since the actual flow rate was temporally varied due to the pulsation flow of the syringe pump, the position of
the interface between two fluids at x = 0 µm was given based on the experimental result. The calculated
concentration distribution was converted into a viscosity distribution based on the relationship between
glycerol concentration and viscosity which was obtained in preliminary experiment. From the measurement
result, the viscosity gradient around 130 µm ≤ y ≤ 230 µm is more moderate at x = 1210.1 µm than x = 144.4µm, which clearly indicates that the mass diffusion in the spanwise direction progressed along the fluid flow.
These results agreed well with the numerical calculation and confirmed the feasibility of the present method.
(b)

(a)

1 1.17 × 10 −2=+ 3.47Pµ

Fig. 3 (a) Comparison of the relationships between 1/μ and 1/P obtained for three different fluorescentmolecules (fluorescein, rhodamine B, and casein-FITC). Measurements were conducted by transmission
observation. (b) Calibration result obtained using casein-FITC by epi-fluorescent observation. The calibration
straight (dashed line) was used for two-dimensional viscosity measurement.

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(b)

(a)

Fig. 4 (a) Viscosity distribution in the Y-shaped microchannel measured by fluorescence polarization. (b)Comparison of spanwise distributions of normalized viscosity at x = 144.4 µm and 1210.1 µm between
fluorescence polarization experiment and numerical calculation.

5. CONCLUSIONSThe present study describes the development of a non-contact and two-dimensional fluid viscosity
measurement technique using fluorescence polarization and its application to the microchannel flow. In theselection of a fluorescent probe, a good correlation between the fluid viscosity and the polarization degree (P)and the largest P value were obtained in casein-FITC case. A calibration experiment using casein-FITC showedthat the reciprocal of P linearly increased with the reciprocal of viscosity in the range 0.8−2.8 mPa·s, which
agreed with the theoretical prediction. By applying this calibration result, a viscosity gradient formed by theinterdiffusion between co-flowing two fluids was clearly visualized in a microchannel at a spatial resolutionof 1.4 × 1.4 µm2 and agreed well with the numerical calculation. This result confirms the feasibility of thepresent technique and implies the future application to microscale analyses in chemical and biological fluids.

NOMENCLATURE
I||, I⊥P
P0

V

fluorescence intensities with parallel andperpendicular polarizations to the directionof excitation polarization (W/m2)
polarization degree ( - )intrinsic polarization ( - )θµτhydrodynamic volume of rotating unit (m3)angle between the direction of excitation
polarization and absorption moment (°)
fluid viscosity (Pa⋅s)
fluorescence lifetime (s)REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]

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