6th Micro and Nano Flows Conference
Atlanta,USA, 9-12 September 2018

Development of Viscosity Measurement Technique in Microchannel
Using Fluorescence Polarization MethodTomotaka NAKAGAWA1, Reiko KURIYAMA1*, Kazuya TATSUMI1, Kazuyoshi NAKABE1* Corresponding author: Tel.: +81-75-383-3608; Fax: +81-75-383-3608; Email: kuriyama@me.kyoto-u.ac.jp
1. Department of Mechanical Engineering and Science, Kyoto University, Kyoto, Japan

Keywords: Fluid viscosity measurement, Microscopy, Fluorescence polarization, Rotational Brownian motion
molecule. Since 1/P is proportional to T/V, the solution viscosity
can be obtained by measuring P if T,  and V are constant.

1. Introduction
Viscosity measurement in microfluidics and biology is an
important issue in terms of designing lab-on-a-chip devices andmeasuring the rheological characteristics and biological andchemical components of the fluid. For example, viscosity of bloodplasma changes with the change in its constituents and acts as anindex of biochemical reactions and the severity of diseases[1].
Therefore, viscosity measurement in microscale is expected tocontribute to elucidation of the pathology and diagnosis with low
sample volume requirements. Since such samples easily solidify, it
is desirable to measure the viscosity non-intrusively.
In this study, we propose a technique for microscale fluid viscosity
measurement based on polarization characteristics of fluorescencewhich is related to the rotational Brownian motion of fluorescentmolecules. Using this method, we can conduct a non-intrusive
measurement for the two-dimensional distribution of viscosity withhigh spatial resolution. This paper describes the measurement
technique and the results of measurement for the mass diffusion
between parallel flows of two solutions in the microchannel.
2. Methods
2.1 Measurement principle
When a fluorescent molecule dissolved in a solution is irradiatedby a linearly-polarized excitation light, the molecule is excited if thedirection of its absorption moment is close to the polarization
direction of the excitation light. The excited fluorescent molecule
emits fluorescence whose polarization direction is parallel to itsabsorption moment. The polarization degree, P, an index of thefluorescence polarization characteristics, is defined as,
P = ( I||  I  ) ( I||  I  )(1)where I|| and I represent the fluorescent intensities of thecomponents parallel and vertical to the polarization of excitation
light, respectively. If the viscosity of the solution is low, rotational
Brownian motion of the fluorescent molecules gets intense and thedirections of their absorption moments are largely randomized by thetime they emit fluorescence. As a result, the fluorescence isdepolarized and P becomes small. Perrin and Weber[2] theoreticallyderived the relationship between P and the viscosity, , expressed as,

 1 1   1 1   k BT     =     1+ P 3   P0 3   V (2)where P0 is the polarization degree of the molecule at stationary state,kB is Boltzmann constant, T is the solution temperature, isfluorescence lifetime, and V is the volume of the fluorescent

2.2 Experimental apparatus
Figure 1 shows a schematic of the optical system for fluorescencepolarization measurement. An inverted microscope (Olympus; IX73), an LED light source (Thorlabs; M490L4), and two highsensitivity cameras (Andor Zyla; 4.2 PLUS, 2048×2048 pixels2,16bit) were used. The light from the LED was linearly polarized bya polarizer, passed through a bandpass filter (Semrock; FF01482/35-25) and was loosely focused to the sample on the microscopestage. Sample solution was introduced into a microchannel, which
was composed of PDMS and a cover glass as shown in Fig. 2(a).
Casein-FITC conjugated (AAT Bioquest; molecular weight: 26000,
: 4ns, excitation wavelength: 494nm, emission wavelength:518nm) was dissolved in sample solution as a fluorescent probe atconcentration of 4.0×10-5mol/L according to the previous study[3].
The emitted fluorescence was collected by an objective lens(Olympus; LMPlanFL N, 10x), filtered through another bandpass
filter (Semrock; FF01-536/40-25) and split into two components (I||and I) by a polarizing prism. I|| and I were simultaneously
measured by camera 1 and camera 2, respectively. The exposure time
and the frame rate were set at 1s and 0.990fps, respectively, and 10images were captured by each camera. The temperature of the stage
was maintained at 30℃ ± 0.5℃ and monitored by thermocouples.
2.3 Numerical calculation
Three dimensional numerical computation was conducted for theflow and viscosity distribution in the microchannel using COMSOLMultiphysics (Ver. 4.3a: COMSOL Inc.). Mass and momentum
conservations equations of the flow and concentration conservation
equation for binary diffusion were solved based on finite element
method for steady-state laminar flow. The equation was discretizedand solved by employing Galerkin method and restarted GMRES(generalized minimum residual) solver. Figure 2(b) shows thecomputational domain. At the two inlets of the Y-shaped channel,
inlet flow with uniform velocity distribution for liquids of water and35wt% sucrose-water solution were applied. Neumann condition
was applied to the channel outlet. No-slip and zero concentration
flux boundary conditions were applied to the channel walls for flow
and mass concentration, respectively. Rectangular mesh was used in
the computation and the minimum and maximum mesh sizes were 7× 7 × 2.5 m3 and 10 × 10 × 2.5 m3, respectively. The number ofmeshes was 264,810. The effect of concentration on the viscosity,density, and diffusion coefficient of the sucrose solution wasconsidered in the computation. Density was calculated from thereference[4] and the diffusion coefficient was interpolated from themutual diffusion coefficient of sucrose and water[5].

6th Micro and Nano Flows Conference
Atlanta,USA, 9-12 September 2018
5. References

3. Results and Discussion
3.1 Calibration experiment
Calibration experiments between 1/P and 1/ were conducted using
seven sucrose solutions with different concentrations. The solution
viscosity was estimated from the relationship between the viscosity
and the sucrose concentration which was preliminarily obtainedusing a rheometer (Anton Paar; MCR301). Each solution was sent
into a straight microchannel by a syringe pump at constant flow rateof 0.56L/min and polarization measurement was carried out.
Distributions of P were calculated from the ten pairs of fluorescentimages and the distributions were averaged temporally and spatially.
Figure 3 shows the calibration result. Each plot shows the averaged
value of four measurement data and the error bar shows the 95%
confidence interval. As predicted in Eq. (2), 1/P increased linearlywith 1/The straight line was obtained by least squares regression
and used as a calibration line. The measurement uncertainty wasestimated to be 5~10% from the averaged value of the error bars.
3.2 Viscosity distribution measurement
Viscosity distribution measurement was performed in the Yshaped microchannel using the calibration result. Water (0.8mPa･s )and 35wt% sucrose solution (2.9mPa･s) were injected into each inletof the channel at flow rate of 0.6L/min by syringe pumps as shownin Fig. 2(a). The measurement region and the coordinate system arealso shown in the enlarged top view in Fig. 2(a).
Figure 4 shows the measurement result, which was obtained byaveraging five instantaneous P distributions. The two-dimensional
distribution of  is visualized at spatial resolution of 1.3m × 1.3mbased on 2×2 pixel binning. In Fig. 4, measurement result in y <50m and y > 150m agree with the viscosities of water and 35wt%
sucrose solution, respectively. The viscosity gradient is observed in50m < y < 150m, and the width of the diffusion layer gets wider
in the downstream. These results show that the viscosity distribution
influenced by the mass diffusion is successfully visualized.
To examine the validity of the present technique, the measurement
result in Fig. 4 is compared with that of numerical calculation. Figure
5 shows the spanwise distributions of the measured and calculated
viscositiesat x =10m and 900m. During the measurement, theposition of the solution interface temporally fluctuated because of
the pulsating flow generated by syringe pumps. To take thisphenomena into consideration in the numerical calculation, theactual positions of the solution interface were determined from themeasured instantaneous viscosity profiles and were used to estimate
the instant flow rates of the solutions. Viscosity distributions weresimulated with the estimated flow rates and then time-averaged.
From the experimental results in solid lines, the viscosity gradient isformed at the solution interface (50m < y < 150m) and thegradient becomes smaller in the downstream region due to the
diffusion of sucrose and water molecules in the spanwise direction.
These distributions quantitatively agree with the results of numericalcalculation in dashed lines, which confirms the validity of thepresent technique based on fluorescence polarization method for theviscosity distribution measurement in microscale.

[1] J. Harkness and R. B. Whittington, Rheologica Acta, 10, pp. 5560 (1971).
[2] G. Weber, Advances in Protein Chemistry, 8, pp.415-459 (1953).
[3] A. Suzuki, K. Tatsumi, S. Horii, R. Kuriyama, and K. Nakabe,Transactions of the JSME, ser. B. 83, pp.1-12 (2017).
[4] Circular C440, U. S. National Bureau of Standard.
[5] P. N. Henrion, Transactions of the Faraday Society, 60 (72),pp72-74 (1964).

(a)Figure 1. Optical system for viscosity measurement.
(b)Figure 2. (a) Top and cross-sectional views of Y-shaped microchannel. (b) Computational domain.

Figure 3. Relationship between 1/ and 1/P.

Figure 4. Two-dimensional distribution of viscosity measured in
Y-shaped microchannel.

4. Conclusions
A non-contact fluid viscosity measurement technique wasdeveloped using fluorescence polarization. The measurement
uncertainty was 5~10% based on the calibration result. The viscosity
distribution in the diffusion layer between two solutions wassuccessfully visualized at spatial resolution of 1.3m × 1.3m. The
measured viscosity gradient agreed well with the results ofcalculation, which confirmed the validity of the proposed method.

Figure 5. Spanwise distributions of viscosity obtained byfluorescence polarization method and numerical calculation.