Proceedings of the First Pacific Rim Thermal Engineering Conference, PRTEC
March 13-17, 2016, Hawaii's Big Island, USA

PRTEC-14717

LIGHT-TUNING OF HEAT TRANSFER PERFORMANCE FOR
LOW REYNOLDS NUMBER FLOW OF MICELLAR SOLUTION
Ken KAWAHARADA1*, Takafumi FUJII1, Takeshi ENYA1,
Kazuya TATSUMI1,2, Kazuyoshi NAKABE1,2
1

Dept. Mech. Engng. & Sci., Kyoto University, Nishikyo-ku, Kyoto 615-8540, Japan
2
Adv. Engng. Research Ctr. of Kyoto University

ABSTRACT
Viscoelastic fluids in low Reynolds number flow regime have the interesting and important potential for heattransfer performance in contrast to Newtonian fluids. To provide a high efficiency heat exchanger, theauthors are aiming at controlling the heat transfer rate actively, in particular, with photo-rheological fluids(PRFs), the properties of which can be tuned by light. In this study, ortho-methoxy cinnamic acid (OMCA)
known as a photo-sensitive molecule was added to an aqueous mixture of cetyl-tri-methyl-ammonium
bromide (CTAB) and sodium salicylate (NaSal) which is known for inducing the formation of wormlike
micelles. OMCA has trans- and cis-arrangements of substituents, and trans-OMCA irreversibly undergoes aphoto-isomerization to cis-OMCA upon exposure to UV light. This transformation alters the molecular
packing at the micellar interface and shortens wormlike micelles, so that the viscoelasticity of the aqueous
solution as a working fluid of heat transfer becomes weaker as the exposure time increases, i.e. trans-OMCA
decreases while cis-OMCA increases. As a result of the experiment, both mean heat transfer coefficient andpressure loss penalty were decreased with an increase in the exposure time. This change is supposed to becaused by weaker viscoelasticity of the aqueous solution that significantly influences flow structure, as
OMCA undergoes a photo-isomerization.

KEYWORDS: Viscoelasticity, Photo-Rheological Fluids, Micellar Solution, Heat Transfer Characteristics, Low
Reynolds Number Flow

1. INTRODUCTION
Surfactants, which are sometimes surrounded with counter-ions in aqueous solution, can assemble
themselves into various molecular associations, such as spherical micelles, wormlike micelles, vesicles, andlamellar structures. Among these aggregate structures, especially, micelles have attracted great interest in
fundamental research and practical application over the past few decades [1]. Under specific experimental
conditions, such as surfactant concentration, salinity, and solution temperature, small spherical micelles cangrow into long, thread-like, and flexible entangled wormlike micelles. The entanglement of such aggregates
results in remarkable viscoelastic properties. This is analogous to that of flexible polymers in aqueous
solution. The network of wormlike micelles, however, constantly breaks and recombines, which is different
from polymers’ behaviours. Moreover, recently, much attention has been paid to smart wormlike micelles,
whose macroscopic physicochemical properties undergo morphological changes in response to external
stimuli. Among various external stimuli, light irradiation presents superior advantage in small scale
application and easy operation. Thus, Photo-Rheological Fluids (PRFs), whose rheological properties arechanged by light, have gathered attention and been researched in some engineering fields [2, 3].
In recent years, industrial equipment is getting smaller and smaller, so in miniaturized channel devices, flow
becomes laminar in low Reynolds number regime and results in depressing heat transfer performance incomparison to turbulence flow. To solve this problem, there is one effective way to use a viscoelastic fluid as*Corresponding Author: kawaharada.ken.23v@st.kyoto-u.ac.jp

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a working fluid. Tatsumi et al. [4, 5] experimentally and also numerically investigated the flow and heattransfer characteristics in a millimeter-scale serpentine channel using a polymer solution as a viscoelastic
working fluid and showed that the polymer solution increases both heat transfer coefficients and wall friction
factors since the viscoelasticity of the fluid causes flow perturbations and generates unsteady secondary
flows. In order to enable the heat transfer enhancement more effectively, we propose to use an aqueous
solution of PRFs and control its heat transfer performance by light irradiation in response to the need of theoccasion and circumstances. This control can be achieved if the viscoelasticity of the fluid is changed byexternal light stimulus successfully.
In this study, we selected ortho-methoxy cinnamic acid (OMCA) as a photo-sensitive molecule which has
trans- and cis-arrangements of substituent. Trans-OMCA is added to an aqueous mixture of cetyl-tri-methylammonium bromide (CTAB) and sodium salicylate (NaSal) which are known for inducing the formation of
wormlike micelles [6]. Trans-OMCA irreversibly undergoes a photo-isomerization to cis-OMCA upon
exposure to UV light. We prepared also CTAB/NaSal/OMCA solutions of several determinate trans- and cisOMCA mixing ratio for reference, and compared the rheological properties and heat transfer characteristics
of both the former irradiated trans-OMCA solution and the latter different mixing ratio solution toinvestigate the effectiveness of light irradiation.

2. EXPERIMENTAL APPALATUS AND METHODS
2.1 Rheological Measurements of CTAB/NaSal/OMCA Solutions CTAB, NaSal, and OMCA arecommercially available, and their mixed solution was stirred for 1 day at 20°C. The concentration of
CTAB/NaSal/OMCA solution was set to be 1.0wt% CTAB, 0.2wt% NaSal, and 0.2wt% OMCA in highpurity H2O. For light-triggered trans-to-cis transition, the solution samples, each of which weighs 300g, wereplaced in a plastic tumbler and irradiated with a 100W mercury lamp (Olympus U-LH100HGAPO) understirring with a magnetic stirrer at 200rpm for a desired time. The top of the tumbler was covered with cling
film to avoid evaporation of the solution, while the bottom and side of the tumbler were covered withaluminum foil to reflect the light back into the tumbler. The distance between the sample and lamp was fixedat 75mm.
To confirm isomerisation, hydrogen nuclear magnetic resonance (1H NMR) spectra of the solutions before
and after 24-hour UV irradiation were recorded on a magnetic resonance spectrometer (Bruker NMR
spectrometer, DPX-400). The measurements were carried out at room temperature. All samples including
0.2wt% OMCA only and were prepared using D2O as the solvent instead of high-purity H2O. Spectral
analysis of the solutions decanting into a quartz cell was also carried out using a spectrophotometer(SHIMADZU UV-Visible spectrometer, UV-2450) at room temperature. The solutions were diluted to theconcentration of 0.01mM OMCA solutions before the analysis since the absorbance at the original
concentration was too high in the UV-Vis spectrophotometric analysis. Rheological properties were
determined using a rheometer (ANTON PAAR, MCR301) equipped with a cone plate, 50mm in diam. The
measurement temperature was controlled at 30°C. Dynamic frequency spectra of elastic and viscous moduli,G′ and G", were determined in the linear regimes of each sample by dynamic stress-sweep measurements.

2.2 Heat Transfer and Pressure Loss Measurements Figure 1 shows the schematic diagram anddimensions of a test section for the experiments. The test section forming a serpentine channel had a squarecross section of 5mm × 5mm and consisted of 10 semicircle units connected periodically in the streamwise
direction. The inner and outer radii of curvature of the semicircle unit were Ri = 5mm and Ro = 10mm,
respectively. The length along the serpentine channel, L, was ca. 470mm. The wall of the test section wasmade of copper blocks isothermally heated up by constant temperature water circulation. The working fluid
was supplied from the pressurized tank to the channel, and the mass of the fluid flowing from the outlet wasweighed on an electronic scale to measure the mass flow rate, . The bulk mean temperatures of the fluid at
the inlet and outlet of the test section, Tb,i and Tb,o, were calculated using the fluid temperatures measured ateach corresponding location and the fully developed velocity profile of a square channel. A single pair ofsheath thermocouples was used to measure the inlet fluid temperature while the outlet fluid temperature was2

PRTEC-14717
measured by 5 K-type bare thermocouples located evenly in the height direction at the center of the channel
width direction. The wall temperature, Tw, was an arithmetic-averaging temperatures measured at 4 locations
where thermocouples were affixed in copper wall blocks.
An average Nusselt number, Num, was defined as follows:
Num 

hm Dh
k


mcp
T  Tb,i  ln w
 hm 
As
Tw  Tb,o (1)where Dh is the hydraulic diameter of the channel and hm is the average heat transfer coefficient calculated
by applying the bulk mean temperature and mass flow rate. As is the total area of heat transfer target wall. cp
and k indicate the specific heat capacity at constant pressure and thermal conductivity of the fluid,
respectively. Fanning’s friction factor, f, and modified Reynolds number, Re*, were, respectively, defined as
andin order to evaluate pressure loss penalty. A
and B are the geometrical constants. The values, n and K, are referred to the ones used to express shear
viscosity, μ, as a function of shear rate, (μ). Both values were calculated from the results of static
viscosity measurement using a rheometer.

Fig. 1 Apparatus of serpentine channel for heat transfer experiment.

3. RESULTS AND DISCUSSION
3.1 PRFs Properties Figure 2 (a) shows dynamic frequency spectra of CTAB/NaSal/OMCA solutions
depending on the UV irradiation time. The data of G′ and G″ are plotted against oscillatory shear frequency,
. In the case without UV irradiation (i.e. 100% trans-OMCA), G′ is smaller than G" in the lower frequency
region. With the increase of frequency, both G′ and G" increase and then intersect with each other at a
certain frequency. After that, G′ continues to increase and exceeds G" as the frequency further increases,
implying that the elastic property of the solution is more dominant than the viscous one in the higher
frequency region. G′ tends to eventually level off and reach an apparent plateau in its increase, while G"
reaches a minimum and then increases slightly again. This trend follows the typical Maxwell model,
indicative of the formation of viscoelastic wormlike micelles. With the increase of UV irradiation time, up to
8 hours, however, the dynamic frequency spectra deviate gradually from the manner of Maxwell model. The
spectra in the case of every 10wt% different trans- and cis-OMCA mixing ratio under the constant OMCA
concentration were also measured and compared with the irradiated trans-OMCA solution data. The case of
8 hour irradiation time, for instance, exhibits a considerably similar trend of the mixing solution of 20wt%
trans- and 80wt% cis-OMCA. Static shear viscosity μ as the function of shear rate is shown in Fig. 2 (b). μdecreases with an increase in , showing shear-thinning behavior which typically characterizes viscoelastic
fluids. μ also decreases as a whole with an increase in the irradiation time. Following these obtained results,
the mixing ratio of trans-OMCA is decreased with an increase in the UV irradiation time. Trans-OMCA

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PRTEC-14717
having a straight structure can promote the growth of micelles due to easy insertion to surfactant molecule
aggregates and mitigate interfacial charge, while cis-OMCA cannot do because of its crooked structure. Thus,
the decrease of trans-OMCA mixing ratio structurally weakens viscoelastic characteristics of the solution
and leads to the degradation of viscoelastic wormlike micelles, depending on the degree of the exposure to
UV light. The band spectrum of OMCA solution measured with the spectrophotometer changes remarkably,
indicating the trans-to-cis transition of OMCA. 1H NMR spectra revealing that 24 hour UV irradiation changes
the 100% trans-OMCA solution to the cis-OMCA one including 4.5% trans-OMCA supplies evidence ofanother kind for the transition.

(a)

(b)

Fig. 2 Rheograms for CTAB/NaSal/OMCA Solutions before and after the UV irradiation: (a) dynamic
frequency spectra exhibiting elastic G′ and viscous G" moduli as the function of oscillatory frequency ω; (b)static shear rheology plotting the shear viscosity μ against the shear rate .

3.2 Heat Transfer Characteristics The flow conditions of heat transfer experiment are listed in Table 1
where the modified Reynolds number range of the solution having different irradiation time (0h ~ 8h) is Re* =1.2 ~ 17. Weissenberg number Wi representing the influence of stress relaxation phenomena was also tabulated
there for reference. Figure 3 (a) and (b) shows, respectively, the average Nusselt number Num and Fanning’s
friction factor f of CTAB/NaSal/OMCA solution plotted against Re* at 4 different irradiation time conditions.
The dashed and solid lines drawn in Fig. 3 (b), respectively, indicate the theoretically-obtained friction factor ofsteady flow in a square duct [7] and the modified one considering temperature dependence of viscosity for thesolution after 8-hour UV irradiation. The maxima of both Num and f are the case without UV irradiation in all
Re* region. With an increase in the UV irradiation time, the both data are decreased as a whole. This trend
indicates that the elastic property of the solution without UV irradiation causes unsteady flow and enhances heattransfer while the property after UV irradiation is mitigated gradually, approaching the steady flow case withsimilar friction factors to the ones obtained theoretically. Temperature fluctuations of the solution measured withthermocouples at the channel exit correspondingly subsides with the UV irradiation time, indicating that the flow
becomes unfluctuating. In addition to this experiment, we are examining another PRF including an azobenzene derivative as a reversible photo-isomerization molecule instead of OMCA. We expect this to control
heat transfer performance with light, similar to OMCA but more effectively.
Table 1 Flow conditions of heat transfer experiment.
Solution
CNO-0hCNO-2h
CNO-4h
CNO-8hirradiation time (h)248Um (mm/s)
36 - 130
43 - 100
31 - 90
34 - 864Re*
1.2 - 17
2.2 - 16
1.9 - 14
2.1 - 12

Wi
71 - 840
49 - 260
19 - 180
7.5 - 120

PRTEC-14717

(a)

(b)

Fig. 3 UV irradiation time dependence of average Nusselt Number Num and Fanning’s friction factor f: (a)Num vs. Re*; (b) f vs. Re*.

4. CONCLUSIONS
Rheological Properties: The viscoelasticity of 100% trans-OMCA solution is mitigated gradually with anincrease in the UV irradiation time, which is caused mainly by the morphological transition from transOMCA to cis-OMCA accompanying the decrease of wormlike micelles.
Flow and Heat Transfer Characteristics: The average Nusselt number and Fanning’s friction factor of
CTAB/NaSal/OMCA solution are both conspicuously decreased by the UV irradiation which weakens theviscoelastic property of the solution and then causes the transition from unsteady flow to steady flow. Ifother chemical substances of reversible photo-isomerization are applied, the heat transfer performance can beeffectively controlled by light irradiation.

ACKNOWLEDGEMENT
The present study in part is supported by Grant-in-Aids of Japan Society for Promotion of Science. The
authors deeply appreciate suitable instruction and suggestion in synthesizing some chemical materials andoperating 1H NMR spectroscopy by Professor S. Kimura and Assistant Professor M. Omae of Kyoto
University, and also valuable discussion with Professor D. Baigle and his Laboratory’s research fellows of
the Chemical Department, Ecole Normale Supérieure, Paris.

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