Polymeric Rheological Metamaterials
2.3. Rheological cloak
2.3.5.2. Experimental method
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Figure 2.3.23. Detailed configuration at microscale of (a) the designed rheological metamaterial cloak and (b) the fabricated rheological metamaterial cloak.
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microparticles with a radius of 3.2 μm (Red fluorescent, Fluoro-MaxTM, CAT.NO.RO300, LOT NO.42259, Thermo Scientific, United States) were dispersed in the water to visualize streamlines of fluid flow. The volumetric concentration of the microparticle/water solution was 0.3 μl/ml. TWEEN® 20 (Polyethylene glycol sorbitan monolaurate, Sigma Aldrich, United States), a nonionic detergent, was added to the microparticle/water solution with a volume concentration of 0.1 μ l/ml to help dispersion and avoid aggregation of the microparticles.
The total experimental set-up is represented in Fig. 2.3.24(a). Particle streamlines were observed by using an inverted fluorescence microscope (IX53, Olympus corporation, Japan). UPlanFL N 4x/0.13 PhP (Olympus corporation, Japan) was used as a microscope objective lens. A color CCD (charge-coupled device) camera (AcquCAM 23G, JNOpTIC corporation, Republic of Korea) was installed to the microscope with a low-magnification C-mount adapter (U-TV0.5XC, Olympus corporation, Japan). The adapter was necessary to take wider images when shooting the microchannel and flow streamlines.
Pressure-driven fluid flow was generated by using a N2 gas pressure pump with a pressure of 0.05 bar (5 kPa). Because the total length of the microchannel is set to 5 cm, this pressure condition is consistent with the simulation pressure condition applying 1 kPa to the geometries. A digital pressure gauge (DPG8001-60, OMEGA Engineering, United States) was used to control pressure values with a precision regulator (100LR, ControlAir Inc., United States) (Fig. 2.3.24(b)). After filling the syringe with the microparticle/water solution, the pressure exerted by the gas pump caused Poiseuille flow in the microchannel.
The streamlines of microparticles could be taken by properly controlling light exposure conditions of the CCD camera. The employed light exposure conditions in the experiment were 40.3 dB grain and 0.125 s exposure time.
Images of the particle streamlines were captured by using a commercial CCD camera- related program, JNOPTIC Capture 2.4 (JNOpTIC corporation, Republic of Korea). The captured images were processed to clearly show the streamlines by using Adobe Photoshop CS6 (Adobe Systems, United States). Color of the streamlines was changed from red to green, brightness and contrast of the images were optimized, and background noise was removed. Also, immobilized fluorescent microparticles that either stick to the microstructures or aggregate each other also removed from the taken images.
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Figure 2.3.24. Experimental set-up for observation of fluorescent microparticle streamlines. (a) A microscope with a fluid-filled syringe and a microfluidic device. (b) A pressure regulator set to apply 5 kPa.
80 2.3.5.3. Experimental results
Experimental realization of the rheological cloak was carried out with the fabricated metamaterial devices. The particle streamlines were captured and compared with the corresponding simulation results (Figs. 2.3.25). The simulated streamlines shown in Fig.
2.3.15(iii) were slightly enlarged and inserted into Fig. 2.3.25 to compare with the experimental results at the same magnification.
The captured streamlines of the bare case were observed to have a parallel shape in all regions without being bent or interrupted by something, like the simulation result of the bare case (Fig. 2.3.25(a)). In the obstacle case, a cylinder obstacle is placed at the center of the microchannel (Fig. 2.3.25(b)). Therefore, the streamlines were perturbed by a drag force generated on the surface of the obstacle. The generation of drag was also confirmed by the microparticles striking the obstacle surface. In Fig. 2.3.25(b), the red dotted line indicates the outline of the obstacle. By observing the streamlines near the red line, it was found that the green streamlines are densely formed along the outline of the obstacle. This phenomenon not only means that the presence of an object can be perceived from a rheological point of view, but also indicates that the overall flow rate of the microchannel is slowed by the drag generated when the fluid hits the obstacle surface. The isopressure lines could be expected from the streamlines since these two lines are mathematically orthogonal to each other. In the bare case, the pressure field is expected to be uniformly formed, but in the obstacle case, it is thought to be disturbed due to the drag on the obstacle surface.
This drag generation can be prevented by surrounding the obstacle with the rheological metamaterial cloak. (Fig. 2.3.25(c)). The streamlines outside the cloak remained in a parallel shape as if there is no obstacle at the center. The shape of streamlines in the cloaking shell is very similar to that in the simulation results. Also, unlike the obstacle case, it could be confirmed that the green particle streamlines are hardly formed on the red dotted line, the obstacle outline. This is experimental evidence that there is little drag on the obstacle surface. It is noticed from the slowly moving particles in the vicinity of the obstacle that the fluid momentum is successfully bypassed around the obstacle surface without generating drag. The drag-free space could be more clearly validated in the cloak- only case (Fig. 2.3.25(d)). In the central cloaked region, the microparticles flowed at about
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0.5 mm/s, which is much slower than the flow rate of the background.
In fact, if the cloaking function operates perfectly, the fluid force must be completely precluded from the central region, so there should be no microparticles in it. In development of transformation rheology, the creeping flow condition was assumed for the simplified form of the Navier-Stokes equations. In this process, the fluid inertia effect was completely excluded from the Navier-Stokes equations. Therefore, the metamaterial cloak could not bypass the fluid inertia force penetrating into the central region. In addition, the approximation made during the multilayer compartmentalization and the unit cell mapping might cause problems with the perfect cloaking performance to create a space with a zero flow rate. In summary, the zero flow rate in the cloaked region, which means a perfect drag- free space, is not feasible due to the fluid inertia and the approximate error in effective media.
Since the rheological metamaterial cloak is designed by the unit cell mapping method, its practical uses are limited. The biggest problem is that the effective viscosity should be increased to several times the base fluid viscosity to make the fluid viscosity greater than 1. In the lab scale experiment, this problem was solved by setting the effective viscosity of the background area to 2.78 mPa∙ s by mapping the microcylinders. Therefore, much advances of the viscosity control technique are essential since the rheological metamaterial cloak itself cannot be used alone. Research for producing arbitrary-shaped cloaks is also very meaningful to widen the application range of this study. Overall, this study presents a new direction for reducing a fluid resistant force through space distortion and is valuable as an original research.
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Figure 2.3.25. Observed streamlines (left), simulated streamlines (center), and microstructures in the experiment (right) for (a) the bare, (b) obstacle, (c) cloaked-obstacle, and (d) cloak-only cases.
83 2.3.6. Conclusions
In this section, a novel strategy to minimize drag was proposed by wrapping an obstacle in the rheological cloak. The Jacobian matrix required for cloaking was calculated based on transformation rheology. Numerical analysis was carried out by using the transformed viscosity tensor, and the cloaking behavior was confirmed theoretically. The design of the rheological metamaterial cloak was sequenced by using the multilayer method and the effective viscosity unit cells. The designed cloak was theoretically pre-tested and fabricated as a microfluidic device. It was experimentally confirmed from the captured streamlines that the fabricated metamaterial cloak can successfully guide fluid flow as designed and dramatically reduce the drag on the obstacle surface. The developed rheological cloak is anticipated to open up the new road to unprecedented control of fluid flow not found in nature. The rheological cloak can be used as an artificial architecture to detour natural meteorological or hydrological disasters. Furthermore, if this concept is extended to aerodynamics, drag-free operation of vehicles, such as aircrafts, automobiles, and submarines, will be possible dramatically increasing fuel efficiency.
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