Herein, we describe a procedure that employs microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. Through calibration, distribution of concentration gradient can be derived from the micro-schlieren image.
In this paper, we introduce the use of microscale schlieren technique to measure mixing inhomogeneity in a microfluidic device. The microscale schlieren system is constructed from a Hoffman modulation contrast microscope, which provides easy access to the rear focal plane of the objective lens, by removing the slit plate and replacing the modulator with a knife-edge. The working principle of microscale schlieren technique relies on detecting light deflection caused by variation of refractive index1-3. The deflected light either escapes or is obstructed by the knife-edge to produce a bright or a dark band, respectively. If the refractive index of the mixture varies linearly with its composition, the local change in light intensity in the image plane is proportional to the concentration gradient normal to the optical axis. The micro-schlieren image gives a two-dimensional projection of the disturbed light produced by three-dimensional inhomogeneity.
To accomplish quantitative analysis, we describe a calibration procedure that mixes two fluids in a T-microchannel. We carry out a numerical simulation to obtain the concentration gradient in the T-microchannel that correlates closely with the corresponding micro-schlieren image. By comparison, a relationship between the grayscale readouts of the micro-schlieren image and the concentration gradients presented in a microfluidic device is established. Using this relationship, we are able to analyze the mixing inhomogeneity from associate micro-schlieren image and demonstrate the capability of microscale schlieren technique with measurements in a microfluidic oscillator4. For optically transparent fluids, microscale schlieren technique is an attractive diagnostic tool to provide instantaneous full-field information that retains the three-dimensional features of the mixing process.
Fluid mixing is an important issue that is found in many industrial processes and biological systems. With the emergence of microfluidics, mixing in microscale has brought much attention due to its challenge in diffusion domination among the mass transport mechanisms. Since designing an effective micromixer required quantitative validation, several measuring methods were developed5-7. Nevertheless, the three-dimensional structure, commonly found in efficient micromixers5, demands a more accurate representation of the concentration field that the common measuring techniques fail to deliver. Due to the limit of viewing angle8 or reaction kinetics6, the aforementioned methods may produce misleading results that do not correctly account for the homogeneity of the mixture.
For optically transparent fluids mixing in optically transparent microstructures, microscale schlieren technique3,9-14 provides an attractive alternative to analyze mixing inhomogeneity. In the past, microscale schlieren technique has been mostly used to visualize compressible flow9-13,15 or phase gradient16. Microscale schlieren technique benefits from both a simple optical layout and high sensitivity and enables not only the non-invasive investigation of specific flow feature that causes optical disturbance but is well suited for use in assessing mixing. In this paper, we construct the microscale schlieren system by inserting a knife-edge in the back focal plane of the objective of a microscope, describe a calibration procedure to realize quantitative analysis, and report a validation measurement in a microfluidic oscillator4. To implement measurements, the working fluids are properly selected so that the refractive index of the mixed fluids varies linearly with the composition, and the thickness of the target microfluidic device is identical to the one used in calibration. Besides species concentration, microscale schlieren technique can be extended to measure the gradient of other scalar quantity that is linearly correlated to the index of refraction, such as temperature or salinity.
1. Fabrication of Microfluidic Device
2. Experimental Setup
3. Calibration
4. Quantitation
The grayscale ratio I/I0 under different Reynolds number for both positive and negative gradients of mass fraction is shown (Figure 2) with a symmetrical band appearing in the middle of the T-microchannel. At low Reynolds number, the tail of the schlieren band is expanded and blurred due to the dispersion across the mixing interface. As the Reynolds number increases, the diffusion length shortens leading to a narrower band. At different downstream locations, the variations of the intensity change ΔI/I0 along the cross-stream direction are depicted quantitatively (Figure 3). The results from the calibration process are represented (Figure 4A and 4B). The relationship between I/I0 and ∂w/∂y is linear and independent of the Reynolds number. From the regression analysis, I/I0 = -110∂w/∂y + 1.03 for ∂w/∂y > 0 and I/I0 = -160∂w/∂y + 0.83 for ∂w/∂y < 0, ∂w/∂y is in µm-1. The relative uncertainties are ±3.8% and ±3.2% in Figure 4A and 4B, respectively. The detection limit is reached where the data points level out. It is noted that the deviation in slopes of the positive and negative gradients is not uncommon3. Using these equations, the variation of mass fraction gradient with time in a microfluidic oscillator4 is seen (Figure 5). The mixing interface is deflected in the cavity region and flow instability commences. This video figure clearly reveals the oscillating nature of the flow in the microfluidic oscillator and demonstrates the capability of the microscale schlieren technique to capture the time-resolved full-field concentration gradient in a microfluidic device.
Figure 1. Schematic of the optical setup. The orientation of the knife-edge produces a dark band with a positive gradient of refractive index. The light deflects toward the direction of increasing refractive index. Because the objective lens inverts the image, blocking the –y region shields the distorted light and produces a dark band.
Figure 2. Ratio of grayscale readouts for mixing in the T-microchannel under different flow configuration. Positive and negative gradients result in dark and bright bands, respectively. As the Reynolds number increases, the band becomes more concentrated.
Figure 3. The variation of the intensity change along the cross-stream direction for both positive and negative gradients. Re = 1 and Re = 5.
Figure 4. Relationship between the gradient of mass fraction and the grayscale ratio. For both positive and negative gradients, grayscale ratio varies linearly with the mass fraction gradient.
Figure 5 (Video Figure). Evolution of mass fraction gradient in a microfluidic oscillator at Re = 250. The mixing characteristic through flow oscillation is successfully captured by microscale schlieren technique.
For fluidic mixing in a microfluidic device, the microscale schlieren technique is able to measure the magnitude of concentration gradient through quantifying change in light intensity. Because the principle of this technique relies on detecting the alternation of light propagation, the working fluids and the microfluidic device have to be transparent to the incident light. In addition, the protocol requires a linear relationship between the refractive index of the solution and its composition so that preliminary assessment of the working fluids is essential. Besides aqueous ethanol solution demonstrated herein, microscale schlieren technique is successfully applied to measure salinity gradient29 and solutocapillary convection30. For accurate measurements, aperture range, illumination level, exposure time, objective lens and microchannel depth used in the calibration procedure have to be identical to those used in the quantitation procedure. Moreover, the depth of correlation of the objective lens has to be sufficiently large to cover the entire depth of the microfluidic device.
The calibration process of mixing in the T-microchannel is the most critical step in the accurate quantitation of microscale schlieren technique. For successful implementation of the proposed method, users need to align the tube connection properly, exploit a small syringe or pneumatics for fluid delivery to avoid flow oscillation23, use a LED light source to reduce excess heat, conduct the calibration procedure at low Reynolds numbers24, and place the microfluidic device in focus to eliminate higher-order optical effects31. The lowest measurable gradient (bright pattern, ∂w/∂y < 0) is linked to the dynamic range of the camera, whereas the highest measurable gradient (dark pattern, ∂w/∂y > 0) is reached when the knife-edge completely blocks the deflected light. To detect a wide range of concentration gradient, a high ISO value is advantageous as long as underexposure or overexposure does not occur. The detection limit, below which the micro schlieren system is unable to discern, depends on the minimal intensity change that the camera is able to resolve. The minimal intensity change is constrained by the degree of noise and the levels of tonal gradation. Hence, a high-sensitivity camera with great pixel depth is desired for low-signal application.
The significance of microscale schlieren technique is two folds; on one hand, it enables unsteady full-field measurements in real time with a simple optical configuration. On the other hand, it is non-invasive so that no alien substance is introduced to disturb the flow field. Because micro-schlieren technique produces two-dimensional projection of the three-dimensional inhomogeneity in a microfluidic device, complex mixing phenomenon that remains veiled by existing methods can be clearly seen. Future applications of this technique include quantifying concentration gradients during an electrochemical process or determining nutrient gradient to study microbial chemotaxis in a micro flow environment.
The authors have nothing to disclose.
This work was supported by the Ministry of Science and Technology of Taiwan under Grant Number 101-2221-E-002-064-MY3.
Permanent Epoxy Negative Photoresist | MicroChem | SU-8 2150 | |
single side polished silicon wafer | Light Technology | S4W1PP5SABUP1 | p-type, diameter: 100±0.5 mm, thickness: 525 ±25 mm, orientation: (1 0 0) |
syringe pump | kdScientific | kds210 | |
syringe, i.e. 10 ml | Terumo | SS-10L2138 | |
Hoffman modulation contrast microscope | Leica Microsystems | DM IL LED | |
5X objective lens | Leica Microsystems | N PLAN | NA = 0.12 |
knife-edge | custom made part | ||
camera, i.e. high speed | Integrated Design Tools | NX7-S1 | |
C-mount adapter HC 0.63x | Leica Microsystems | 541537 | |
camera operating software | Integrated Design Tools | MotionPro X Studio 2.02.01 | |
polydimethylsiloxane (PDMS) | Dow Corning | Sylgard-184 silicone elastomer kit | |
Teflon tubing, i.e. O.D. x I.D. 1/16 in. x 0.031 in. | Supelco | 58700-U | |
micro glass slide | Matsunami Glass | S2215 | |
hot plate | Yeong-Shin | HP-303DN | |
distilled water, i.e. HPLC grade | Alps Chemicals | ||
ethyl alcohol, i.e. reagent grade | Nihon Shiyaku Reagent | EA448652 | |
image processing software | Mathworks | MATLAB R2009a | |
computational fluid dynamics package | ESI group | CFD-ACE+ 2008 |