The microscale systems
1.1 Microscale System
Microscale systems have gained significant attentions among the academia and industrialists because they offer many advantages and possess vast potentials. Microscale lab analysis is able to generate high throughput quickly and cheaply with small amount of sample and reagent (1), (2). Therefore it is especially desirable in the functional screening of combinatorial chemistry libraries, the examination of gene shuffling and evolution of proteins as well as the evaluation of pharmacokinetic response to drug candidates (3). A lab-on-a-chip device is a highly integrated microfluidic system that is capable of performing multiple tasks such as mixing, extraction, separation and detection (2). The notable usages of lab-on-a-chip devices are point-of-care diagnostics and environmental monitoring (3).
Microfluidic system as the name implies is in micrometer range. The small particle sizes and device dimensions result in a strictly laminar flow (low Reynold number), in which the main mass transport effect is molecular diffusion (4), (5). Microfluidic flows are categorized into pressure
driven flow and electrokinetic (electroosmotic or electrophoresis) driven flow (5). Figure 1 shows that a pressure driven flow exhibits parabolic velocity profile whereas an electrokinetic flow exhibits uniform velocity profile in the cross-section of the capillary column.
Micromixing is indispensible in a microfluidic system. Therefore a good model of micromixing process is vital in optimizing the design of a microfluidic system. There are two categories of micromixers: active and passive. Active mixer requires additional source of energy to induce mixing while passive mixing does not (2). Although active mixer allows more efficient mixing, passive mixer is usually preferred because it is relatively simpler in operation and is much cheaper (2), (1), (4).
This article aims at understanding the passive micromixing of Rhodamine 110 (R110) and water. A micromixer with an aspect ratio of 5 was used and the flow rates ratio was maintained at 1:1 throughout the experiment. Confocal miscrosopy was used to study how different flow rates and positions in the micromixers affect the mixing. With an appropriate diffusion coefficient, the 2D model proposed by Nguyen and Wu (4) was compared with the experimental results.
1.2 Analytical Model
Nguyen and Wu (4) simplified the 3D mixing system into 2D analytical model as depicted in Figure 2 based on the assumption that the velocity profile across the microchannel was uniform, resembling that of electrokinetic driven flow shown in Figure 1 (b). It was assumed that no diffusion flux exists in the direction normal to the plane of the flow direction and the channel width. These assumptions are only valid with mixing streams of similar viscosities and when the microchannel is flat with low aspect ratio (ratio of width to height).
where W is width of the slit, U is the average velocity of the flow, D is the diffusion coefficient and n is an arbitrary constant in the Fourier series with the value of the approximation of Fourier series approaching that of real value as (6).
The cosine term in Equation 1 corresponds to the concentration variation in the channel width while the exponential term corresponds to the whole trend of concentration distribution down the mcirochannel. The Peclet number and the dimensionless mixing length, x* were found to be the most important parameters in the convective-diffusion mixing (4). With equal flow rate, α = ½.
Further details of the model and its derivation can be found in..
There are a range of in situ analytical techniques that have been developed for the analysis of the fluid kinetic and dynamic within the microfluidic system such as confocal fluorescence microscopy, magnetic resonance imaging, fluorescent lifetime imaging microscopy (FLIM) and so on (7).
Confocal microscopy was used in the experiment. Compared to the conventional wide-field fluorescence microscopy, confocal microscopy is able to control the depth of field, eliminate or reduce the background noise (which degrades the image) (8), and is able to capture images of thick specimens at different depths (9). Confocal microscopy is especially useful in biological analysis as it provides the capacity to capture image of the living specimens with minimum sample preparation (9). Figure 4 shows the main components of confocal microscopy and the optical pathways within the microscope.
Contrary to the wide-field microscopy which illuminates the whole specimen with the incident light, confocal microscopy uses point illumination - only a single point is illuminated at a time, to avoid unwanted scattered light. The detector pinhole aperture acts as a filter to reject the returning rays that are not directly from the focal point (8), (10),(11). The ‘desirable' light rays are then detected by photomultiplier tube which transforms the light signal into electrical signal (9), (11).
In confocal microscopy, only one point is observed at any instant and the detected light from one illumination point represents only one pixel in the resulting image. Visualization of the whole image is done by image reconstruction in the computer pixel-by-pixel and line-by-line as the laser scans over the plane of interest with the resulting brightness corresponds to the relative intensity of the light ray detected (9), (11). A 512 x 512 pixels image is usually done at a frame rate of 0.1-30Hz.
The laser excitation source in confocal microscope is used as a source of incident light (photon). As the photon collides with a fluorescent molecule, it is absorbed and the molecule is excited into a higher energy state from the ground state. Since it is thermodynamically unstable, an excited molecule will inherently dissipate the energy to return to the ground state. Some of the energy is dissipated through collisions with the surrounding molecules and further reduction of energy is achieved by spontaneous emission of light with longer wavelength (11). The excitation and emission points on a specimen in confocal microscopy can be shifted by refocusing the objective lenses (8). In this experiment, blue incident light was used and the sample returned green fluorescence as depicted in .
3.1 Microchannel Fabrications
Early micromixers were made of silicon and glass. However, a number of polymeric micromixers have been successfully fabricated and tested (1). Polydimethylsiloxane (PDMS) microfluidic
prototyping has been increasingly used in microanalytical systems because the technology is widely accessible and the fabrication procedures are fast and cheap. The replica molding of PDMS can be employed in making valves, pumps, electrophoretic separation systems, gradient generation and many other processes. Furthermore, PDMS is optically transparent (produces no significant background signal at the desired wavelength) and its surface chemistry can be easily modified (12), (7).
The PDMS two-inlet micromixer used in the experiment was prepared by photolithographic fabrication based on the procedures outlined in (7). Figure 3 shows the schematic of the microfabrication procedures. However, some modifications were done here to match the requirements of confocal microscopy. Firstly, instead of the SU-8 photoresist that fluoresces, a non-flourescent material was used in step (a) of Figure 5. Secondly, PDMS mould was exposed to air plasma to produce a mechanically strong adhesion to the glass substrate.
3.2 Imaging with Confocal Microscopy
R110 and water were pumped at equal flow rates with pump syringe into the 8 cm x 500 µm x 100 µm microchannel. The flows were induced downstream by gravitational force. Images of the flows in the mcirochannel were obtained using Leica TCS SP5 confocal microscope in z-stack mode. Ten 512 x 512 resolution images were obtained at each position - 1 cm, 2.5 cm, 4 cm, 5 cm and 6.5 cm (from the inlet). The flow rates used were 0.05 ml/min and 0.02 ml/min. Due to some unidentified reasons, further reduction in the flow rate resulted in bubble formation in the microchannel, rendering the data at lower flow rate unusable. Data at flow rate = 0.005 ml/min used in the following analysis were provided by B. Le and V. Vishe.
Z-stack mode was used to obtain the concentration profile at different height of the microchannel to allow for 3D imaging. Time series option was not used because the system of interest was a steady-state system and thus the properties were expected to be constant at any point. Lambda series were not used as there were only two types of molecules in the system, one excitation source was sufficient to make meaningful data analysis.
MATLAB was used to analyze the data acquired from the experiment and to compare the experimental results with the analytical solutions outlined in Section 1.2. Figure 6 shows that the fluorescent dye was pump at the right hand side of the channel. Comparing the axis of Figure 6 and Figure 4, it was identified that the solutes of experiment (fluorescent dye) and that of the model were in opposite direction in y-axis. Therefore the analytical solution needed to be ‘flipped' in the MATLAB code (see attachment) to provide meaningful comparison.
The average of the 512 sample points across x-axis was used in the analysis. As for the y-axis, at each position, only a pixel range corresponds to the channel width was chosen. The pixel range was approximated with the optical data. Figure 7 shows an example of how pixel range was chosen for Q = 0.05 ml/min and x = 1 cm.
The normalized concentration of the flow rate was assumed to be equal to the normalized intensity.
As confocal microscopy is highly sensitive, some images taken in the experiment were unusable. The images taken at Q = 0.05 ml/min and x = 4 cm and the images taken at Q = 0.02 ml/min and x= 6.5 cm were found to be physically and theoretically impossible. Therefore they were omitted from the analysis.
The positions where confocal images were taken in the experiment were different from that obtained by B. Le and V. Vishe. The only position where valid images of all three flow rates were available was x= 2.5 cm. To allow for more comparisons, average values (for the flow Q = 0.005 ml/min) were taken between points. For example, data at x = 5 cm were obtained by averaging the data at x = 4.5 cm and x = 5.5 cm.
4.RESULTS AND DISCUSSIONS
4.1 R110 concentration profiles at a fixed position
Another value of D, 4.4 x 10-5 cm2/s, was found to be able to match the analytical and experimental values better at the R110-dominant side but not the water-dominant side. No value of D provides satisfactory matching for both sides better than D = 6.2 x 10-6 cm2/s.
From all the figures examined in this section, it can be clearly seen that with appropriate D the analytical solution suggested by Wu and Nguyen (4) was able to predict the behavior of micromixing of R110 and water in the experiment satisfactorily.
4.3 Additional information from mesh and surface concentration plots
Figure 16 shows the analytical concentration profiles in y-direction with respect to the length of the microchannel. It can be seen clearly that mixing is more pronounced with increasing x* and at lower flow rate. Therefore the 3D analytical trends agree with that of 2D ones found in Section 4.1 and 4.2.
Figure 16 Analytical concentration profile across x and y (a) Q = 0.05 ml/min and (b) Q = 0.005 ml/min. D=6.2 x 10-6 cm2/s.
Figure 17 to Figure 19 show the 3D concentration distributions at different positions in the microchannel. The surface plots (plan views) show the development of the mixing area from the initial interface of R110 and water at the inlet - ½ y*. As expected, with increasing x* and slower flow rate, the concentration distributions varied more significantly (indicating by more significant shape changes). The corresponding mixing areas (non- deep blue or deep red region in the color map) were larger and moved further away from the initial interface. Figure 17 Mesh and surface concentration plots of the flows in microchannel at (a) x=1 cm (b) x=2.5 cm and (c) x=5 cm.
5.1 Diffusion Coefficient
Gendron et al. (13) have revised the molecular diffusion coefficient of R110-water system to 4.4 x 10-6 cm2/s from typical 3.0 x 10-6 cm2/s. However, the diffusion coefficient found in the experiment was 6.2 x 10-6 cm2/s. This suggests that the effective diffusion coefficient in a convective-diffusive transport system is greater than the molecular diffusion coefficient (in a stationary system). The relationship of molecular and effective diffusion coefficient was explained in details by X. Chen and Y.C Lam (14).
As shown in Section 4.2, at Q = 0.005 ml/min and high x*, analytical solution with diffusion coefficient 4.4 x 10-6 cm2/s fits the experimental concentration profile better than 6.2 x 10-6 cm2/s in the fluorescence-dominant stream. This suggests that at low enough flow rate and high x*, the diffusion coefficient is reduced to that of molecular diffusion in the high-solute concentration stream. The reduction of diffusivity can be explained thermodynamically. In a broader concentration band, dimerization/aggregation effects become more prominent (13). Since the stream flow slowly, the convective effects become less prominent and the system behaves similar to that of a stationary system.
At Q=0.005 ml/min and x≥3.5, the 2D model proposed by Wu and Nguyen (4) was not able to predict the concentration profiles of the water-dominant stream even with a change of coefficient diffusion. Using variable diffusion coefficient (as a function of solute concentration) in the analytical solution may help to eliminate this deviation. If the situation persists, it is suggested that there are some limits associated with the model resulting from the assumptions or simplifications. These limits should be identified before it is used for microfluidic system design.
5.2 Concentration profile
In the inlet, R110 and water entered into the channel and the streams flow side-by-side with no diffusion across the interface. Since the flows were laminar with low Reynolds numbers, the mixing of the two fluids down the stream was governed by diffusion rather than convection (3). As the streams flowed down the channel, interdiffusion between the two fluids across the interface caused spanwise concentration variations, which were in the direction perpendicular to the flow. As shown in Section 4, the concentration variations were found to be position and flow rate dependent. The concentration variations band (or mixing zone) broadened at higher x* and slower flow rate.
These observations can be attributed to the residence time τ. Increasing τ allows better mixing as the molecules have more time for diffusion. τ is related to the flow rate by τ =L/U (4) and to the distance traversed by Einstein's equation of motion, x=(2Dτ)1/2 (15). A dimensionless parameter, κ was introduced in determining if good mixing is achieved where κ=x*/Pe (4). Higher κ indicates better mixing.
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