ABSTRACT Title of Document: AN EXPERIMENTAL INVESTIGATION ON SOLUTE NATURAL CONVECTION IN A VERTICAL HELE-SHAW CELL Dana Ehyaei, Doctor of Philosophy, 2014 Directed By: Professor Kenneth T. Kiger Department of Mechanical Engineering An experimental analogue was developed to investigate instability propagation of a multicomponent fluid system in porous media. This type of flow pattern has been observed in a broad range of applications from oil enhanced recovery to geological storage of byproduct materials such as CO2. The main focus of this study is on the engineering instrumentation and implementation of experimental measurement techniques in microfluidic systems, more specifically in a thin-gap device that is used as a model for a saturated porous medium. Initially, quantitative in-plane velocity measurement by means of particle image velocimetry (PIV) within thin gap devices subject to a large depth-of-focus and Poiseuille flow conditions is studied extensively. The temporal velocity measurement is then coupled with a simultaneous concentration measurement by means of LED induced fluorescence (LIF). The primary obstacles to a reliable quantitative PIV measurement are due to the effects of the inherent wall-normal velocity gradient and the inertial migration of particles in the wall-normal direction. After quantification of both effects, a novel measurement technique is proposed to make quantitative velocity measurement in microfluidic systems and narrow devices by manipulating the particles to their equilibrium position through inertial induced migration. This single camera technique is significantly simpler and cheaper to apply comparing to the existing multi-camera systems as well as micro-PIV implementations, which are restricted to a small field- of-view. A demonstration of a reliable PIV measurement under appropriate parameter design is then discussed for diffusive Rayleigh-Bénard convection in a Hele Shaw cell. For concentration measurements, the main difficulty of making LIF quantitative is its highly sensitive response to the experimental settings due to extreme sensitivity of the fluorescence to the environment factors and illumination conditions. A calibration procedure is required prior to performing any meaningful quantitative measurements. Additionally, the effect of photobleaching can be significant, which impairs the measurement as will be discussed later in further detail. Eventually after calibration and correction methods for velocity and concentration measurement techniques, a simultaneous PIV/LIF is performed to quantify the behavior of instability fingers in the developed experimental system. AN EXPERIMENTAL INVESTIGATION ON SOLUTE NATURAL CONVECTION IN A VERTICAL HELE-SHAW By Dana Ehyaei Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park, in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2014 Advisory Committee: Professor Kenneth T. Kiger, Chair Assistant Professor Amir Riaz Professor James Duncan Professor Michael Zachariah Professor Srinivasa Raghavan © Copyright by Dana Ehyaei 2014 ii Table of Contents Table of Contents .......................................................................................................... ii List of Tables ............................................................................................................... iii List of Figures .............................................................................................................. iv Chapter 1: Introduction to the problem ......................................................................... 1 Problem statement ..................................................................................................... 1 Literature review ....................................................................................................... 5 Chapter 2: Velocity measurement in narrow channels ............................................... 11 Introduction ............................................................................................................. 11 Experimental and simulation procedure ................................................................. 23 Result and discussion .............................................................................................. 31 Effect of non-uniform velocity with uniform tracer concentration .................... 31 Effect of non-uniform tracer concentration ........................................................ 39 Interpretation of Roudet et al. (2011) ................................................................. 45 Possible solutions ................................................................................................ 46 Chapter 3: Rayleigh-Benard convection in Hele Shaw cell........................................ 49 Problem statement ................................................................................................... 49 Design parameters ................................................................................................... 55 Chapter 4: Quantitative concentration measurement in Narrow Channels ................ 58 Experimental setup.................................................................................................. 58 Caliberation procedure ............................................................................................ 66 Data Reduction........................................................................................................ 69 Chapter 5: Simulteneous Velocity and Concentration measurements of Rayleigh Benard convection in Hele Shaw ............................................................................... 75 Result and discussion .............................................................................................. 75 Chapter 6: Final Thoughts ......................................................................................... 94 Conclusion .............................................................................................................. 94 Ideas for future ........................................................................................................ 98 Appendix A ............................................................................................................... 100 Bibliography ............................................................................................................. 101 iii List of Tables Table 4.1 diffusion coefficient for different species present in the fluid mixture in water ........................................................................................................................... 61 Table 5.1 experimental parameters ............................................................................. 79 iv List of Figures Figure 1.1 enhanced oil recovery using CO2 ............................................................... 4 Figure 1.2 a schematic of CO2 solution trapping in saline aquifers and the effect of cap rock ........................................................................................................................ 4 Figure 1.3 a schematic of a reservoir ........................................................................... 6 Figure 1.4 the density of methanol and ethylene-glycol (MEG) mixed with water, for MEH solutions with 61% (weight percent) ethylene-glycol ........................................ 9 Figure 2.1 sample of correlation map for one interrogation window of a unidirectional flow (figure from synthetic images with number of particles of NI=9) ..................... 14 Figure 2.2 schematic of a volumetrically illuminated narrow channel, illustrating the variability in velocity due to random location of particles across the gap ................. 15 Figure 2.3 (a) micro-PIV implementations; in its simplest form it includes a volumetric illumination of the test setup, a microscope and a suitable objective lens to capture the motion of markers within a narrow region of the device (δz) (b) a schematic of defined depth-of-field and depth-of-correlation in micro-PIV implementations ......................................................................................................... 19 Figure 2.4 the physical system of microsphere migration within a channel .............. 21 Figure 2.5 three different criteria for velocity profile and particle concentration distribution across the gap ......................................................................................... 23 Figure 2.6 a schematic of the single component flow setup for large field of view PIV ..................................................................................................................................... 26 Figure 2.7 (a), (b), (c) are samples of correlation maps while (d) is the calculated ensemble average correlation map ............................................................................. 29 Figure 2.8 middle slice of the correlation map for different particle sizes from simulation in comparison with autocorrelation of particle images used in experiments ..................................................................................................................................... 29 Figure 2.9 synthetic particles (a) dτ=4 [px], (b) experimental images, (c) dτ=10 [px] 30 Figure 2.10 (a) Probability distribution function of streamwise displacements for a Poiseuille flow, sampled across the wall-normal direction. (b) autocorrelation of v experimental particle images (c) convolution of the autocorrelation with flow displacement PDF ....................................................................................................... 33 Figure 2.11 ensemble average of correlation maps for a uniformly sampled Poiseuille flow (particle image size, = 4 pixels, maximum displacement ∆xm = 25 pixels) measured in experiments at x’ =5×10-6, and given by the convolution of the particle image autocorrelation function with the theoretical distribution shown in figure 10.2a. Displacements are normalized by the peak centerline displacement ......................... 33 Figure 2.12 PIV interrogation correlation function as a function of particle image size for a) large centerline displacements (∆xm=15 pixels) and b) small displacements (∆xm =1 pixel). c) PIV displacement estimate scaled with centerline velocity, (∆xpiv/∆xm) as a function of particle image size d and maximum displacement, ∆xm, for uniform tracer particle concentration ....................................................................................... 37 Figure 2.13 Valid detection probability for the displacement correlation peak as a function of the effective number of particle images within an interrogation window (NIFIF∆). Note that three expected integer peak locations are tracked near the maximum displacement (no sub-pixel interpolation), and compared to the results of a uniform displacement (shown in red) ........................................................................ 39 Figure 2.14 normalized averaged correlation functions, depicting their evolution due to combined effects of velocity gradient and particle concentration inhomogeneity, (a) experimental, (b) simulation ...................................................................................... 41 Figure 2.15 a) Streamwise alignment of tracer particles for large x’ values. The effect of the directional arrangement of tracer particles on the experimental correlation peak in: b) stream- wise direction, c) lateral direction ....................................................... 44 Figure 2.16 illustration of hydrodynamic focusing .................................................... 48 Figure 3.1 a schematic of the experimental setup for velocity measurements in Hele shaw cell. The pressure tanks were designed to hold a deformable cup inside them to hold the seeded fluids. Details of the setup can be found in appendix A .................. 50 Figure 3.2 schematic of the test setup for diffusive Rayleigh-Bénard convection a) (MEG 61 wt% is shown in green and water in the bottom layer is transparent). b) Image of convective fingering instability, 1000 seconds after isolation ................... 52 vi Figure 3.3 (a) instantaneous velocity field, (b) a more focused view of velocity field and (c) vorticity field for the diffusive Rayleigh-Bénard convection with large depth of field PIV ( , ) .................................................................... 54 Figure 3.4 (a) interrogation window size as a function of Hele-Shaw gap thickness (b) required development length needed during filling to ensure Case III conditions as a function of Hele-Shaw gap thickness and particle size (Rec= 2.3). Current operating conditions are noted by the red star. Dashed line indicates d > 0.1 δ ....................... 56 Figure 4.1 a Jablonski diagram and corresponding spectra, demonstrating the fluorescence process: initial creation of an excited state by absorption and subsequent emission of fluorescence at a higher wavelength ...................................................... 60 Figure 4.2 (a) spectral characteristic of the LED (blue light; λmax=462 nm), (b) fluorescence properties of the dye (λmax-excitation=490 nm) ........................................ 62 Figure 4.3 schematic of the experimental setup from above. Camera 1 is used for PIV measurements, and camera 2 records the florescence while the optical filter extracts the pumping light ....................................................................................................... 63 Figure 4.4 the long-pass optical filter performance, cut-on of 515 nm ..................... 63 Figure 4.5 a schematic of the experimental setup ....................................................... 64 Figure 4.6 snapshot images of the field of view at t=1000 s. image a from camera 1 is used for velocity measurements while the second image is used for fluorescence .... 65 Figure 4.7 effective fluorescence for Fluorescein in water ......................................... 68 Figure 4.8 effective fluorescence for Fluorescein in MEG 61% ................................ 68 Figure 4.9 different fluorescence behavior of the dye in different solvents ............... 69 Figure 4.10 (a) averaged offset image (cell filled with pure water) ̅ (b) averaged maximum intensity image (MEG and uniform dye concentration of 0.05 (mg/ml)); ̅ (c) raw instability image ⃗ 0) ................................................. 71 Figure 4.11 a sample of measured concentration field at t*=1000 seconds ................ 74 Figure 4.12 (a) mean concentration over region 2; ̅, (b) a focused view of ̅ demonstrating its periodic behavior, (c) mean concentration over region 3 ̅ ......... 73 Figure 5.1 a focused view of the Hele shaw cell cross section. The microspheres are manipulated to a known location across the gap before reaching to the field of view ..................................................................................................................................... 75 vii Figure 5.2 calculated velocity and concentration from processing recorded images from camera 1 and 2 respectively ............................................................................... 77 Figure 5.3 mapping raw images from camera 1 to corresponding images taken from camera 2 after transformation ..................................................................................... 78 Figure 5.4 Rayleigh-Bénard flow evolution obtained from LIF concentration measurements ........................................................................................................ 80-86 Figure 5.4 interface tracking by thresholding (cf=0.8) ................................................ 88 Figure 5.5 temporal fingers generation profile at the interface (a) (0 15 pixels), the errors consistently give a bias of 30%, returning a value close to the gap-averaged value of 2∆xm/3. While this consistency is an improvement, we note that this requires relatively large particles in comparison to the window size, forcing one to sacrifice precision in the sub-pixel interpolation (which has an optimal near dτ = 2 pixel (Westerweel 2000 [26]) and increases in proportion to the particle size) or to push the particle concentrations to unreasonably high levels due small interrogation windows (i.e. a 2 pixel particle diameter would require an interrogation window of no greater than 6 pixels in width). It should be noted that the latter could be effectively achieved in steady flows through the use of ensemble correlation. In addition to the particle-size bias error, measurements resulting from a single interrogation will have random correlation noise due to a small effective image particle density, NIFIF∆. The effective image density consists of NI, which is the 39 particle image density, FI represents the loss of correlation pairs due to in-plane translation, and F∆ represents the loss of correlation due to in-plane gradients. The random correlation component is a well-documented and important effect in traditional thin-light sheet PIV, and has led to the standard guideline of maintaining an average of 8 to 10 particle images in an interrogation region to ensure a yield of 95% valid vectors (Kean and Adrian 1992 [27]; Adrian and Westerweel 2010 [11]). The highly non-uniform velocity PDF greatly increases this requirement if one is to ensure that the interrogation peak will repeatedly occur at a known position (either near the maximum displacement or perhaps at a known biased value, as was shown to be the case in figure 2.12). The numerical simulations were used to quantify the likelihood of a valid detection from a single interrogation depending on the effective image density, NIFIF∆, the results of which are shown for the case of ∆xm=15 pixels and dτ= 4 pixels in figure 2.13. The most likely peak location for these conditions was 1 pixel less than the peak displacement (∆xm – 1) due to the particle size bias effects mentioned above (note that no sub-pixel interpolation was used). Even so, including approximately 100 particles within the interrogation window produced only an 83% probability of making measurement that would provide even a biased estimate. If one were to consider the neighboring displacements of ∆xm and (∆xm – 2) also as a “valid” measurement, this would increase the likelihood to approximately 94% (black curve). This does not give one confidence in making a very reliable measurement under these conditions, as one must sacrifice considerable spatial resolution to attain such a high effective seeding density. These simulations are also optimistic, in that effects of sensor noise and particle non-uniformities are not 40 accounted for, which would further decrease the probability of a valid measurement. Results for simulation of a uniform displacement for all particles are shown in the figure for comparison. Figure 2.13 Valid detection probability for the displacement correlation peak as a function of the effective number of particle images within an interrogation window (NIFIF∆). Note that three expected integer peak locations are tracked near the maximum displacement (no sub- pixel interpolation), and compared to the results of a uniform displacement (shown in red). 2.3.2 Effect of non-uniform tracer concentration As mention in the introduction, the correlation peak is also influenced by any non-uniform distribution of tracer particles across the gap, which is expected to occur gradually throughout the flow evolution. Indeed, in small depth-of-focus systems, its influence has been used to extract both velocity and concentration profiles (Nguyen et al. 2011). The prior work by Roudet et al. (2011) delineated an expected evolution time required for the particles to migrate to their stable equilibrium positions, Tm = 2.66 zeq δ 3/V Rec a 3. However, this was shown to be only a rough indication, as the net influence of the particle concentration field on the correlation is the true measure 41 of how it will influence the PIV interrogation. To observe this effect experimentally and numerically, tests were conducted to interrogate the flow under different development stages, over a range of 10-6 < x’< 10-1 (Note that x’ and Tm are related by t/Tm = 27δx’/2 zeq). Fig 2.14 shows the results of the experiments, alongside results produced from synthetic images of tracer particles migrating according to the theory of Ho and Leal (1974). Starting from an effectively homogeneous concentration distribution (x’<10-6), a broad correlation function is found with a maximum value corresponding to the centerline velocity across the gap, as discussed in the previous section. The correlation function starts to evolve as particles begin to migrate across the channel, providing a biased sampling of the velocity distribution and distorting the correlation function relative to the uniformly seeded condition. A second peak emerges as the particles rapidly move away from the wall, becoming clearly visible around x’ ~ O[10-4], exceeding the peak corresponding to the centerline velocity by x’ >10-3. As the particles subsequently migrate from the center plane in later times, the two peaks eventually merge into a single sharp and symmetric peak (x’ ~ 10-2). This occurs when the majority of the tracers have reached their equilibrium position located close zeq/δ = 0.3. Downstream of this position, the correlation remains unchanged, with a peak value that would predict Upiv = 0.64Vmax. 42 Figure 2.14 normalized averaged correlation functions, depicting their evolution due to combined effects of velocity gradient and particle concentration inhomogeneity, (a) experimental, (b) simulation Starting from an effectively homogeneous concentration distribution (x’<10-6), a broad correlation function is found with a maximum value corresponding to the centerline velocity across the gap, as discussed in the previous section. The correlation function starts to evolve as particles begin to migrate across the channel, 43 providing a biased sampling of the velocity distribution and distorting the correlation function relative to the uniformly seeded condition. A second peak emerges as the particles rapidly move away from the wall, becoming clearly visible around x’ ~ O[10-4], exceeding the peak corresponding to the centerline velocity by x’ >10-3. As the particles subsequently migrate from the center plane in later times, the two peaks eventually merge into a single sharp and symmetric peak (x’ ~ 10-2). This occurs when the majority of the tracers have reached their equilibrium position located close zeq/δ = 0.3. Downstream of this position, the correlation remains unchanged, with a peak value that would predict Upiv = 0.64Vmax. Although a similar evolution was observed in both the experimental and simulation correlation functions ,only approximate matching of x’ values was possible, most likely due to a small amount of migration occurring prior to entry into the Hele-Shaw cell. Multiple particle interactions could also have a significant effect, but were neglected in the simulations. The analysis of Ho and Leal (1987) gives the condition that multiple particle effects on particle migration can typically be neglected provided that Ф < (a/δ)3/2, where Ф is the particle volume fraction. One example of particle-particle interaction effects that can occur for long development lengths and higher particle concentration is illustrated in figure 2.15, where the particles have aligned themselves into ordered chains or clusters of particles in the flow direction, similar to that reported by Matas et al (2004) [28]. In this case, neighboring interaction between clusters of particles in the same plane resulted in the formation of linear streamwise-aligned particle arrays. Matas et al (2004) showed that these clusters occur more frequently with larger Reynolds number, and likely result 44 from a reversed streamlines created by the disturbance flow due to the leading particle. The rearrangement of the tracer particles did not affect the location of the correlation peak, but broadened the low amplitude tails of the distribution along the streamwise direction due to the non-random anisotropic ordering of the particles (figure 2.15). The chains themselves were found to be unstable and slowly diffuse once the uniform streaming flow was stopped). 45 Figure 2.15 (a) streamwise alignment of tracer particles for large x’ values. The effect of the directional arrangement of tracer particles on the experimental correlation peak in: (b) stream-wise direction, (c) lateral direction 46 2.3.3 Interpretation of findings of Roudet et al. (2011) In the work of Roudet et al. (2011), they showed empirically for their Case II test conditions that a PIV interrogation returned a velocity magnitude equal to the average gap velocity (Upiv = V = 2Vmax/3) when the channel Reynolds number is small (Rec < 80). Our findings are not in agreement with this as a universal conclusion, as one would expect based solely on the velocity PDF that the PIV interrogation would return an expected value close to the centerline velocity. The discussion in the previous section would suggest that although migration may not have completed for their flow conditions, perhaps the evolution was sufficient for the secondary correlation peak to surpass the amplitude produced by the centerline flow. The experiments and simulations in the prior section suggest that this should occur for x’ > 10-3, which would correspond to a flow time t/Tm > 0.045 (taking V = x/t). This condition was satisfied only for the largest Rec cases and largest particle sizes used in Roudet et al. experiments, rendering this cause unlikely for the smaller Rec conditions. This is also in agreement with their suggested speculations. The question remains, then, as to what caused the unexpected result of Upiv = V? We contend that this was most likely due to the particle size bias summarized in figure 2.12. For Roudet et al. (2011) PIV measurements, they stated an image size of 3 pixels with an interrogation window of 32 pixels. They also state that the interframe timing was adjusted such that the maximum displacements were between 1/20 and 1/8 of an interrogation cell 47 (1.6 < ∆xm< 4 pixels, assuming the displacements were those observed from the interrogations, which were shown to be the gap-averaged displacements). Examining figure 12.2, this produces a bias error that is 25 to 33%, giving an expected measurement result of 1.0 < Upiv/V < 1.13, which is quite close to their observed values of ~1.05 shown in their figure 6. Thus we would suggest that their observations are actually the result of a particle image size bias effect as explained in section 2.3.1. 2.3.3 Possible Solutions The presence of multiple and shifting peaks within the expected correlation function due to particle migration makes the probability of choosing a consistent and meaningful displacement for Case II conditions unlikely as a generalized testing point. The exception to this would be for carefully controlled transient conditions where one can ensure that measurements are stopped prior to significant migration, as was the case for the measurements by Roudet et al. (2011). Even so, one would have to restrict the maximum displacement or use quite large particle images relative to the interrogation window size (as noted in section 3.1) to remain in a consistent measurement region due to particle image size effects. Both of these restrictions reduce the effective dynamic range for the measurement, either through the integer displacement or uncertainty in the subpixel estimation (i.e. for the case of Roudet et al. (2011), their peak displacement of 1.5 to 4 pixels with a 0.1 pixel uncertainty in the subpixel interpolation gives an effective dynamic range for a single measurement of 40:1 to 15:1). 48 This leaves Case I and Case III as more reliable solutions for quantitative measurement. Case I is likely difficult to achieve in many flow conditions, as it only applies to early times when t < (δ/2)2/ν and the parabolic velocity profile is far from being established. This leaves Case III as the most general condition to provide a reliable measurement, as it removes the disadvantages incurred by the wall-normal velocity gradient and having an unknown and changing sampling of the velocity distribution due to particle migration. The challenges with Case III, however, are in how to manipulate the particles into their equilibrium positions prior to making the intended measurements. The simplest case would be to extend the geometry of the thin-gap flow cell to ensure sufficient evolution such that the particles have reached their segregated state, corresponding to x’ ~ O[10-2]. We have conducted experiments where the Hele-Shaw cell was designed with an extra length section to provide sufficient development length during filling to ensure full segregation, as will be presented in chapter 3. Alternatively, if a longer filling length could not be accommodated, generating an oscillatory flow within the gap could be used to drive the particles toward their equilibrium position by using numerous short strokes in alternating directions; provided the Womersley number was kept small enough to ensure a quasi-steady parabolic profile (Wo < 1).   fWo 22 2.21 Where δ is the gap thickness, f is the strokes frequency in cycles and ν is the kinematic viscosity of the fluid. Finally, work of Mielnik et al. (2006) [29] could also be adapted for this purpose, who introduced selective seeding of thin particle “sheets” into their channel 49 by manipulating the flow through a series of T-junction inflow channels, confining the particle laden flow to a specific cross-gap location. While this has the added complication of a complex inflow supply manifold, it has the advantage of being able to seed a particle sheet to almost any cross-stream location, obviating the need for a significant development region. All of these solutions would allow for use of what is known about standard thin-sheet PIV measurement, and hence take advantage of the demonstrably improved accuracy and resolution that is possible under uniform displacement conditions. However, since these measurements rely on the fluid flow profile and particle position across the gap to be known a priori, they become insufficient in cases of more complicated micro-fluidic devices with 3-dimensional flow fields. In these cases, performing a large field of view measurement becomes impossible unless local fluid flow and tracer particle concentration distribution across the gap are available. On the other hand, there are a variety of techniques such as confocal scanning microscopy or astagmatism that are capable of measuring a 3- dimensional velocity field over much smaller regions (Cierpka et al. 2011) [30]. Figure 2.16 principle of hydrodynamic focusing 50 Chapter 3: Rayleigh-Bénard convection in a Hele-Shaw cell, PIV demonstration 3.1 Problem Statement and experimental setup This section presents a sample measurement utilizing Case III conditions that were generated through the manipulation of the filling conditions to ensure particle migration to their equilibrium position prior to measurement. The flow of interest is the onset of solutal driven Rayleigh-Bénard convection in a Hele-Shaw cell, which is used as an analog for similar behavior in porous media in the context of carbon dioxide sequestration in saline aquifers. The initial conditions for the experiment consist of two stably stratified stationary fluids of different density, which exhibit the property that the resulting mixture has a greater density than either two of the original fluids. As the two fluids undergo diffusive mixing at the interface, a thin layer develops that is gravitationally unstable, resulting in the onset of convective plumes and an increase in the bulk mixing of the two layers (figure 3.1). The experimental setup consists of the Hele shaw cell similar to the previous setup with the same gap thickness (δ=127 µm). The U-shaped shim was replaced with a closed rectangular shim. A disadvantage of a pump is the pulse, which disturbs the filling process. In this phase of the project, the syringe pump was also replaced with pressure cups to fill the cell smoothly and provide a sharp, steady interface during filling procedure. Both tanks were fed with the same compressor, but the pressure at each tank could be slightly adjusted using separate pressure regulators for each tank. 51 Figure 3.1 a schematic of the experimental setup for velocity measurements in Hele shaw cell. The pressure tanks were designed to hold a deformable cup inside them to hold the seeded fluids. Details of the setup can be found in appendix A. The initial conditions for the experiment consist of two stably stratified stationary fluids of different density, which exhibit the property that the resulting mixture has a greater density than either two of the original fluids. As the two fluids undergo diffusive mixing at the interface, a thin layer develops that is gravitationally unstable, resulting in the onset of convective plumes and an increase in the bulk mixing of the two layers. It should be noted that for the analog between the Hele- Shaw cell and porous media to be valid, the density driven currents must maintain a parabolic velocity profile across the gap. Fernandez et al. (2002) [31] reported that this condition will be met if the Rayleigh number based on the gap thickness is restricted to values Raδ< O[100], where ∆𝜌 is the driving density difference, g is the acceleration due to gravity, D is the effective binary diffusivity of the two fluids, and ν is the effective dynamic viscosity of the mixture. 52    D gRa 12 3 3.1 The working fluids are methanol/ethylene-glycol (MEG) and water, which has been used in similar studies in porous media (Neufeld et al. 2010 [5]). The example shown in figure 3.2 used a MEG solution that was 61% Methanol by weight (𝜌MEG = 972.5 kg/m3, µMEG = 0.003 kg/m.s) mixing with water (𝜌H20 = 997.0 kg/m 3, µH2O = 0.001 kg/m.s), producing a maximum specific gravity of approximately 1.01. The cell was designed with an extended streamwise development length (L = 300 mm) to ensure that the tracer particles present within the mixtures have migrated into their known stable position before reaching to the measurement window. The difference in viscosity between the two streams necessitated different flow rates to produce a similar pressure drop in each liquid layer, which was required to maintain a straight interface between the two fluids. The filling process and measurement location were such that the particles migrated to their equilibrium wall-normal position, which was checked by sampling the correlation function of a PIV interrogation during the filling process and confirming that a single symmetric correlation function was obtained (see figure 2.14). Although particle streaks formed in the more fully evolved water layer, these quickly dissipated into a random field as the particles gradually settled during onset of convection and during the cross-stream motion of the convective fingers. 53 Figure 3.2 schematic of the test setup for diffusive Rayleigh-Bénard convection (a) (MEG 61 wt% is shown in green and water in the bottom layer is transparent), (b) Image of convective fingering instability, 1000 seconds after isolation Measurements were then performed after stopping the flow and isolating the cell from surroundings by a combination of toggle/check valves. Images were acquired with the same camera and light system used in the earlier experiments. The magnification was set M0=0.35 (38 pixel/mm), with an effective particle image size measured to be approximately 5 pixels. A decreasing size_multipass interrogation was applied, used in conjunction with adaptive correlation windowing (Wieneke and Pfeiffer, 2010 [32]), starting from 48x48 and reducing to 24x24, with a 75% overlap (Note that the adaptive masking gives a minimum interrogation width of effectively 54 12 pixels in high shear regions). No ensemble averaging was used, since this flow is inherently unsteady and spatially non-uniform. A sample measurement of the convection under these conditions is illustrated in figure 3.3. From this figure, it can be seen that the convective plumes are approximately 2 mm in width, setting a desired spatial resolution of approximately 0.25 mm, with peak velocities on the order of 60 µm/s in the measurement plane. 55 Figure 3.3 (a) instantaneous velocity field, (b) a more focused view of velocity field and c) vorticity field for the diffusive Rayleigh-Bénard convection with large depth of field PIV ( , ) 30 µm 56 3.2 Design parameters The execution of such an experiment requires a careful tradeoff in the test cell design and particle selection in order that Case III conditions can be attained. First and foremost is determination of a suitable gap thickness, as once the working fluids have been selected, this sets the gap Rayleigh number (Raδ) and the length scales of the convective plumes. These considerations are summarized in figure 3.4, which bounds the limits on the desired interrogation window size, DI, as a function of the gap length, δ. The first constraint is the assumption of Raδ < 100, which ensures that one is well within the recommended region for Poiseuille flow to be maintained within the unstably stratified gap (Fenandez et al., 2002 [33]). (Here we have taken mixture values for the properties of µ=0.002 kg/m.s, ∆𝜌= 10 kg/m3, and D=1.2x10-9 m2/s). A second constraint is provided by requiring DI to be smaller than the relevant length scale of the flow, which we specifically take to be 4 0MDI  3.2 In the current problem, the initial wavelength is well predicted by linear stability theory to be (Riaz, et al., 2006 [8]): 207.0 24   g D  3.3 Giving: rr I gd DM d D    0 07.0 6 3.4 when accounting for the image magnification and expressing it in terms of image pixels. A third constraint is given by the minimum particle image density needed to have a high probability of a successful interrogation, typically assumed to be NI > 10. For the Case III conditions, an upper bound on the concentration that can be used 57 exists due to the fact that all of the particles must be eventually packed into two parallel planes of the channel. Assuming the particles should remain separated by at least 5 diameters (s = 5d) to prevent significant hydrodynamic interactions gives the constraint: rr I d sMd D 010 3.5 The current experimental conditions are indicated by the symbol (red star) in figure 3.4, indicating that not much margin remains for improvement of the measurement conditions when using the current working fluids. Figure 3.4 (a) interrogation window size as a function of Hele-Shaw gap thickness (b) required development length needed during filling to ensure Case III conditions as a function of Hele-Shaw gap thickness and particle size (Rec= 2.3). Current operating conditions are noted by the red star. Dashed line indicates d > 0.1δ 58 The particles then need to be selected such that they reach their terminal migration position within a reasonable length, which is controlled by the Reynolds during filling and (a/δ)3. Using the condition that L/X > 0.01 from figure 2.14 for complete migration, the required flow development lengths are given in Fig 10b. This gives a required length of: ca L Re36.0 3     3.6 For the more conservative conditions of the flow in the MEG layer, the current conditions (d = 2a = 15 µm, δ = 127 µm, Rec = 2.3) give a required development length of L = 303 mm. The lower viscosity of the water layer requires a higher Reynolds number to produce the same pressure drop, leading to a development length of 46 mm. Going to a smaller particle size would lead to a much larger development length (e.g. using half the diameter would require a channel length of 2.4 m), while going larger would require particles that are rapidly becoming a significant fraction of the gap width. 59 Chapter 4: Quantitative concentration measurement in narrow channels 4.1 Experimental Setup The motivation for this part of the project is to quantify the temporal concentration field of Rayleigh-Bénard convection in a Hele-Shaw cell and eventually couple it with velocity measurement to estimate the total flux density of MEG in water. Backhaus et al. (2011) [6] developed an experimental model with a different fluid system and performed optical shadowgraph to determine the wave number selection, the time scale, the finger width, and the mass transport rate. Hartline et al (1970) [33] applied pH-indicator method to visualize the convection pattern of thermal convection in a Hele-Shaw cell and confirmed the critical Rayleigh number for the onset of convection to be 4π2. There are various other measurement techniques that have been used previously to quantify the scalar transport within multi-component fluidic systems (See Walker et al. 1987 [34]). Measurement of concentration based on induced fluorescence is a common technique that was also used in this study to quantify the concentration profile within the system. For instance, Koochesfahani et al (1986) [35] used LIF to investigate the entrainment and mixing in reacting and nonreacting turbulent mixing layers or the work Ferrier et al (1993) [36] that discusses the use of the measurement technique and methods of corrections to study plumes in stratified fluids in details. 60 In a general LIF experiment (Laser/LED induced Fluorescence), the dye is excited by an illumination light source whose wavelength closely matches the excitation frequency of the dye. The intensity of light emitted from a dyed region of flow is proportional to the intensity of excitation energy and to the concentration of dye. If the excitation energy is locally uniform, then the emitted light intensity will be linearly related to the dye concentration. By performing a calibration procedure as will be discussed in the following section, the emitted light intensity can be directly converted to dye concentration. To perform a reliable concentration measurement by means of LIF, multiple steps needs to be taken to overcome the challenges inherent to fluorescence. These practical steps are the subject of this chapter. The challenges include:  Maintaining linear relationship between intensity of emitted light and concentration  Perform correction methods due to non-uniformity of illumination across the field of view and background intensity variations  Sensitivity to environment effects (solvent effect)  Photobleaching due to exposure to light The fluorescence process consists of three stages: First, a photon is absorbed by the fluorophore, increasing its energy to an excited state. Second, the fluorophore remains in this excited state for a finite period, called the fluorescent lifetime, which lasts typically 1–10 ns (very small relative to the flow time scales O(10 seconds)). Third, the fluorophore releases a photon of energy, and returns to its ground state (figure 4.1). The released photon is then detected by a sensor, a CCD camera detector in this case. Due to energy dissipation during the excited state lifetime (non-radiative 61 relaxation), the energy of this photon is lower, and therefore of longer wavelength, than the excitation photon (for detail discussions on fluorescence, refer to Principles of fluorescence spectroscopy by J. Lakowicsz [37] or Practical fluorescence by G. Guilbault [38]). The energy difference is related to the Stokes shift, which is the wavelength difference between the absorption and emission maximum: absorptionemissionstokes   4.1 Figure 4.1 a Jablonski diagram and corresponding spectra, demonstrating the fluorescence process: initial creation of an excited state by absorption and subsequent emission of fluorescence at a higher wavelength Although LIF has been widely used for determining the scalar transport and mixing of multicomponent fluid systems, there are also drawbacks to this technique that necessitates a well calibrated measurement setup. Relevant to this work is photobleaching of fluorescent molecules that is a process by which exposure to excitation light chemically alters a fluorophore rendering it non-fluorescent. The rate of photobleaching of a fluorescent dye depends on the photon flux, and may be caused by large excitation light intensities over short periods or lower intensities over 62 long periods. Photobleaching is a common problem in fluorescence-based experiments like this study where the fluorophore remains excited for long durations. The experimental test setup was modified to be able to extract temporal velocity as well as concentration fields simultaneously. However, this chapter focuses on calibration procedure for concentration measurement while the coupling of the concentration and velocity measurements will be the subject of the next chapter. In addition to polystyrene microspheres that were used as tracer particles for velocity measurement in both of the fluids, a known amount of Fluorescein sodium salt (C20H10Na2O5 Sigma-Aldrich F6377) was added to the fluid reservoir containing the mixture of Ethylene glycol and Methanol (MEG), to be used as tracers for concentration measurements. The diffusivity of the dye into water is close to the diffusivity of Ethylene glycol in water, while the diffusivity of Methanol in water is 4 times larger. Molecular diffusivity (𝒟) of the different species and the dye in water is listed in table 4.1. Diffusion Coefficient for the Different Species Ethylene glycol [39] 0.37 × 10-9 (m2/s) Methanol [40] 2 × 10-9 (m2/s) Fluorescein [41] 0.52 × 10-9 (m2/s) Table 4.1 diffusion coefficient for different species present in the fluid mixture in water To excite the fluorescence tracers, the halogen light was replaced by a high- power LED illuminator (IL-106X-Blue, HARDsoft) in continuous mode. Spectral 63 characteristics of the light source and the dye are presented in figure 4.2. A second camera was also added to the system to record the magnitude of fluorescence from a similar field-of-view as of camera 1 (figure 4.3). The cameras and the lenses used in the setup were identical (Imager pro X 4M, sensor size = 2048 x 2048 pixels, dr = 7.4 µm pixel size) and recorded images of about 75 x 75 mm region (M0~0.2), using 105 mm lenses (f1# = 8 and f2# =2.6; Exposure time1=0.05s and Exposure time2=0.1s). The depth of field of the system, δz was set larger than the channel gap spacing as before so that the tracer particles across the entire gap were mapped identically in the image plane (δz1 = 4 mm, δz2 = 0.5 mm). An optical long-pass filter with a transition wavelength of 515 nm was inserted close to camera 2 in its optical axis to separate the fluorescence emission photons that form the final image on detector 2 from the excitation light and scattering particles (MELLES GRIOT 03FCG083-rectangular 50.8×50.8 mm2) (figure 4.3). As explained in previous chapters, polystyrene particles are manipulated into the equilibrium position before they reach to the desired field of view. The experiments were conducted using a vertically oriented Hele-Shaw cell similar to previous setup but the all-round supporting frame that was found vulnerable to buckling was replaced by two edge-to-edge supporting clamps, holding the fixture on the top and bottom (figure 4.5). The two rectangular tempered glass plates were also replaced by longer pieces (12.7 x 610 x 127 mm3) to ensure full segregation of tracer particles in the field of view (L=330 mm) and also to avoid regions of any possible non uniform behavior at the outlets (refer to appendix A). The spacer shim was pressed between the plates by the designed aluminum clamps, with a bolt spacing 64 of 8 cm along the top and bottom edges to ensure a uniform compression and a constant gap thickness (δ=0.127 m; the bolts were fastened by a torque wrench by a value of 1700 N-mm). Sample images recorded simultaneously by the two cameras, are presented in figure 4.6. Figure 4.2 a) Spectral characteristic of the LED (blue light; λmax=462 nm), b) Fluorescence properties of the dye (λmax-excitation=490 nm) Figure 4.3 Schematic of the experimental setup from above. Camera 1 is used for PIV measurements, and camera 2 records the florescence while the optical filter extracts the pumping light 65 Figure 4.4 the long-pass optical filter performance, cut-on of 515 nm 66 Figure 4.5 a schematic of the experimental setup 67 Figure 4.6 Snapshot images of the field of view at t=1000 s. Image a from camera 1 is used for velocity measurements while the second image is used for fluorescence 68 4.2 Calibration procedure Details of the execution of a reliable velocity measurement is covered in the previous chapters, however extraction of temporal concentration field from raw images recorded from the second camera requires a calibration procedure to quantitatively relate the intensity and absolute concentration field. If attenuation of the illumination light within the cell is negligible and the concentration of the dye is low enough that there is no saturation (both fluorescence and detector), then the detected fluorescence would be proportional to intensity of the excitation illumination and local concentration of the fluorophore (Walker et al 1987 [34]). ),( )( ),( ni txcxItxI nf  4.2 In this equation, x (x1,x2) represents both the position in the object plane and image plane (since a mapping presumably exists between object and image plane). The excitation power distribution field generated by the LED is shown as ),( txI i . The detected fluorescence ),( txI f is related to Ii and the average dye concentration distributed across the gap of the cell by the proportionality factor α.   0 21 ),,,(1 dztzxxcc 4.3 Initially, a series of calibration experiments were performed to determine the range of linear response of fluorescence intensity to its concentration variations. A known concentration of the dye was added to 200 ml of deionized water and the well stirred mixture was then pumped through the cell. The recorded images from camera 2 were averaged over the entire field-of-view after background subtraction and then were temporally averaged over 1000 images recorded at 1Hz. For all the tests the cell 69 and LED were kept fixed to the optic table carrying the experimental setup and the LED power was also kept constant. It can be observed from figure 4.7 that the relationship between the effective fluorescence and the flourophore concentration under conditions described above becomes nonlinear at around 0.5 (mg/ml). In order to be able to use equation 1, the concentration of the dye needs to be smaller than this critical value. It should be noted that a larger f# and smaller exposure time was used in the calibration test to avoid any possible camera saturation (f#4 and Exposure time2=0.03 s). However a smaller f# and a larger exposure time were used to obtain a greater dynamic range with a conservative concentration value of 0.05 (mg/ml) for the rest of the experiments (f#2.6 and Exposure time2=0.1 ms). As explained in previous chapters, the initial condition for the experiment consists of stably stratified stationary fluid columns of MEG at the top and water at the bottom. Both of the fluids are seeded with microspheres for velocity measurements, and additionally MEG is also seeded with dye tracers with a concentration of 0.05 (mg/ml) for which the fluorescence shows a linear behavior in its vicinity (figures 4.7 and 4.8). As the dye tracers diffuse into water from the MEG column, the fluorescence is expected to deviate due to the change in solvent. A series of dilution tests were performed by providing different aqueous MEG mixtures, pumping them into the cell and recording the fluorescence as described in previous calibration tests (figure 4.9). For instance, the data point describing 0.2 aqueous MEG mixture is the result of mixing 40 g MEG from the original batch of MEG with a dye concentration of 0.05 (mg/ml) and 160 gr deionized water; the resultant mixture then contains a dye concentration of 0.01 (mg/ml). Due to dependency of fluorescence to 70 environmental factors such as viscosity, a linear function was found to be a poor estimate of the fluorescence behavior in the aqueous MEG mixture ( µMEG = 0.003 kg/m.s and µwater = 0.001 kg/m.s; effective fluorescence in water is 0.95 of fluorescence in MEG; black square symbol). It should be noted that temperature fluctuation was less than 1oc during the entire measurement period. Figure 4.7 effective fluorescence for Fluorescein in water Figure 4.8 effective fluorescence for Fluorescein in MEG 61% 71 Figure 4.9 different fluorescence behavior of the dye in different solvents 4.3 Data Reduction Following the data acquisition, the images need to be processed to obtain concentration information based on the detected intensity field from camera 2. The experimental procedure starts with performing the instability test with the appropriate design conditions as was explained in previous chapters and recording the intensity field; Iraw ( ⃗ , t). To take into account for the image background intensity, a series of images were then recorded from the same field of view and similar conditions to the initial test after flushing the cell with deionized water multiple times; Ioffset ( ⃗, t) . In the final step, the distribution of light intensity across the field of view was quantified by obtaining 1000 consecutive images when the cell was filled with only MEG and uniform dye concentration of 0.05 (mg/ml); ⃗ ). Several sub-regions were 72 defined and used for normalization purposes (as shown in figures 4.10-4.13) to make the concentration measurements quantitative. The calculation procedure is as follows:   1000N ),,(1)( 1000,N ),,(1)( maxmax txINxItxINxI offsetoffset 4.4 ⃗) ̅ ⃗) ̅ ⃗) 4.5   1 1 1 1 5050 ),(1 region iRi NxINI 4.6 ⃗) ⃗) 〈 〉 4.7 ⃗ ) ⃗ ) ̅ ⃗) 4.8   1 1 1 1 5050 ),,(1)( region fRf NtxINtI 4.9 ⃗ ) ⃗ ) 〈 )〉 4.10 ⃗ ) ⃗ ) ⃗) 4.11 ⃗ ) ⃗ ) 4.12 ⃗) ̅ ⃗) ̅ ⃗) 4.13 50050 ),,(1)( , 50050 ),,(1)( 3 3 2 32 2 2 2   NtxcNtcNtxcNtc regionregion 4.14 constant3),(),( ctxctxc  4.15 ])([ ),(),( constant32 ctc txctxc f   4.16 73 Figure 4.10 ̅ ⃗) on the left and ̅ ⃗) on the right Figure 4.11 ⃗) on the left and ⃗) on the right region 1 74 Figure 4.12 ⃗ ) on the left and ⃗ ) on the right Figure 4.13 ⃗ ) on the left and ⃗ ) on the right region 1 region 2 region 3 75 Equation 4.7 represents the normalized field for the illumination power, while equation 4.10 corresponds to the normalized detected fluorescence. In the final step, the intensity value c can be related to the concentration of the dye by data points collected previously to quantify the dye fluorescent behavior in different fluid components (figure 4.9). Presuming that the dye, methanol and ethylene glycol all stay in nearly the same proportions as they diffuse in water, the detected fluorescence represents the propagation of MEG in water. In theory, ⃗ ) should change from 0 corresponding to zero concentration of the dye and 1, representing the initial concentration of the dye (0.05 (mg/ml)). However, in practice, there is a continual decrease of fluorescence intensity of the dye due to the exposure to light, i.e. photobleaching that negatively affects the measurements. The mean concentration calculated form equation 4.1 4 over region 2 is presented in figure 4.14. Since there is pure MEG in this region during the entire experiment, the estimated concentration mean is expected to remain constant, provided that the temporal variations of illumination power remains constant. This decrease in fluorescence intensity due to photo-bleaching can be significant (5% in the time scale of the tests) and is undesirable as it could be incorrectly interpreted as a reduction in concentration. A simple method to avoid photo-bleaching is to pulse the LED rather than a continuous illumination to decrease the effective period of time fluorophore particles are exposed to the light. However in the pulse mode due to the device limitations, the required light pulse width could not be achieved with an appropriate power levels to excite the dye particles. The second option was to correct the images by first choosing an arbitrary region in the upper 76 layer where there always exists pure MEG (region 2) and calculating the mean concentration value in this area 〈 )〉. Then choosing an arbitrary region in the bottom layer and calculating the mean concentration value in this area 〈 )〉 (region 3). And finally, normalizing the concentration field by ) after subtracting the offset value ). A snapshot of the calculated concentration field is shown in figure 4.13 (on the left) by correcting the images. The offset value ) doesn’t remain constant during the entire experiment as fingers containing the dye particles reach to the bottom of the cell but during the initial phase where there is pure water, light intensity remains constant and this value was used as the offset value for the entire set 〈 〉 (figure 4.14) 77 Figure 4.14 (a) mean concentration over region 2; 〈 )〉 (b) a focused view of 〈 )〉 demonstrating its periodic behavior, (c) mean concentration over region 3; 〈 )〉 78 Chapter 5: Quantitative concentration measurement in narrow channels 5.1 Result and Discussion Challenges associated with performing quantitative particle image velocimetry (PIV) and LED-induced fluorescence (LIF) in thin gap channels were discussed in details in previous chapters. In this chapter, the results for a simultaneous velocity and concentration measurement for Rayleigh-Bénard convection in a Hele- Shaw cell are discussed in further detail. Specifics of the experimental setup were covered in the previous chapter, a simple schematic of the experimental setup in presented here in figure 5.1. Figure 5.1 a focused view of the Hele shaw cell cross section. The microspheres are manipulated to a known location across the gap before reaching to the field of view 79 Figure 5.2 shows a snapshot of images from both velocity and concentration cameras at t*=1000 s or using the scaled time of t=1.45 using equation 1.9. Due to the in line positions of the cameras facing each other, the corresponding images from the two cameras are reversed. As explained in previous chapters, a simultaneous velocity and concentration measurement of a determined region of the device can lead to estimations of the flux from the top layer to the bottom layer ( cDcuJJJ diffusionconvection  ). There are two printed vertical lines on one of the glass walls with a distance of 70 mm used for determining the region of interest of the flow pattern. This region is defined far enough from the inlets to ensure a sufficient development length required for particle manipulation (L). The lines are printed on the outer side of the glass so they don’t interfere with the flow (due to change in surface energies, implementing the lines in contact with the flow resulted in formation of bubbles on the lines). Although field-of-view of both cameras include the designated area between the vertical lines but since each camera was calibrated separately, they were not perfectly aligned and did not share a common optical axis. Subsequently, one further processing step and determining a transformation procedure was needed to match each pixel on the images from camera 1 with the corresponding pixel on the image taken from camera 2 at each time. The transformation consists of a linear magnification, a planar translation and a planar rotation. Figure 5.2 b and c demonstrates the combined images to report a well matched pattern. 80 Figure 5.2 calculated velocity and concentration from processing recorded images from camera 1 and 2 respectively 81 Figure 5.3 mapping raw images from camera 1 to corresponding images taken from camera 2 after transformation In the figure series 5.3, the estimated concentration field is presented for different time scales to investigate the flow behavior at different regimes. As discussed in the previous chapter concentration field is a value from 0 where there is water to 1 where there is pure MEG. To track instability plumes, a region of the flow where there are instability fingers was determined by defining a concentration 82 threshold values e (0.2 < cf < 0.8). It should be noted that all the variables are non- dimensionalized with the scaling parameters as discussed in chapter 1. Important scaling parameter values are as follows: Experimental parameters H 0.045 m t’ 682.57 s Ra 2472.3 3 Table 5.1 experimental parameters The experiment starts with a sharp interface at t=0. As the top column diffuses into the water, the boundary layer becomes thicker until it reaches to a point where it becomes unstable and instability plumes in the form of fingers start to propagate downward. From the analytical work of Riaz et al (2006), the critical time is estimated to be around 4 seconds (equation 1.28), however in this work initial fingers are not observable before t=0.088 (t*=60 s). The average wavelength of the fingers at t=0.176 (t*=120 s) is close to 1 mm across the entire filed-of-view. After some time, neighboring fingers tend to merge together and form thicker plumes (t=0.5). This is probably due to presence of stronger rising plumes and the existing vorticity pattern. After a while a new set of fingers start to develop at the interface (t=0.75) that become absorbed in existing fingers. The total number of fingers at the interface decreases continuously, for instance at t=0.75 (t*=510 s) the average wavelength of fingers increases to about 1.63 mm. The number of fingers at different heights for a 83 single time also decreases as they move further in the reservoir. At t=3 (t*=2045 s), there are close to 30 fingers at the interface while this number at a distant 25 mm from the initial interface is around 15. Newly developing fingers yield the existing flow pattern and are swept aside, eventually merging to the older descending streams. Although these streams are exceedingly dynamic close the interface, they are less active farther down. They mostly act as paths to transport MEG from the top layer to the bottom boundary. Fingers are usually wider at their tip comparing to their body and a few of them split at their tip on their way down as an ascending finger cuts through them. This is the case when the tip of the descending finger is not well defined and has a rift due to presence of multiple sub-fingers that previously joined together. Fingers reach the bottom boundary of the cell at about t=5 (t*=3413 s) and after this point diluted MEG start to accumulate at the bottom while the dominant streams start to get thicker (t=7.5). The evolution of the fingers can be viewed in figure 5.3. 84 85 86 87 88 89 Figure 5.4 Rayleigh-Bénard flow evolution obtained from LIF concentration measurements 90 As the top layer mixes into the bottom column and pure MEG is consumed, the interface starts to recede from its initial position. By comparing the concentration field at t=0 and t=20, it can be observed that the interface has receded significantly. The distance between the two interface locations was measured to be around 13.5 mm. To be able to track the interface from the concentration field, a threshold value (cf=0.8) was defined as mentioned earlier. In figure 5.5 the concentration profile from an arbitrary vertical line across the height of the entire field for a snapshot (t*=1000 s) is shown, along with the level defining the interface position. Individual finger can be highlighted by subtracting the base profile from the extracted interface (a quadratic function fit to the elevation profile at each instant in time, giving the fluctuation of the interface about the spatial mean value). The evolution of generated fingers at the interface is presented in figures 5.5-5.6. As it can be observed, the number of fingers generated increases until t~8, then fingers generation decelerates as system starts to saturate. The amount of MEG descending into the reservoir can be determined by measuring the area A between the initial interface and the subsequent interface at a certain time. This value was then normalized by the reservoir height (H=0.045 m) and the length in which the fingers are being sampled (L=0.07 m). As it can be observed from figure 5.4, the amount of MEG being advected increases linearly until t~7. At this time most of the dominant fingers have reached to the bottom of the cell while the front running fingers had reached the bottom boundary at about t=3. The flow rate can also be extracted from the interface retraction, figure 5.6 predicts a rise and fall of the flow rate. Flow rate Q* is defined as: 91 dxuQ erface int* 5.1 (a) (b) (c) Figure 5.5 interface tracking by thresholding (cf=0.8) 92 Figure 5.6 temporal fingers generation profile at the interface (a) (0