Measuring a three-dimensional parabolic flow profile inside a microchannel using the General defocusing particle tracking laboratory

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PETTER ANDERSSON

Master thesis

Department of applied physics KTH Royal institute of technology

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ISSN 0280-316X SE-100 44 Stockholm

ISRN KTH/FYS/–16:69—SE SWEDEN

This thesis concludes the diploma project of Petter Andersson for a Master of science degree in en-gineering physics from the Poyal institute of science (KTH) in Stockholm, Sweden. The research was conducted in the Ultrasonic research group at the department of Applied physics during the fall 2016 under the supervision of Ida Sadat Iranmanesh. The examiner at KTH was Professor Martin Wiklund. © Petter Andersson, November 2016

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appendix B. In conclusion, it is possible to track seed particles in three dimensions using GDPTlab and conventional microscopy equipment.

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List of abbreviations

η viscosity

µPIV micro-particle image velocimetry Cref reference mixture

D smallest resolvable distance

DOF depth of field

F F T fast Fourier transform

F OV field of view

I A interrogation area

n index of refraction

N .A. numerical aperture

Q volumetric flow rate

QE quantum efficiency

Rhyd hydraulic resistance

Re Reynolds number

W D working distance

3DTFPCM three dimensional tracking of one fluorescent particle with confocal microscopy

CCD charge-coupled device

DBS dichroic beamsplitter

GDPTlab General defocusing particle tracking laboratory HVM holographic video microscopy

ICCD intensified charge-coupled device iii

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Introduction and background

In the past, researchers interested in particle tracking have built physically massive measurement se-tups, for example, to study air flows. Contrary to modern Lab-on-a-chip research groups, who con-struct small measurement setups to study microchannels and other small vessels. The microchannel can contain chambers in different symmetric shapes or a straight channel usually transparent with a glass ceiling and bottom. These are often used in microfluidic systems. One of the research groups that perform experiments on microfluidic systems is the ultrasonic research group at the department of Applied physics at the Royal institute of technology (KTH). After a meeting with the head of the ul-trasonic research group at KTH, this project is brought to life.

Similarly to many Lab-on-a-chip research groups, we are interested in tracking microparticles in-side a microchannel. Another such research group is Ohlin et al. (2015) see reference [1]. They tracked microparticles in two dimensions inside a microchannel chamber. Introducing a novel soft-ware called General defocusing particle tracking laboratory (GDPTlab), the project at hand aims to track microparticles in three dimensions inside a microchannel using, to some extent, similar exper-imental equipment as reference [1]. This GDPTlab software operates from inside MATLAB ®version R2015a or a more recent release and it is developed by Rune Barnkob at the Institute of fluid me-chanics and aerodynamics at the Universität der Bundeswehr in München. In more detail, the aim of this project is to study and analyze microchannel flow using inexpensive conventional technical instruments and equipment that are found in any microfluidics laboratory. The software GDPTlab is the seed particle tracking tool used in this study. A range of flow rates and particle concentrations is used to evaluate the tracking tool. To begin with, it is of interest to review the fundamentals of the microscope, fluorescence microscopy and selected particle tracking techniques in order to make an evaluation of our measurement apparatus and tracking software.

1.1 About the microscope

In this section, some features of conventional microscopes are discussed with focus on the objec-tive and its features for example the numerical aperture (N .A.), magnification, smallest resolvable distance (D) and other parameters. In figure 1.1, there are two microscopes depicted to the left an inverted microscope and to the right an upright microscope. Both microscopes carry turrets with a number of objectives marked with their magnification Mobjand numerical aperture.

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Figure 1.1: Photographs of an inverted microscope to the left and an upright microscope to the right with the illumination light paths indicated on both of the microscopes. Courtesy of reference [2]

The total magnification of the microscope is the product of Mobjand the eyepiece magnification Meye

for ocular inspection. If a camera is mounted on the microscope, one can install an adapter lens at-tached to the camera. However, bare in mind, that large magnification does not mean good resolution. It is the light collecting angle and aberrations of the objective that affect the resolution. Furthermore, the pixel size on the light sensor in the camera needs to the matched with the optical resolution of the microscope [2]. Next, the numerical aperture (N .A) is an important parameter that describes the maximum resolving power of a specific objective.

N .A. = n · sin(α) (1.1)

This index of refraction (n) refers to the immersion medium in the microscope objective in equation 1.1 moreoverα is half of the light collecting angle of the objective. The N.A. specified on the objec-tive together with the wavelength of the emitted fluorescent lightλ are used to calculate the smallest resolvable distance (D) between two point sources that can be seen through the objective

D =0.61λ

N .A. (1.2)

From equations 1.1 and 1.2, it is found that n,α and λ are the parameters that effect the resolution of the microscope. Meaning that an immersion fluid with a high index of refraction, for example oil (e.g. n=1.2), results in a higher resolution compared to objectives where water or air is used as the immersion medium. Moreover, a low N .A. of the objective results in a long working distance (W D) formulated in equation 1.3

W D = 1

2 · N .A. (1.3)

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and the coverslip when the specimen is in focus. It is common to use a short working distance in different microscopy techniques. The last parameter, mentioned here, is the depth of field (DOF ) which is defined as

DOF =λ p

n2_{− N .A.}2

N .A.2 (1.4)

and it describes the distance between the nearest and farthest object planes that are in focus.

1.2 Fluorescence microscopy

In order to realize a fluorescence microscopy setup, it is possible to use a conventional microscope, see examples in figure 1.1, together with a plan fluorite objective and an excitation source often a mercury arc lamp, see figure 1.2.

Figure 1.2: The emission spectrum of a mercury arc lamp commonly used in fluorescence microscopy. The figure is marked as Figure 1 at Carl Zeiss website. Courtesy of contributing author Michael W. Davidson at Florida state university and Carl Zeiss corporation see reference [3].

The light emitted from the mercury arc lamp excites the fluorophore inside the trace particles occu-pying the microchannel. At this point, it is important to separate the light from the excitation source and the emission light from the objects under study. This can be done by guiding the light through a dichroic beamsplitter and optical filters where the excitation light (blue-shifted) is reflected away and the fluorescence light (red-shifted) is transmitted to either the eyepiece or a camera. This is called epi-illumination. The fluorescence light is emitted incoherently meaning in all directions making the whole shape of the object visible. This is important when studying complicated specimen structures such as proteins. Moreover, the contrast between the fluorescence light and the next to totally dark background makes details smaller than the limit of the Rayleigh criterion distinguishable. In figure 1.3, a schematic illustration of fluorescence microscopy is provided.

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Figure 1.3: This is a schematic of a wide-field optical microscope using the Köhler illumination which is the standard illumination system. It produces an uniformly illuminated object. Moreover, the figure shows the light rays from the light source to the object under study for trans-illumination bright-field microscopy, epi-illumination bright-field microscopy and epi-fluorescence microscopy. In bright-field microscopy, it is white light that is directed onto the objective. While, epi-fluorescence microscopy utilizes a wavelength sensitive dichroic beamsplitter and filters to reflect the short wave-lengths (excitation light) and transmit the long wavewave-lengths (emission light). The objects can be stud-ied either by the naked eye in the eyepiece or recorded by a camera [2]. Courtesy of reference [4].

1.3 The Reynolds number

The motivation behind this section is to reach a simple expression for the Reynolds number (Re) valid under the experimental conditions discussed in subsection 2.2.6 and the linear Navier-Stokes equa-tion. To begin with, the equation for the Reynolds number originates from the Navier-Stokes equation for compressible fluids

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whereρ is the density, ∂tv is the velocity gradient, v is the velocity, p is the pressure,β is a dimension-less constant (≈ 5/3 for water) and η is the viscosity of the fluid more specifically ηwater(20°C) = 1.002

mPas finally g is the gravitational acceleration. The fluid used in the flow experiments addressed later in the text is water and due to the fact that water is an incompressible fluid (i.e. a Newtonian liquid) ∇v = 0 1.5 becomes

ρ[∂tv + (v∇)v] = −∇p + η∇2v + ρg (1.6)

the Navier-Strokes equation for incompressible fluids 1.6. Next, the Navier-Stokes equation is non-dimensionalized meaning that all physical variables are expressed in units of characteristic scales. There is one length scale, here L0=4750µm, and one velocity scale, V0.

r = L0r and v = V˜ 0v˜ (1.7)

The tilde (˜) stands for a non-dimensionalized quantity meaning it is a pure number. Next, the scales for time (T0) and pressure (P0) are established [5].

t =L0 V0˜t = V0˜t and p = ηV0 L0 ˜ p = P0p˜ (1.8)

Next, Bruus (2011) states that the viscosity (η) dominates over density (ρ) in microfluidics meaning that P0= ηV0/L0is more correct thanρV₀2. The equations 1.7 and 1.8 are inserted into 1.6 and the

termρg has been excluded giving the following expression

p[V0 T0 ˜ ∂tv +˜ V₀2 L0 ( ˜v∇) ˜v] = −P0 L0 ˜ ∇ ˜p +ηV0 L2 0 ˜ ∇2v˜ (1.9)

Before continuing, a calculation example is called for to show why the termρg called the body-forces [5] could be excluded.

d p

d z = ρg → pmax= ρg h (1.10)

where h is the height of the microchannel here h =110 µm, the gravitational acceleration is g =9.82 m/s2and_{ρ =1·10}3kg/m3_{→ p}max=1.0802 Pa which is a negligible number considering the numerical

values in the remaining terms. Next in the search of a simple equation for the Reynolds number, all terms in equation 1.9 are divided byηV0/L2₀giving

Re[ ˜∂tv + ( ˜˜ v ˜∇) ˜v] = − ˜∇ ˜p + ˜∇2v˜ (1.11)

and consequently the expression for the Reynolds number based on a simplified Navier-Stokes equa-tion becomes

Re ≡ρV0L0

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This flow occurs in a steady-state flow pushed forward by a hydrostatic pressure. This generates a pres-sure difference∆p between the two ends of the channel letting the particle solution travel through a long straight and rigid channel with length L. The direction of the flow is strictly horizontal along the x-axis and the gravitation acceleration in z-direction is minimized to zero by the hydrostatic pressure. Moreover, the cross-section is the same through the whole channel meaning that the particle solution is only changed by the pressure drop along the x-axis in the channel [5]. Alterations to the concentra-tion of particles in percent in the soluconcentra-tion will give the corresponding change to the Reynolds number. Poiseuille flow is fundamental to the understanding of liquids in microfluidic lab-on-a-chip systems [5]. Meaning that, the veolcity field is reduced to only the x-component v = vx(y, z)ex=0. In this way, the non-linear term in the Navier-Stokes equation is omitted (v∇)vx=(vx∂x)vx(y, z)ex=0 and it be-comes the linear Navier-Stokes equation. The Poiseuille flow gives rise to a parabolic flow profile if the following conditions are met: identify only one singular velocity vector vxin the flow, the non-slip boundary condition along the wall(s) of the channel, Re <2100 [6], low flow rates and the microchan-nel is designed as stated above. To explain, the Poiseuille flow figure 1.4 is included below.

Figure 1.4: An illustration of a parabolic flow profile where h/2 is half of the width of the channel and v = vx(y, z) is the velocity of the Poiseuille flow (i.e. a parabolic flow profile) measured in [m/s]. The velocity has its maximum in the center of the channel and zero at the walls and corners. Courtesy of reference [7].

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For a rectangular cross-section h < w, the following equations from reference [5] govern the parabolic flow profile for a Newtonian liquid starting with the velocity vx(y, z)

vx(y, z) = 4h2∆p π3_ηL ∞ X n=1, odd 1 n3 " 1 − cosh(nπ y h) cosh(nπ_2hw) # sin(nπz h) (1.14)

and the volumetric flow rate Q is expressed inhm_s3iin the microchannel

Q ≈ · 1 − 0.630h w ¸_h3_w 12ηL∆p. (1.15)

In the coming calculations, it is assumed that the volumetric flow rate with which the fluid enters is equal to the flow rate of the fluid that exits the channel motivated by a system without leakage nor alternative taps. It should be mentioned that according to reference [5] there is a 13% error in equation 1.15 when applied on a channel with a square cross-section meaning h = w. The last parameter is the hydraulic resistance Rhydexpressed in Pas/m3for when h = w. It is crucial in designing channels for

microfluidics Lab on a chip applications.

Rhyd= 28.4ηL

1

h4 (1.16)

When∆p is a constant pressure drop over the length of the channel and Q is constant, it is possible to formulate the Hagen-Poiseuille law

Rhyd=∆p

Q . (1.17)

The common SI-units applied to the Hagen-Poiseuille law are which the pressure difference∆p is within reach.

1.5 Particle tracking in macro systems

This section is dedicated to particle tracking velocimetry (PTV) and particle image velocimetry (PIV) including instrumentation and experimental procedures. These two tracking techniques use the fun-damental definition of velocity to calculate the velocity of a selected particle at a certain point in a three dimensional space, see equation 1.18.

V = lim∆t → 0∆S

∆t (1.18)

where∆S is the displacement of the particle and ∆t is a small, but non-zero, time-step. In the case of PIV, equation 1.18 does not give the movement as a function of time but only the displacement of a particle. On the other hand, the PTV technique has solved this issue, however, at the cost of

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frame are denoted as i = 1,2,3,..., If. Furthermore, the position of the i th particle inside a specific frame [ f ] is labeled as x_if, where x=(x, y, z). Moreover, when moving from one frame to the next for example from [ f ] to [ f +1], the particle is expected to be found in r1a so called neighborhood centered

around e_if +1 [8].

e_if +1= xif + u f

i∆t (1.19)

The center of the neighborhood is calculated based on a direct linkage in regards to the direction of particle movement in the previous frames.

In equation 1.19, u_if=((u_if)x,(u_if)y,(u_if)z) is the velocity components in three dimensions and again∆t is the time-step between two consecutive images according to reference [8]. In figure 1.5 below an illustration of the nearest neighbor procedure is presented.

Figure 1.5: A schematic of the nearest neighbor procedure including the names of the four frames and notations. Courtesy of reference [8].

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As it is illustrated in figure 1.5, the trace particles are denoted as "i" in the current frame, "j" in the search frame and "k" in the acceleration frame.

1.5.1 Particle tracking velocimetry

A conventional PTV system consists of flow markers of some kind, illumination lights, cameras to record the flow markers and, units for digitization, storage and data processing are also needed [9]. This equipment demand a spacious laboratory and the system as a whole is rather expensive to pur-chase. The flow markers must float neutrally and their density should match the one of the flow medium to make to flow markers move at the same velocity as the flow medium. The smaller the flow markers the better the velocity match [9]. The requirements on the illumination are as follows: High intensity point light sources projected through an optical system . The light source is pulsed with a frequency and phase that is match with the cameras. The light intensity should be homogeneously distributed in the observation volume. It is common to use lasers, strobelights or continuous light from a light bulb with an additional pulse mechanism [9]. The most suitable cameras are equipped with solid-state sensors because the tube camera carry geometric instabilities and converting from high resolution film to photos takes a long time. The digitization unit is some kind of analogue to dig-ital converter making it possible store the photographs or the video recording on discs or a hard drive for processing. The mathematical model used to determine the positions of the flow markers in three dimension is shown in equation 1.20 and figure 1.6 from reference [9].

   x_i0− xh y_i0_{− y}h −c    = λi· R ·   Xi− X0 Yi− Y0 Zi− Z0   (1.20)

Where (Xi,Yi,Zi) are the object point coordinates, (X0,Y0,Z0) are the camera projective coordinates,

R=ri j are the elements of a 3·3 rotation matrix with angles ω, φ and κ, and (x

0

i,y

0

i) are the image co-ordinates, (xh,yh) is the image principle point, c is the image principle distance andλi is the scale factor.

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Figure 1.6: An illustration of the collinearity condition where the camera model is inverted for drawing purposes. Courtesy of reference [9].

Equation 1.20 is solved for the image coordinates in order for it to function as observation equations in a least square adjustment when determining the camera position (X0,Y0,Z0,ω,φ,κ,c,xh,yh) in the calibration and the object coordinates (Xi,Yi,Zi) in locating the particle [9]

x_i0_{= x}h− c · r11(Xi− X0) + r 21(Yi− Y0+ r31(Zi− Z0)) r13(Xi− X0) + r23(Yi− Y0) + r33(Zi− Z0) (1.21) y_i0_{= y}h− c · r12(Xi− X0) + r 22(Yi− Y0+ r32(Zi− Z0)) r13(Xi− X0) + r23(Yi− Y0) + r33(Zi− Z0) (1.22)

Finally, it should be pointed out that the mathematical model presented here has to be modified to take into account the physical properties of the experimental setup. Each ray of light traveling from the object to the light sensor has to pass through optical media (water, glass and air) with different indices of refraction and the image coordinates are corrected for effects of lens distortion and digitization [9]. One of the first research groups to apply PTV is reference [10] where Chiu and Rib (1956) constructed a measurement apparatus shown in figure 1.7.

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Figure 1.7: The measurement setup is built to study the energy dissipation in low velocity turbulent air jets. Two Crown graphic 4·5 inch cameras are positioned in stereo in front of the observation volume with a grid in front to limit the xz-plane to 80·80 cm and the depth of view (DOV) is 40 cm in the y-direction. Each square in the grid measures 20·20 cm. The photographs are taken with 135 mm lenses having f-number 4.7 and the exposure time was half a second or less. An air-blower and two stroboscopes are installed to the left of the grid. Courtesy of reference [11] and [10].

The air-blower spreads lint particles in the observation volume with exit velocity 63cm/s and con-secutive strobes with a fixed frequency make the lint particles appear as dots in the photographs as they move in the xz-plane. The ( ¯x, ¯y, ¯z)-position and the average velocity components ¯u, ¯v and ¯w of the lint particles are calculated in cubes of space with the dimensions 20·20·20 cm3in the xz-plane. The depth of view is divided at y=6,12,18,20,24 and 30 cm in order to obtain three dimensional un-derstanding of the flowing lint particles [11] and [10]. Figure 1.8 depicts flow results obtained by reference [10].

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Figure 1.8: A figure illustrating the xz-plane at y =18 cm depicting ¯v in cm/s with dashed lines and ¯u in cm/s with solid lines. In the xz-plane, the field of view is 40·40 cm2. Courtesy of reference [10].

1.5.2 Particle image velocimetry

This brief review of particle image velocimetry (PIV) has its focus on one specific experimental system using a water jet containing microscale particles to study a turbulent flow. It is illustrated in figure 1.9. This apparatus system is used in the fields of aerodynamics and hydrodynamics [12]. The apparatus is built-up by an open tank of water with the dimensions 450·600·600 mm3and from above a vertically inserted water tube with a nozzle attached measuring 26.9 mm in diameter. On the bottom of the tank, there is a horizontal impinging plate. In the foreground, the illumination source is passed through optical components creating a thin light sheet that illuminates the water jet orthogonally onto the water impinging plate. The exit velocity of the water jet is v =244±2 mm/s [12]. On the right-hand side, the video recorder alternatively a high speed camera is aimed on the light sheet. The Reynolds number based on the exit velocity and the nozzle diameter amounts to Re=6564 [12] putting this experiment well into the regime of turbulent flow.

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Figure 1.9: A particle image velocimetry apparatus used for recording a turbulent water flow. Courtesy of [12].

The illumination source is a Q-switched double-pulsed ruby laser (Apollo lasers model HD22). The laser beam is formed into a∆z0=1 mm thick and∆y0=21 mm wide light sheet with an output energy

Eout≈2 J. Moreover, the microparticles in the water jet have a diameter from 2 µm to 10 µm and a

concentration of approximately 40 particles/mm3 [12].

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Figure 1.11: A detail of the recorded image field describing the water flow indicated by microparticles in the y x-plane from the experiment apparatus in figure 1.10 The image covers 20·30 mm2of the field of view. Courtesy of [12]

Similar to PTV, the nearest neighbor procedure is applied during the data processing. The photographs are illuminated by a He-Ne gas laser under a microscope objective to project the interrogation re-gion in the photographs onto a two-dimensional array detector. A 256·256 pixel element photodiode array from EG&G Geticon and frame grabber from Poynting products inc. are used to digitize the photographs. A DEC VaxStation II computer connected to a Numerix NMX432 array processor and software perform an automatized interrogation procedure.

1.5.3 Laser particle image velocimetry in three dimensions with one cylindrical

lens

This technique, laser particle image velocimetry (LPIV) is similar to conventional PIV discussed in subsection 1.5.2 with the difference that a pulsed laser is used, for example, a pulsed Nd:YAG laser (Neodymium-doped yttrium aluminium garnet) frequency doubled (1064 nm→532 nm) to emit a green light and one or more cylindrical lenses are inserted.

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Figure 1.12: A schematic of particle image velocimetry with one cylindrical lens. There are two Nd:YAG laser cavities, some mirrors to reflect and direct the light, a beam combiner to make two pulsed laser beams converge into one beam with consecutive pulses. And, the combination of a harmonic separa-tor and an IR-dump work to reflect away the wavelengthsλ>532 nm. Courtesy of reference [15].

The harmonic generator in figure 1.12 converts the emitted light wavelength fromλ=1064 nm in the infrared (IR) toλ=532 nm in the visible spectrum. A frequency doubled Nd:YAG laser is a suitable illumination source due to its high light intensity. In order to overcome the time delay between con-secutive pulses, two laser cavities are running simultaneously in the measurement setup in figure 1.12. The reasoning behind frequency doubling is to gain light emission in the green-blue spectrum where the camera light sensor is the most sensitive and it is visible contrary to_{λ=1064 nm is in the infrared} spectrum [15].

Figure 1.13: An illustration on how to achieve short time lapses between photographs using a high-speed camera. Courtesy of reference [15].

At least two images of the same particles moving in the liquid flow need to be recorded in order to study particle displacement. If it is necessary to perform high flow rate experiments or if the area of imaging is small, this requires a high-speed camera recording in the kHz range or cameras with progressive scan architecture with <1µs time-lapse between two images according to reference [15]. Furthermore, if the particles are small or emit a low-intensity light the Peltzier cooled charge-coupled device with quantum efficiency equal to QE = 0.7 is on of the best light sensors on the market, see reference [15]. The procedure to obtain particle displacement is commonly called cross-correlation of images see equation 1.23.

~vi=~ri (t ) M∆t (1.23) Where,~vi = h d x d t, d y d t, d z d t i

i describe the velocities of i individual particles in the images,~ri(t ) is the displacement of the same particles, M is the magnification of the lens(es) and_{∆t comes from the} time-delay between two consecutive images. A time-effective procedure to perform the cross-correlation

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Figure 1.14: An illustration of the steps from the selected images to a complete velocity-vector field. To the left, there are two images with a time-delay between them. In the middle, one interrogation area (I A) extracted from each image that depict the particles to be cross-correlated. To the right, the Fourier transform containing the information of one particle displacement and one average velocity vector. Finally, in the bottom, the complete average velocity vector field is presented. The coordinates are assumed to be in pixels where indicated. Courtesy of reference [15].

For example, the number of computations are reduced fromO(N4) toO N2l og2N when considering

image cross-correlation in two dimensions. The Fourier transform applies the correlation theorem in equation 1.24

F{ f ∗ g } =F{ f }∗·F{g } (1.24)

which shows that the cross-correlation of two functions equals the complex conjugate multiplica-tion of their Fourier transforms reference [15]. By definimultiplica-tion, the FFT assumes that the input data is periodic which may lead to aliasing if the displacement is larger than half of the interrogation area r (t )>IA/2. However, the impact of aliasing can be reduced by increasing the interrogation area or reducing the time-delay_{∆t [15]. Another problem is that bias errors occur when the particle has} partially exited the fixed interrogation area in the second image with increasing displacement [15].

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This bias error leads to a reduced peak amplitude for all displacements separated from zero [15]. Ac-cording to Törnblom (2004), this error can be reduced if a weighting function is applied on the cross-correlation. To conclude, the laser particle image velocimetry give a very detailed velocity vector field here limited to two dimensions.

1.6 Particle tracking in micro systems

Contrary to the tracking techniques discussed above, particle tracking in microsystems involves stud-ies of trace particles viewed through a microscope.

1.6.1 Micro-particle image tracking

In contrast to the conventional PIV technique, micro-particle image velocimetry (µPIV) includes a mi-croscope to track micro-scale particles inside a microchannel. It is applicable in microfluidic systems often used in biological research. This section is based on the experiments performed by Santiago et al. (1998) to give an example ofµPIV. To begin with, there are few important criteria for successful µPIV experiments. The seed particles must be small enough to flow through the microchannel with-out clogging the device and the imaged particles should be distinguishable. Nonetheless, they should be big enough to reduce the effects of Brownian motion. In their experiments, Santiago et al. (1998) used spherical polystyrene particles with diameter d=300 nm (Bangs laboratory), a specific gravity ρp=1.055 and emission light wavelengthλe=509 nm.The relative error from Brownian motion²B is given by equation 1.25 ²B= 1 u s 2D ∆t (1.25)

where, the steady flow has the characteristic velocity u=50µm/s and the image time interval ∆t=0.068 s and the diffusion coefficient D first derived by Einstein (1905). It is calculated using equation 1.26

D = kBT

3πµd (1.26)

where kBis Boltzmann’s constant, T is the absolute temperature ,µ is the dynamic viscosity of the fluid and d is the diameter of the seed particles. Their error due to Brownian motion amounts to²B=9%. Santiago et al 1998 had an epi-fluorescent microscope equipped with an intensified charge-coupled device (ICCD), an oil immersion objective with magnification M =100 and N .A.=1.4. The objective has a high light collection efficiency and a rather narrow depth of field. For more details see figure 1.15.

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Figure 1.15: A epi-fluorescent microscope in theµPIV measurement setup. Courtesy of reference [17].

In conventional PIV systems the depth direction is defined by the thickness of a laser sheet. However that kind of systems are not suitable for microfluidic experiments. Here, the range of image intensities are limited to the depth of field only. Meaning, that the particles outside of the depth of field do not contribute to the cross-correlations of image intensities. Observe, the microscope in reference [17] is equipped with a motorized positioning system with micrometer sensitivity to facilitate recording the volume made up by the depth of field (1.5µm) and the imaged trace particles are analyzed using a nearest neighbor algorithm developed at the University of California at Santa Barbara and a commer-cially available from TSI Inc [17].

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In the results, Santiango et. al (1998) show a vector field of approximately 900 velocity vectors in a 120 µm·120 µm FOV and every velocity vector is calculated in a 6.9 µm·6.9 µm·1.5 µm volume.

1.6.2 Holographic video microscopy

This section is based on the holographic video microscopy (HVM) experiments by Cheong et al. (2009) They built up an experimental apparatus around an inverted microscope (Zeiss axiovert 100 STV), an oil immersion objective with 100 times magnification and 1.4 in numerical aperture. The illumination is a solid state laser (Coherent Verdi 5W) with emission wavelength,λ=532 nm. The colloidal spheres under study here scatter a fraction of the incident light and the scattered light interferes with the un-scattered portion in the focal plane of the objective. The resulting interference pattern is projected on a low noise and gray-scale video camera (NEC TI324 IIA) finally they used a video recorder (Poineer H520S). The total magnification of the experimental setup is Mtot=101 nm/pixel.

Figure 1.17: A figure depicting the experimental setup for holographic video microscopy. It is limited to the microscope objective and the sample stage to the left with an enlarged view of the image plane to the right. In addition, the gray-scale images in the bottom-left corner show the optical or recorded image together with the fit to the predictions of the Lorenz-Mie theory. Courtesy of reference [18].

The intensity of the light is measured at r = (x, y, z) in the image focal plane is described by

I (r ) = |E0(z − zp) + Es(r − rp)|2 (1.27) where the incident plane wave is E0(z), the propagation direction z and Es(r − rp) describes the scat-tered wave that propagates from the particle position rp(t ) to the point of observation r . In addition, the scattered field is described by the Lorenz-Mie theory [19] and depends on the radius of the particle ap, its refractive index nprelative to the refractive index of the surrounding medium nmreference [18]. Subsequently, the recorded image in figure 1.17 is fit to equation 1.27 to obtain the three-dimensional position and radius of the micro-particles to a nanometer precision. [18]. The results are depicted in figure 1.18.

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Figure 1.18: Results from the holographic video microscopy experiment. In (a), the particle displace-ment of 500 colloidal spheres with diameter d=1µm moving in a pressure driven flow. In (b), the Poiseuille flow profile based on the results from (a) where particles from the shades areas are omitted. The dashed line is the theoretical profile. Reference [18]. Courtesy of reference [18].

The dimensions of the microchannel are 2 cm long, 100µm wide and 17 µm deep. The flow of seed particles are imaged in a 50·70 µm2area close to the middle of the channel. The focal plane is approxi-mately set to 5µm under the lower glass to water interface. The displacements of the seed particles are linked from one image to another with a mathematical method called maximum-likelihood algorithm described in reference [20] producing the particle trajectories,~rp(t ). The sample-rate of the seed par-ticle location is 60 Hz. Cheong at al. (2011) found that the trajectories of faster moving parpar-ticles and slower once overlapping each other could not be determined. To conclude this brief review of this HVM study, the maximum speed of the colloidal spheres that are presented in figure 1.18 approaches 400µm/s.

1.6.3 Three dimensional tracking of one fluorescent particle with confocal

mi-croscopy

In their article, Germann and Davis (2014) aim to illustrate three dimensional tracking of one fluo-rescent particle with confocal microscopy (3dtfpcm) using four laser foci positioned in a tetrahedral pattern to obtain an effective collection of light aimed into one detection channel. Contrary to con-ventional confocal fluorescence apparatus systems they insert one polarizing beamsplitter and two SPADs to obtain greater polarization resolving capabilities. The experimental apparatus in reference [21] have temporally modulated laser diodes and apply time-gated single photon counting for three dimensional position estimation. The speed of the laser modulation should preferably be greater than the speed of the photon counter to avoid limitation of the speed of the position determination. How-ever, the frequency of the three dimensional piezo stage f =0.54 kHz is the upper limit of the tracking bandwidth. Here, the four excitation focal volumes are overlapping to obtain a constant laser light irradiance from the center of the light beam to its boundary.

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The average detection efficiency of the system is determined using fluorescence correlation spec-troscopy and calibration measurements. The experimental apparatus in figure 1.19 consists of

Figure 1.19: A schematic of the beam combining apparatus. Courtesy of reference [21].

four 632 nm laser diodes (Lasermate T63E-PFC1-21-S4) fluorescence excitation sources. The light beams are each channeled through a 4/125µm single-mode fiber (SMF) to spatially filter the beams to achieve next to diffration-limited light. A driver board with power up to 1 mW and modulation frequency up to 100 kHz (Lasermate APCT-42X). After, a fiber coupler connects the SMF and the colli-mator (Thorlabs , discontinued similar to F280APC-A) producing a focal length of ≈3.12 m, however, for two of the beams five 100µm thick washers are inserted in the passage producing a focal length of ≈0.85 m. Three 50% beamsplitters (BS) are inserted according to figure 1.19 in order to obtain next to collinear beams. The last step is to let the laser beams go through a polarizer to give all of the beams the same linear polarization [21]. All of the four laser beams have the same size at 1.33 m away from the collimators with two beams converging and two beams diverging [21]. The mi-croscope objective (Olympus UPLSAPO 20x/1.2 water immersion n=1.33) with L1=100 mm (Thorlabs AC254-100) L2=300 mm (Thorlabs LA1509-A)in 1.20. The inverted microscope with epi-illumination is modified to the requirements of the experiment. The beams are reflected on a fused silica beam sampler (Newport 10Q40NC.1) with reflection efficiency 0.068 measured with a power meter (Coher-ent LM-2 VIS). Later, the fluorescence light passes through a bandpass filter used to reflect scattered laser light (Omega 3RD660-740) and imaged by L3=250 mm (Thorlabs LA1461-A) then into a pinhole (Newport UNH-150) working as a spatial filter. The light is collimated L4=150 mm (Thorlabs LA1433-A) and split by a polarizing splitter (Thorlabs PBS121) and then focused by 8 mm asphere lenses (Thor-labs C240TME-B) ending on two SPADs (Perkin-Elmer SPCM-AQR-15) connected to micro photonic devices [21].

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Figure 1.20: Schematic of the four-focus microscope. The list of components are a 100 mm lens (L1), a 300 mm lens (L2), a beam sampler (BS), a beam dump (BD), an objective (O), sample (S), piezoelectric stage (PS), filter (F), mirror (M), a 250 mm lens (L3), a 150 mm lens (L4), polarizing beam splitter (PBS), single-photon avalanche diode (SPAD). The modulation of the laser diode is controlled by a PCI 6602 card , the count of transient-transient logic (TTL) pulses and PCI DIO-96 communicates with the piezoelectric stage. The experimental apparatus is controlled through Labview installed on the host computer [21]. Courtesy of reference [21].

The fluorescent polystyrene bead (Life technologies 660/680 fluoSpheres ©, F-8789) used in the track-ing experiments are 40 nm in diameter. The position of one strack-ingle nano-scale particle is determined by the linear approximation in equation 1.28

(x0, y0z0) = P3 i =0Ni(∆x,∆y,∆z)i P3 i =0Ni (1.28)

where (x0, y0, z0) the nano-scale particle position with respect to the center of the excitation volume and Ni i =0,1,2,3 is the photon count determined in a calibration [21]. The displacements∆x and ∆y are found in the beginning of the alignment by adjusting the beamsplitters and mirrors while record-ing the reflection of the laser beams from the surface of the coverslip [21]. Moreover, the∆z displace-ment is obtained from the initial difference of each beam from exact collimation which come from F1 and F2 in figure 1.19. The results presented in the experiments performed by reference [21] are shown in figure 1.21.

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Figure 1.21: In the three dimensional plot, the track of one single nano-scale particle from blue to red is indicated and the scale on all three axes is inµm. Courtesy of reference [21].

To conclude the findings in the tracking experiments of reference [21], it should be pointed out that the precision in their position measurements are about 60 nm on plane and about 300 nm on axis when the particle is in the center of the tetrahedral region with 10 photon counts in total [21].

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Chapter 2

Experimental equipment and

procedures

This chapter contains a description of the experimental equipment used in the laboratory and the experimental procedures applied to acquire data.

2.1 Experimental equipment

In the laboratory, fluorescence microscopy is realized using the following equipment. Fluorescent beads called fluorsbrite ™ yellow/green carboxylate microspheres with a 1.5µ diameter catalog num-ber 09719-10 10 ml bottle. The fluorescent beads are mixed in a solution of distilled water and 0.01% TWEEN20 viscous liquid. Plastic tubes with lids 10 ml from Sarstedt AG and company, Germany, to contain the various bead mixtures. These micrometer scale beads are excited by the following light source. An HBO 100 W FTZ Serialnumber C-207/89 mercury arc lamp is the excitation light source from Carl Zeiss, Germany. This excitation light source is connected to an inverted microscope called Axiovert 40 CFL from Carl Zeiss, Germany see the left side of figure 1.1.

Figure 2.1: The microchannel used in the flow experiments.

The microchannel is placed and fixed on the manually adjustable stage of the microscope Moreover, a digital camera,α77 from Sony, Japan is also connected to the microscope. Sony α77 has a sensitive light sensor which is important when recording fluorescent beads. Among the objectives on the man-ual five-fold lens turret, the selected objective is a LMPlanFL 20x/0.4 from Olympus where 20x is the magnification and the numerical aperture N .A.=0.4 see table 2.1 for more parameters.

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This objective together with the camera and the microscope mentioned above are the central parts of the laboratory equipment.

Figure 2.2: A .TIF image extracted from one of the flow experiment videos depicting the field of view using the objective LMPlanFL 20x/0.4 under light microscopy. The field of view is 1440·1080 in pixels.

The .MP4 video recordings are converted to series of .TIF images exemplified in figure 2.2. The se-lected straight and uniform segment of the microchannel where the fluorescent particles are traveling in the flow experiments have the dimensions 4750µm long and has a 110·110 µm2quadratic cross-section area. A mechanical distance sensor called Heidenhain ND281 from Germany is attached on the microscope to measure the relative vertical movement of the microscope stage in tens of microm-eters. A syringe pump model SP210IWZ from World precision instruments is fitted with maximum two general use syringes 3 ml product number 309656 from Becton, Dickinson and company (BD), Canada. An ultrasonic bath called 1510E-DTH from Branson company is used to uncouple beads in mixtures and to clean the microchannel. A mixer called Vortex Genie 2 ®from Scientific industries is used to further maintain an homogeneous mixture. Distilled water from a Millie-Q water purification system and ethanol with a 70% concentration are used to dilute mixtures and clean the microchannel respectively. When injecting bead mixtures inside the microchannel, two different tubes are used. A thin tube for fluid transportation called Tygon AAD04127 with a 1.016 mm inner diameter and a 1.7780 mm outer diameter. Moreover, a thick silicon tube with product code 11743845 from Fisher scientific with a 1 mm inner diameter and a 3 mm outer diameter is cut in ten millimeter long bits to function as

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connectors between the taps on the microchannel and the taps attached to the syringes. Continuing the list of equipment used in this project, pipettes are used to transfer an exact amount of fluid from one vessel to another. Table 2.2, below, mentions two pipettes that repeatedly extracted the expected amounts of fluid for mixtures.

Accepted amount

of fluid Manufacturer Usage

0.5 − 10µl Thermo electron_company Transfer beads and_TWEEN20 200 − 1000µl Finnpipette digital, Finland Transfer mixtures

Table 2.2: The pipettes help the operator to extract a rather exact amount of a fluid during the experi-ments. Proper Biosphere ® are attached to the corresponding pipette prior to fluid extraction.

At this point, it should be pointed out that the volume of the extracted fluid is approximated in two procedures. The larger volumes are measured with a 3 ml BD syringe and the smaller volumes are calculated by emptying the fluid into the inner cylinder of the thick rubber tube. To take an example, 100 mm of the tube carries 314µl. Biosphere ® quality tips 10 µl are used to create plugs to block the two taps on the microchannel. The fluorescent beads stand still when both of the taps are blocked. These blocks are made in two steps, to begin with, the narrow tip is sealed using the solder from Weller ® Germany, and then, the sealed tip is inserted inside the thicker rubber tube. The rubber tube is cut short enough to house the tap on the microchannel. Next, the part of the tip not inserted in the rubber tube is cut off. Two powerful software are also a part of the experimental equipment. MATLAB 2015a from Mathworks, USA is used for conversions from MP4 videos to .TIF images in gray-scale. ImageJ developed by the National Institute of Health, USA, is used to calculate the scale factorµm/pixels in the .TIF images. General defocusing particle tracking laboratory (GDPTlab) is a graphical interface for MATLAB ® developed by Rune Barnkob [22] [23]. This concludes the section on the experimental equipment.

2.2 Experimental procedures

The laboratory is equipped according to the experimental equipment described in section 2.1. This section covers the preparations in the laboratory 2.2.1, the crucial calibration 2.2.2 making it possible to locate specific fluorescent beads in the depth direction (i.e. z-direction) and the tracking software General defocus particle laboratory 2.2.3. Moreover, the scale in the photographs 2.2.4 is needed to convert from pixels toµm in the user interface of GDPTlab. Different bead concentrations 2.2.5 are established to find out how the software handles overlapping fluorescent beads. The final part under experimental procedures is called a parabolic flow profile 2.2.6.

2.2.1 Preperations in the laboratory

The necessary equipment in the laboratory is replaced to its original spot and the working benches are wiped clean prior to experiments. The author received safety and operational instructions for the laboratory.

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microscopy. At this point, the mixture of fluorescent beads is injected inside the microchannel and the microchannel taps are closed using the blocks mentioned in 2.1. The block tubing is filled with distilled water before being attached to microchannel to avoid air bubbles inside the microchannel. Under fluorescent microscopy, one confirms that the beads are standing still in x-direction, y-direction and are fully separated. Now, the microchannel is closed and placed in an absolutely dark and sealed box to let the beads sink to the bottom of the microchannel. In this project, the bead sinking pro-cess is monitored on a daily basis and it is completed after seven days. To conduct the calibration under fluorescent microscopy, the operator needs to locate a group of beads that are still and resting on the bottom of the microchannel. The individual beads must be separated by at least 25µm center to center to avoid overlapping bead-defocus-images in the calibration images. In the next step of the calibration, the distance sensor Heidenhain ND-281 is turned on and calibrated by pressing down the sensor pin until the display value starts to shift, moreover, set the unit of distance to millimeters by pressing the "MOD" button and locate "POI INCH" press the button "-" to set "POI INCH OFF". Next, the fine-focus-knob on the microscope is used to place the selected beads in absolute focus. Now, back to Heidenhain, press the "0" button followed by the "ENT" to make the bead-in-focus position 0.0_{µm. The fine-focus-knob is rolled back until the Heidenhain ND-281 display shows -55.0 µm. At} this point, the distance sensor needs approximately one minute before stabilizing at a value usually ±1µm away from the target value. The fine-focus-knob is rotated until the display on the distance sen-sor once again reads -55.0µm. Now, back to Heidenhain, press the "0" button followed by the "ENT" to make the -55µm position the new 0 µm position. The last passage covers the recording of images. The first photograph is taken with the cameraα77 and analyzed to confirm that the edges of the broad bead-defocus-images of the fluorescent beads do not overlap. Again, the fine-focus-knob is rotated lightly until the display on Heidenhain ND-281 shows "1.0µm" and the second photograph is taken. This process is repeated until the display on Heidenhain ND-281 shows "110µm" and consequently 111 calibration photographs are taken with a 1µm distance in z-direction between each photo. The set of 111 photographs is processed in GDPTlab to create a calibration file. Concluding this section, it is worth mentioning that the Z-coordinates are inverted when comparing the position of a fluores-cent bead in the microchannel on the microscope stage and the visualization of the same bead in a three-dimensional plot.

2.2.3 General defocusing particle tracking

This tracking technique rests on three legs. The software General defocusing particle tracking labora-tory (GDPTlab) developed by Rune Barnkob, the calibration images ultimately the MATLAB ®.m data

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file that is produced by the Make cal command inside GDPTlab see section 3.1. The third and final leg is the experimental apparatus which consists of a camera preferably with a light sensitive CCD, one or more lenses to select a portion of the channel used for flow experiments. It should be pointed out that the equipment used to perform the calibration is the same for the flow experiments.

Figure 2.3: An illustration of the GDPT technique. It is a single-camera tracking technique where flow experiments can be conducted with a camera, a lens and a microfluidic device. The shape of the particles change at different depths. Courtesy of reference [23].

The working principle of General defocusing particle tracking laboratory (GDPTlab) [23] depends on the set of calibration images described using Ic(X , Y )kwhere k = 1,2,3,..., N and X ,Y are the in-plane coordinates in image space. Ic is the relative fluorescent light intensity of the calibration flu-orescent particle. One randomly selected calibration image shows one or more recorded fluflu-orescent particles with a specific shape corresponding to a certain depth coordinate zk [23]. The depth of the microchannel is calculated using Hk= zN− z1.

N X k=1

zk− zk−1= 1µm (2.1)

Equation (2.1) shows that the distance between two consecutive photographs is equal, here 1µm, throughout the whole set of photographs where N = 111. When starting a data run from a flow ex-periment in GDPTlab, the software searches the loaded data for target particle images, It(X , Y ), in the (x, y) plane. Itis the relative fluorescent light intensity of the target beads. The search is done using an image segmentation algorithm. At this point, each It(X , Y ) is compared to Ic(X , Y )kin the set of cal-ibration images. To evaluate the level of similarity between Ic(X , Y )kand It(X , Y ) quantitatively, the normalized cross-correlation function is used that according to reference [24] is written as

c(u, v) = P X ,Y[Ic(X , Y ) − ¯Ic][It(X − u,Y − v) − ¯It] {P X ,Y[Ic(X , Y ) − ¯Ic]2PX ,Y[It(X − u,Y − v) − ¯It]2}1/2 . (2.2)

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Figure 2.4: An illustration of the depth determination of one fluorescent bead. Courtesy of reference [23].

The in-plane position, (X,Y)-position, is found using the conventional and robust nearest neighbor technique (see 1.5) to obtain the displacement trajectories of the fluorescent beads moving from one image to another during analysis. When operating the GDPTlab, there are a number of parameters that can be changed in the software user interface.

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Figure 2.5: The user interface of the software without any loaded data nor calibration.

After creating a calibration file make sure it is loaded in MATLAB ® ˙The next step is to load a series of project images. Now, changing the number under segmentation (i.e. light intensity) the software will decrease or increase the light intensity threshold. Under minimum area, one tells the software how small the particles in the image are allowed to be during the analysis. Depth determination is acti-vated and a rather high minimum correlation coefficient is set to avoid including overlapping beads, strongly distorted images due to changes in light intensity and beads sinking in the microchannel dur-ing flow experiments. The boundaries for the movement of the fluorescent beads in the images are set under particle displacement. Display options include a number of selection. Segmentation provides a green ring around a bead if it has been found. Shapes gives a orange cross with circle on the bead if a Z-coordinate is assigned to it. Vectors results in a displacement vector indicating the direction of the particle. Tracks shows the full track of the bead as it moves in the loaded series of images. The refresh button is used to test the selected segmentation and minimum area values and the Run button is pressed to accumulate the tracks, three dimensional plot and data name which must start with a letter. Scale X and Scale Y are discussed in subsection 2.2.4 and the Scale Z is discussed in subsection 2.2.6. Guassian and median filters can be applied go obtain a smooth green ring around a certain bead.

2.2.4 Photograph scale

It is crucial to insert the scaleµm/px in x-direction and y-direction in the GDPTlab to understand how far the fluorescent beads have moved between photographs in the unitµm. The microchannel is cleaned using the push and pull technique described in 2.2.2. The video recordings can commence when the microchannel is considered clean when inspected through the LMPlanFL 20x/0.4 objective. The videos have the .MP4 MPEG-4 format with average bit-rate: 12 Mbps, average frame-rate: 25 fps and image size: 1440·1080 pixels (px). The length of each video is about 10 seconds long with the top of the channel walls in focus to simplify the determination of the microchannel width in pixels. The video files are split up into sets of .TIF images in MATLAB ®Mathworks utilizing the built-in Video-Reader in a simple .m script see appendix A. The software ImageJ developed by the National Institute

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A-chamber volume is 0.1 mm3_{=0.1 µl=1·10}−4_{ml and its dimensions are 1 mm square sides and 0.1}

mm deep. The next step is to count the fluorescent beads. The bead concentration is documented in .JPEG photographs described in table 2.3.

Image size (px) ISO number Exposure time (s)

6000·4000 1000 1/60

Table 2.3: Camera settings for concentration recording in .JPEG photographs.

The LMplanFL 20x/0.4 objective is selected on the microscope. It is possible to count the fluorescent beads in a sixteenth of one A-chamber in each photograph. Eighty photographs are taken each

in-Figure 2.6: One of the eighty photographs taken to calculate the concentration of a 10 ml mixture comprised of 1_{µl beads and purified water with a 0.01% concentration of TWEEN20.}

cluding one sixteenth of the A-chamber subsequently covering in total five A-chambers. seeking a small error. The fluorescent beads are slightly out of focus in the photos to facilitate counting and making the borders visible. Only, the outer border is considered meaning that the whole A-chamber

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is included in the bead count. Afterwards, equation 2.3 is applied to the number of beads counted to calculate the concentration of what later is referred to as the reference mixture Cref.

Beads/ml = (beads/0.1 mm3) · 103· dilution factor (2.3) where the volume of one A-chamber is 1·1·0.1=0.1 mm3. The concentration of beads in the mixture called reference mixture is Cref=3.98·107beads/ml and the error analysis resulted in the standard

de-viation in the population of beadsσCref=±2.34 · 10

6_beads/ml

2.2.6 The flow experiments

To conduct the flow experiments, the setup in figure 2.7 is complemented with the syringe pump model SP210IWZ loaded with syringes.

Figure 2.7: A detailed view of the microchannel fastened on the microscope stage where the input tube is connected to the syringe pump that pushes the fluorescent beads through the microchannel. The output tube is simply an outlet ending in a petri dish. The vertical height of the 3 ml plastic pump on the syringe pump model SP210IWZ, the microchannel, and the petri dish where the output tube rests is equal to avoid unnecessary pressure differences in the liquid blow. The rubber tubes are cut short.

The raw data consists of videos in the .MP4 MPEG-4 format, size 1440·1080px and average bit-rate 12 Mbps. The camera isα77 from Sony, Japan. A number of settings on the camera are changed between different data series, see table 2.4.

Data series Frame-rate (photos/s) ISO number Exposure time (s) Video duration (s) 160521 25 1600 1/20 10 160709 25 800 1/20 10-20 160710 25 1250 1/20 20

Table 2.4: Camera settings for .MP4 video recordings. The date of the recording is used as the name. The ISO number is changed to counter depletion of fluorescent light intensity. The exposure time is fixed to 1/20 by the camera in video recording mode.

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Table 2.5: The relative bead concentrations of the mixtures used for flow experiments.

The SP210IWZ syringe pump is loaded with a 3 ml Bec. Dic plastic syringe with a diameter equal to 8.59 mm filled with a fixed wolume of 2 ml bead mixture. The flow rate is set on the syringe pump and the microscope is refocused so that the beads traveling farthest away from the middle of the microchannel in both directions have the same sized defocus images. Air-bubbles are removed from the tubes and microchannel by pressing fluid through the system. When the syringe pump has been running for about two minutes into each flow experiment. T beads are traveling with constant velocity and the video recording starts. Observe, the first recording is conducted under light microscopy in order to determine the placement of the microchannel in the images and later in the MATLAB ® figures. These light microscopy images are similar to figure 2.2. Next, the microscope is switched over to fluorescent mode and the flow experiments are conducted in accordance to table 2.6.

Data series Flow rate seriesµl/min 160521 0.2, 0.3, 0.4, 0.5, 0.6 0.7, 0.8, 0.9 and 1.0 160709 0.2, 0.3, 0.4, 0.5, 0.6 0.7, 0.8, 0.9 and 1.0 160710 0.2, 0.3, 0.4, 0.5, 0.6 0.7, 0.8, 0.9 and 1.0

Table 2.6: There are three data series conducted at different dates and the corresponding flow rates used in the experiments.

The videos are converted to grayscale .TIF images acceptable for processing in GDPTlab. It amounts to 61474 images demanding ocular inspection where about 750 images are dedicated to each flow rate and one concentration. To exemplify, 750 images covers Q=0.2_{µl/min with C}ref. This is

neces-sary in order to find series of three images each where particles can be tracked. More specifically, the fluorescent beads in the images must travel in the microchannel under the following conditions: (1) uninterrupted without overlapping other beads, (2) they must be clearly visible in respect to the back-ground and (3) no collisions may take place. This concludes chapter 2 and the presentation of results follows below.

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Chapter 3

Results

The results of this thesis are divided into sections 3.1 and 3.2 treating the calibration of the software to identify the seed particles and the parabolic flow profiles extracted from the flow experiments re-spectively. Naturally the results are based on the experimental procedures and equipment presented in chapter 2.

3.1 Calibration

The software, GDPTlab, is opened in MATLAB® and the 111 grayscale .TIF images with 1µm spacing in z-direction between each photo are loaded into the GDPTlab. Next, the values for segmentation threshold, minimum area, Scale Z and calibration name are filled in. The boxes for vectors, segman-tation and tracks are ticked marked. One can also alter the values for Gussian filter and median filter. These values are left unaltered in this experiment. In figure 3.1, all five beads resting on the bottom of the microchannel are valid and found by the software indicated by the green rings around the beads. The parameter Scale Z is calculated using equation 3.1.

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Figure 3.1: A figure showing the post refresh results.

Scale Z =nfluid nobj · zdist=

1.33

1.33· 1 µm = 1 µm (3.1)

The parameter called Scale Z multiplied with a specific image number tells GDPTlab the real particle position in the Z-direction. The settings in GDPTlab are stated in table 3.1.

Segmentation Minimum area px2

Scale Z

µm Gaussian filter

90 600 1 5·5 kernel

Table 3.1: The settings in GDPTlab during data processing to create the calibration file.

These settings are found to be correct when the yellow/orange ring with a tilted cross in the middle ap-pears. Meaning, that the fluorescent beads are tracked in all 111 images and 110 steps corresponding to the full depth of the microchannel, h=110µm.

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Figure 3.2: A figure showing the post run results.

Actual Z [real units]

0 10 20 30 40 50 60 70 80 90 100 110

Measured Z [real units]

0 100 Correlation Coeff. 0.96 0.98 1

Figure 3.3: An evaluation of the calibration images that shows the results from the normalized corre-lation function and how close the relative intensity of the experimental images are to the theoretical values.

The average value of the 111 Cmvalues is Cmavg=0.9943. This indicates a minute difference between the

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3.2 Parabolic flow profiles

The ocular inspection of the .TIF images from the flow experiments resulted i 116 series of three im-ages where the fluorescent particles are tracked. In GDPTlab, two figures are obtained from each data series. One shows a screen print of the graphical user-interface with the tracked particles and the other figure shows a MATLAB® figure of the tracked particles moving in negative X-direction in the three dimensional microchannel see an explanatory example in figure 3.4 or appendix B for more details. During the data processing in the GDPTlab user interface, one starts by matching the light intensity in the fluorescent beads with the vertical bar immediately to the right of the image. Half of the matching numerical value is a good starting value to insert under Segmentation threshold. When the light intensity of the beads differ, a range of values is tried out in order to track as many beads as possible. The value under Minimum area should be big enough to avoid including background noise. The value of Cm(min. corr. coeff.) can be increased from the default value (i.e. 0.8) to omit changes

in the Z-coordinate during bead displacement. However, this means that a fewer number of beads are tracked. An Output name is typed in to save the X, Y and Z coordinates of the beads in a .MAT file. Finally, the Run button is pressed to generate the three dimensional plot.

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Figure 3.4: The GDPTlab user interface shows eleven identified fluorescent beads illustrated with green rings, six beads which direction is known by GDPTlab and four tracked beads indicated by or-ange rings corresponding to their shapes and a turquoise (or blue) track line. Due to a slightly tilted camera, the beads appear to move in a slope. This is rectified in the presentation of flow results by letting the first Y-coordinate be the constant Y-coordinate of one specific bead trajectory in the mi-crochannel. Similarly to other particle tracking studies, the trajectories of overlapping beads are diffi-cult and sometimes impossible to obtain. Here, regardless of segmentation and min. area values.

When satisfied with the results, the three dimensional plot (i.e. a .FIG image) is exported to a .PNG im-age for presentation see figure B.1b and the coordinates of valid tracked beads are manually extracted from the saved .MAT file to be plotted in assemblies of flow results. It should be mentioned that X=0 is the starting point of all the velocity vectors from figure 3.6 to 3.21 however the length of the fluorescent bead displacement is preserved.

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Figure 3.5: Data generated by GDPTlab and depicted in a MATLAB ®figure. One single tracked fluo-rescent bead is extracted from this image series (i.e. three consecutive .TIF images Q=0.2µl/min and Creffrom 160521)

In this section of the thesis, the experimental flow results (i.e. tracked particles) from one individual flow rate are inserted into a MATLAB® figure showing one assembly of flow results where the particles are propagating in positive X-direction presented in one YX-plot and one ZX-plot for respective flow rate. The X-axis is labeled with the velocityµm/s. The velocities of the fluorescent beads are calculated using the time delay between consecutive images see equation 3.2.

∆t = tvid

Nimg− 1=

10s

250 − 1≈ 0.04 s/gap (3.2)

where tvidis the length of the video recording of the flow experiment and Nimg− 1 is the total

num-ber of time delays between the images from the recording. The time gap=0.04 s is a description of the time delay between consecutive images. Observe, the displacement inµm from the three dimen-sional MATLAB ® plot is divided by∆t=0.08 s because the processed image series contain three im-ages. Flow experiments with two different concentrations (Crefand 54Cref) are presented. However,

in practice, parabolic flow profiles can not be extracted from data with concentrations higher than Cref. In appendix B, one can see that the particles in focus are often excluded even though a range

of segmentation values are used attempting to locate these fluorescent beads. This might explain the limited tracking capabilities in the Z-direction and the misleading range approximately from 42µm

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to 58µm but not the fact that Z=55 µm is supposedly the exact middle of the microchannel. Meaning that the range indicated on the Z-axes of all the ZX-plots can be incorrect.

3.2.1 Assemblies of flow experiments with C

ref

The three dimensional plots presented below include particles that travel straight with only small devi-ations in z-direction. In addition, it is crucial that the whole width of the microchannel is represented in the results to confirm the non-slip boundary condition. The flow rate Q is converted into a velocity V0= Q/A where A is the cross-section area of the microchannel. The Reynolds number is presented

for each experiment conducted under a specific flow rate. The concentration Cref± σCref=3.98·10

7_±

2.34 ·106beads/ml is used in the flow experiments under 3.2.1. The flow experiments start with Q=0.2 µl/min

Flow rate 0.2µl/min

The assembly of the experimental flow results in figure 3.6 show a parabolic flow profile that covers the whole width of the microchannel counting from 65_{µm to 175 µm on the Y-axis and the} veloc-ities decrease closer to the walls according the non-slip condition. The Reynolds number is Re≡ ρV0L0/η=0.0013 placing the flow well within the range of laminar flow (i.e. Poiseuille flow) and the

linear Navier-Stokes equation is valid in the experiment.

X axis [ µm/s] 0 50 100 150 200 250 300 350 400 Y axis [ µ m] 60 80 100 120 140 160 180

Figure 3.6: The assembly of the tracked particles subject to the static flow rate 0.2µl/min in an YX-plot.

In the ZX-plot, the velocity vectors only represent a small portion of the 110µm deep microchannel in detail from 42µm to 58 µm from the bottom of the channel. However the velocities of the particles at 58µm is greater than that of the particles closer to the bottom. In figure 3.7 there are a number of par-ticles traveling slightly upwards or downwards, this is a phenomenon that can be explained by a low correlation coefficient threshold adjusted under Cm(min corr. coeff.) in the GDPTlab user interface.