Microalgae particles Chlorella vulgaris (UMACC 001) as shown in Fig. 1 have an average diameter of and are chosen as the test particles due to their rigid cell wall, spherical shape and unicellular cell. This tropical Chlorella were cultured in Bold basal medium (BBM) and maintained under controlled-environment incubator at 28 °C, illuminated with cool white fluorescent lamps (Philips, TLD 18W/54-765) providing 42- PAR for 12 hours of light: 12 hours of dark cycle. All the characterization measurements were carried-out at room temperature of 25 °C.

Fig. 1.

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	Fig. 1. (color online) Chlorella vulgaris under light microscope with 10× magnification.

Chlorophyll-a (Chl-a) concentration was determined via spectrophotometric method (Strickland & Parson, 1968). Firstly, a 20-mL algal culture collected on a glass-fiber filter paper (Whatman GF/C, ) was mashed into small pieces by using tiny glass rod. Hand-homogenizer with 10-mL analytical grade 100% acetone was used to soak the sample. The test tube with samples were then covered with aluminum (Al) foil and left overnight in dark in the refrigerator (4 °C). On the next day, the samples were centrifuged (3000 rpm, 10 minutes, 4 °C) and absorptions of the supernatant were measured at 630 nm ( ), 645 nm ( ), and 665 nm ( ), respectively. The Chl-a concentration was calculated from where , is the volume of acetone used for extraction, and is the volume of culture.

Carotenoid content of microalgae was determined with the same method used for determining the Chl-a, however the supernatant absorption was measured at 452 nm (IO452 nm). The absorbance of the pigment was extracted following the colorimetric method described by Vonshak and Borowitzka.^[47] Carotenoid content was then calculated as , where is the absorbance at 452 nm, is the volume of acetone used for extraction and is the volume of the algal culture filtered (mL). Both supernatant absorption on Chl-a concentration and Ca content were measured using Shimadzu UV-vis spectrometer.

The potential stability of the colloidal system, i.e., whether the cell will aggregate or disaggregate depends on the magnitude of zeta potential.^[48] Zeta potential is the measure of surface charges of cell where high potential corresponds to strong electrical repulsion between the algal cells, which leads to highly stable suspension. Meanwhile, lower Zeta potential means that the particles will attract each other by the van der Waals force and flocculated effect.^[49] Zeta potential was measured via a zeta analyzer (Malvern Instruments Ltd.) with water as dispersant. Fresh algae medium solution, BBM at pH 6 was used as the background fluid. The viscosity of the BBM was measured by using falling ball viscometer (Thermo Fisher Scientific) and repeated five times to obtain the average. Results of algae and medium parameters characterizations are summarized in table 1.

Table 1.

Table 1.

Table 1. Algae and medium parameters characterization results. . Algae and medium parameters Values Number of cell (NP) 3539700 cells Chlorophyll content (Chl-a) 0.0013 ±0.001 mg/L Carotenoid content (Ca) 0.2850±0.0001 mg/L Zeta potential (ζ) −20.1 ±5.79 mV Viscosity of medium ( ) 1.11 ±0.13 mPa/s Temperature (T) 25.0 ±0.1 °C

Table 1. Algae and medium parameters characterization results. .

The presence of ionic group such as carboxyl and phosphate in C Vulgaris cell wall leads to the formation of negatively charged surface.^[50] We will now refer to microalgae as the particle in our next discussion unless otherwise mentioned.

Experiment was conducted via a microfluidic chip device in a pressure-driven control system as shown in Fig. 2. It consisted of pressure controller, reservoir, flow sensor, Y-junction microfluidic chip, high speed CCD camera, and zoom lens. The system was pressurized using air compressor. Supplied pressure was stabilized and controlled via the pressure controller where the feedback when pressure changes was monitored on computer. Additionally, the pressure controller was coupled with a flow sensor and through the feedback loop to control the flow rate into the microfluidic setup. This feedback loop allowed us to maintain the stability and responsiveness of the pressure driven flow. All the tracking was done within 24 hours to avoid contamination within the algae suspension due to its respirational waste product.

Fig. 2.

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	Fig. 2. (color online) Schematic setup of the microfluidic flow experiment.

The chip was initially filled with deionized water, and then the BBM solution with a flow rate of to wash away the dirt and unwanted suspensions. Then, particle suspension dispersed in BBM was pressurized inside the reservoir before it was released into the microfluidic chip by controlling the pressure between inlet and outlets via pressure controller (OB1 Elvesflow) to initiate the intended flow rates. In these experiments, the flow rates were chosen to be and due to the stabilities of flow produced. The flow was then allowed to stabilize for 10 minutes. The motion of particles was captured at a distance of L = 2.1 cm away from the entrance of the channel using a Mikrotron CCD camera. Images were captured at frame rates from 2000 fps to 3000 fps depending on the applied flow rates with the aid of illumination by a high-power LED light source. The light was focused using the mirror located under the microfluidic stage. Capturing the motion of fast particles with high frame rate will reduce the image quality due to less photons hitting the sensor; yet small frame rate means less information about the particles motion. Hence, the suitable frame rate was chosen by compensating for the speed of the flow and light illumination, which was in a range of 2000 fps–3000 fps.

The procedures for particle tracking involves two steps, namely (i) segmentation step thereby the particles are identified from the background in each frame, and (ii) linking step: identifying similar particles from frame to frame and making connections.^[36] The implementation of the individual particle tracking was performed using FIJI Track Mate plug in particle tracking open source software.^[51] The outcomes of these procedures are shown in Fig. 3 for one image frame.

Fig. 3.

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	Fig. 3. (color online) Visualization of images preprocessing: (a) raw input image, (b) far field correction, (c) image enhancement, (d) pseudo-fluorescence image, and (e) particle detection.

Raw images obtained from the microfluidic experiment were hardly visible as shown in Fig. 3(a). Therefore, using image processing technique, better contrast of particles from the background was achieved (Fig. 3(c)). The images pre-processing was carried-out using FIJI image-processing software. Steps of pre-processing consist of background subtraction, image enhancement and pseudo-fluoresce transformation as shown in Fig. 3(d).

Dirt on the camera lens is a common type of artifact in digital imaging system as spotted in the image shown in Fig. 3(a). To remove this artifact, the second image from the stack images was chosen as the “flat-field” reference image, where the correction is done by exerting the division arithmetic operation on the images i.e., img1 = img1/img2 producing image as shown in Fig. 3(b). The white spots are the artifacts left from the particles, which appeared in the second images, whereas the black spots are the particles of interest. Next, the enhancement of particles spots was achieved using nonlinear filter such as minimum filter to dilate the spots and also to remove the artifacts left from previous image corrections. These spots were enhanced by dilating the spots to size of two pixels. After this, the image brightness and contrast were adjusted to create dark objects against the bright background (Fig. 3(c)). Then, the logical XOR operation was exerted onto the image to transform transmitted light contrast images into pseudo-fluorescence images, enabling them to be suitable for processing by tracking tools design for fluorescence microscopy as shown in Fig. 3(d). Finally, the particles were tracked based on their threshold minimum radius, maximum linking distance and the maximum gap between images. Maximum linking distance is chosen by measuring the average minimum distance of the particles between the frames, which is .

For this pressure driven flow system, we assumed the uniform Poiseuille flow profile has been fully developed inside the microchannel. In this flow, near the channel wall region, velocity of flow was minimal while maximum velocity developed near the center of the channel as illustrated in Fig. 4. The particles introduced inside the channel will inherit the velocity from the flow profile. Consequently, the rate of particles transport will be differed with respect to the profile regions.

Fig. 4.

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	Fig. 4. (color online) Schematic diagram of studied problems. The lighter color areas refer to near wall boundaries NB1 and NB2, respectively. The darker color region represents the center region C.

Therefore, we grouped the particle trajectories with respect to the region of flow profile, namely near the wall boundary NB₁ near the wall boundary NB₂ and center C. In order to roughly estimate the flow regions, we used the expected equilibrium position migration of particles termed as Segré–Silberberg radius,^[4,52,53] which is 60% with respect to the center plane as our reference. For the symmetrical rectangular channel of (width × height), we obtained the equilibrium position of with respect to the hydraulic radius of the channel R. Based on the , the estimate length of near wall boundaries regions are given as and , respectively, whilst the center of channel region as . Here, the x direction corresponds to the (longitudinal (streamwise) direction and the y direction is the transverse direction, perpendicular to the x direction.

Trajectories of individual particles were found using the FIJI plug in algorithm that links a particle in one field to the most probable closest particle in the next field with travel distance less than inter particles spacing. The relevant particles trajectories were chosen based on imposed criterions on the mean velocity, duration of track, displacement and number of spots to avoid tracking “fake” particles. In addition, due to the presence of upper wall in z direction some of the particles might turn stuck and become immobile. These immobile particles were excluded from our analysis.

Figure 5 illustrates the trajectories of microalgae particles at each respective flow rate. One can observe “oscillation” like trajectories of particles at (Fig. 5(a)). This oscillatory motion was observed by other researchers,^[15] and occurred due to some of the particles trapped between the particles layer/volume layer. Additionally, deviation of the particles from the streamlines can also be explained due to the particles becoming trapped in minimum potential.^[54] Under the Poiseuille flow, the acceleration of flow profile and the fluctuations perpendicular to the flow direction caused the particle mean position to shift in potential via . In NB₁ and NB₂ regions, some of the particles diffuse normally before their motion follows the streamlines.

Fig. 5.

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	Fig. 5. (color online) Representative sample of particles trajectories under flow rates of (a) and (b) .

Trajectories of the particles under flow rate (Fig. 5(b)) are “smoother” than under the flow rate. The particle motions follow the streamline, yet one can notice that some of particles undergo sudden jumps. The particles trajectories are expanded into their respective x and y directions as illustrated in Fig. 6.

Fig. 6.

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	Fig. 6. (color online) Spatial x and y trajectories of the representative sample of 43 particles under flow rate of . (a) Trajectories in the streamwise x direction. (b) Trajectories perpendicular to flow in the y direction.

We used the time averaged MSD (TAMSD) at lag time τ over a trajectory length M to characterize the particle dynamic 7 Particle trajectories data points were trimmed into a minimum of 100 points for , and 50 points for . Then, the TAMSD of the individual particle at time t was obtained by averaging MSD at each lag time τ. Figure 7 shows the TAMSD where in each case, the thin line represents from 20–102 different trajectories. Meanwhile the solid black line represents their average . Thus, the scaling exponent can be extracted by using the linear least squares regression on the log–log TAMSD curve. In this case, slope of the curve represents the scaling exponent.

Fig. 7.

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	Fig. 7. (color online) Log–log plots of TAMSDs of individual particle trajectories against lag time in (a) the x direction and (b) the y direction.

In the direction perpendicular to the flow (Fig. 8), we observe two power law regimes on different time scales in all regions for slow and fast flows. The scaling exponents in the short time interval ( ) or ( ) in the respective different flow rate cases indicate the existence of the slow transport, which later ( ) or ( ) switches to the fast transport mode.

Fig. 8.

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	Fig. 8. (color online) Log–log plots of MSD in the perpendicular direction versus lag time for three different regions NB1 (blue circles), NB2 (green triangles), and C (red rectangle) under flow rates: (a) and (b) .

Under slow flow rate , the particles behave sub-diffusively at shorter time with MSD scales as , , and for NB₁, NB₂, and C respectively as seen in Fig. 8(a). However, in long time it changes into a faster dynamic , , and . The scaling exponents in both near wall boundary regions NB₁ and NB₂ respectively, show the strong sub-diffusion behavior at shorter time, then switch to the weak sub-diffusion at longer time. Interestingly in the region of the channel core, the scaling exponents at shorter time show weak sub-diffusion behavior then change into normal diffusion in longer time interval. This shows the presence of slow and fast modes, which can be related to caging effect and dispersive transport respectively. On a small time scale, motion is sub-diffusive corresponding to thermal motion in viscoelastic medium since the MSDs have exponents less than 1. The crossover takes places at , which reflects the rheology and speed of the flow. The maximum scaling exponent is observed in region C, where the particle transports are in accordance with normal diffusion or Brownian motion.

Under fast flow at , the particles behave sub-diffusively in a shorter time with MSD scale as , , and for NB₁, NB₂, and C respectively, as seen in Fig. 8(b). The scaling exponent values show reducing trend from NB₁, NB₂, to C regions. Sub-diffusion NB₁ and NB₂ is due to the wall effect that restricts the perpendicular displacement of particles. At the same time, channel center sub-diffusion may occur if stagnation or recirculating region exists in the fluid flow causing the particles to be trapped. Some of particles in the region C migrate quickly to the NB₁ or NB₂ where they are trapped for instant, while others move back to the C region. This has also been reported elsewhere.^[15] Yeo and Maxey^[15] suggested that the explanation of this behavior was due to the length scale restriction by the size of confinement that leads to the large-collective motion such as the formation of hydro-cluster by the size of confinement. In a long time, this changes into super-diffusive for faster dynamic with MSD scale as , , and for NB₁, NB₂, and C respectively, due to the irregular jump and particle entrapment in particle layers. We also observe a similar pattern of transition pattern to that in the previous case, but in a much shorter time as .

There are noticeable changes of scaling behaviors as we observe two power law behaviors at both slow and fast flow. Thus, one can model the transition based on the SBM by introducing different scaling exponents for short time α₁ and long time α₂ as shown below. 8 where is the crossover time. The results are summarized in table 2.

Table 2.

Table 2.

Table 2. MSDs scaling in perpendicular direction results. . Flow rate/ Cases α1 α2 /ms NB1 0.23±0.01 0.88 ±0.01 3.00 0.2 NB2 0.16 ±0.03 0.85±0.02 3.00 C 0.19 ±0.02 1.05 ±0.01 3.00 NB1 0.73 ±0.03 1.70 ±0.03 2.00 0.3 NB2 0.61 ±0.03 1.69 ±0.01 2.00 C 1.62 ±0.03 2.00

Table 2. MSDs scaling in perpendicular direction results. .

Presuming that both the NB₁ and NB₂ regions are symmetrical with respect to the center C, we observed that the scaling exponents obtained are different as seen from the results in table 2. At the early flow time, the percentage differences of the scaling exponent α₁ between regions NB₁ and NB₂ are 36.0% and 18.0%, in the cases of and , respectively. The large percentage differences observed in symmetric regions NB₁ and NB₂ indicate that the particle dynamic is not-symmetric. This behavior seems to contradict our assumptions on the symmetrical Poiseuille velocity flow profile. Meanwhile, for latter flow time, the percentage differences of α₂ are significantly reduced to 3.5% at , and 0.6% at , respectively. The particles eventually exhibit almost symmetrical behavior as the flow develops. The non-symmetrical particle behavior at early time can be explained in terms of the instability of the local flow. In the simulation, one can perfectly assume flow symmetry with respect to the region of interest. However, in the real fluid flow experiment, theoretical assumption of Poiseuille can only be approximately valid due to the contributions of the local variations in the flow.

Next, as we compare regions NB₁ and NB₂ with region C, the percentage differences of scaling exponent α₁ are 19.0% and 17.1%, respectively for 0.2 L/min. Meanwhile for , the differences in respective percentage of between these regions are 28.1% and 10.3%, respectively. At latter time, the percentage differences of scaling exponent α₂ are 17.6% and 21.1% for and 4.8% and 4.2% for in the respective flow regions. The difference of the scaling exponent α₁ is relatively high at early stage while at the latter time, the difference is almost in the same order of magnitude. This behavior can be explained in terms of high fluctuation existing at the early time of particle flow due to the wall effect and flow instabilities before the fluctuation diminishes at the latter time.

In our initial assumptions, the C Vulgaris cells are considered to behave like passive tracers where the effects of their mass and inertia are negligible. Thus, the cells will instantaneously acquire the velocity profile from the fluid flow. However, C Vulgaris is a naturally buoyant and finite-size particle. Finite-size particles have finite sizes and mass values. Due to the particle’s inertia, they are not able to instantaneously adapt themselves to fluid velocity as described by the Maxey–Riley equation.^[55] It is worth mentioning here that the addition of the stochastic term in the Maxey–Riley equation can gives rise to the fluctuation on the path experienced by the particle.^[56]

Introduction of the cross-over time, enables us to characterize the dynamic of the particles in different time regimes. At early transient time ( ), the particle inertia contributes to slower dynamic. As the flow evolves, at latter time , the particle eventually acquires the fluid velocity. During this excursion period, the path of the particle tends to fluctuate. This is attributed to the mismatch of the particle’s velocity to the flow’s velocity. Even the small mismatch of these velocities can give rise to the stagnation point in flow.^[57] We observed that the cross-over times are ms for the case of and ms for (refers to table 2), respectively. The difference in the suggests that at slower flow, the particle takes a longer time to overcome its inertia at lower flow before it can be transported along by the local flow.

For the flow rate of , in the stream-wise direction, we observe bi-scaling power-law regimes on different time scales as shown in Fig. 9(a). The short-time scale particles for all regions behave as weak super-diffusion with MSD scales as , , and for NB₁, NB₂, and C, respectively. However, for longer time, it changes into a faster dynamics with MSD scales as , , and and for NB₁, NB₂, and C respectively. The crossover of the particle dynamics occurs at transition time which is similar to that in the case of perpendicular direction. For the particles located at the center of the channel, the wall effect has a minimum role in the transport of the microalgae. When the particle is initially placed at a distance hfrom the wall to the center of particle ( ), the presence of particle-wall interaction changes the value of scaling exponent/diffusivity of the particle.

Fig. 9.

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	Fig. 9. (color online) Log–log plots of MSD at streamwise direction versus lag time for three different regions NB1 (blue circles), NB2 (green triangles), and C (red rectangle) at (a) and (b) .

The percentage difference in scaling exponent α₁ between NB₁ region and NB₂ region is 5.0% and that in scaling exponent α₂ is 4.4% for . These relatively small percentage differences suggest the behaviors of the particles are nearly symmetric in these regions, which is opposite to the case of perpendicular direction. This symmetrical nature is due to the fact that the particles dynamics in streamwise direction has less fluctuations. For the particles at the near wall boundary, the space for the surrounding fluid to interact is reduced and the corresponding drag force in the direction of the wall is therefore higher, thus causing the scaling exponent value to decrease.

Comparing the scaling exponents in regions NB₁ and NB₂ with that in region C, we note that percentage differences of 1.7% and 3.5%, respectively for α₁, while for α₂ the percentage differences are both 2.2%. Again, this result indicates the near symmetrical behavior of the particles in both regions NB₁ and NB₂. Surprisingly, we find the small reduction in the scaling exponent values of α₁ and α₂ in region C compared with those in the NB₁ region (see table 2). These reduced scaling exponents in region C can be explained by the fact that some of the particle core region quickly moves to the NB₁ region, thus causing the motion of the particle to slow and the isotropy of the particle MSD in the Poiseuille flow to break.

At a higher flow rate of , no significant transition of the scaling exponent is observed in all the three regions; resulting in MSD scales as , , and for NB₁, NB₂, and C, respectively with mono-scaling exponents as shown in Fig. 9(b). The percentage differences in scaling exponent between regions NB₁ and NB₂ is 2.0%. When comparing the regions NB₁ and NB₂ with C, the resulting percentage differences are 3.1% and 0.5%, respectively. The behavior of the particles can be assumed to be almost symmetric. The particles are transported almost at the same rate. Under the fast fluid flow, advection dominates the transport of the particles, so that the particles in regions NB₁ and NB₂ do not experience significant wall effect.

Like the case of perpendicular direction, we observe noticeable changes in scaling behavior only at the lower flow rate and the MSDs shows mono-scaling behavior for higher flow rate. We note that the crossover time appears at , which is the same as in the case of motion in the perpendicular direction. However, this transition only occurs in the case of . Once again, one may relate this behavior to the fact that C Vulgaris has finite particle size and undergoes higher fluctuations at slower flow. At the particle undergoes transient state, where it takes the time to overcome its inertia before it can move along the surrounding flow at . In the case of fast flow ( ), the fluctuations diminish as as a result of high advective flow. The particle is able to adapt its motion with local fluid velocity without experiencing any transient state. The results are summarized in table 3.

Table 3.

Table 3.

Table 3. MSD scales in streamwise direction. . Flow rate/( ) Cases α1 α2 /ms NB1 1.20 ±0.01 1.86 ±0.01 3.00 0.2 NB2 1.14 ±0.02 1.78±0.01 3.00 C 1.82 ±0.01 3.00 NB1 none 1.92 ±0.01 none 0.3 NB2 none 1.97±0.01 none C none 1.98 ±0.01 none

Table 3. MSD scales in streamwise direction. .

The limitations and sources of error of the system used in this study, which may affect the accuracy of the MSD values are briefly discussed below. Among the factors that influence the microfluidic chip operation and contribute to experimental errors are the instability of the applied pressure at low flow rate, unpredictable pressure differences, change of pH of the suspension from the algae cell activities, and heating of solution due to constant exposure to light from illumination source. Since the flow rate plays a key role in microfluidic system operation, the feedback control between the pressure controllers with flow sensor is monitored constantly. Yet, there is possibility that the particle will accumulate in the sensor capillary. Therefore, to ensure that the flow rate feedback is accurate, the device must be cleaned after use to prevent the solids from depositing.

A critical parameter for high quality fast video-based particle tracking is the number of photons that can be detected by the camera CCD array. Higher frame rate means that the shorter exposure, which implies higher illumination level, is needed. Therefore, as the frame rate increases, spatial resolution decreases. For the future study, the accuracy of particle tracking experiment at the high flow rate can be improved by using coherent light source to provide high and focused illumination without damaging the cells. In addition, burst of high frame rate is also limited by computer memory, leading to small sampling time and additional issues in data processing. The accuracy of TAMSD calculation depends on the algorithm used for particle tracking. During the pre-processing stage, there are possibilities to artificially create spurious spots, which may lead to the creation of artificial ‘particles’ and hence trajectories. A careful observation shows that the artificial particles due to the noise induced image artifacts are dim and smaller, while the aggregates of endogenous particles are large and bright. To improve accuracy, we manually examine the observed trajectories by closely following the consecutive frames to ensure that the proper trajectories are used for determining the time average mean squared displacements.