I. INTRODUCTION

Section:

ChooseTop of pageABSTRACTI. INTRODUCTION <<II. MATERIALS AND METHODSIII. SWIMMING BEHAVIOR OF...IV. MICROALGAE SEPARATION...V. A SIMPLE MODELVI. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCESWhile the potential applications of microswimmers and microrobots in biomedicine and biotechnology are developing rapidly,11. A. I. Bunea, D. Martella, S. Nocentini, C. Parmeggiani, R. Taboryski, and D. S. Wiersma, Adv. Intell. Syst. 3, 2000256 (2021). https://doi.org/10.1002/aisy.202000256 an efficient manipulation of fluid flow to drive them to a target zone remains a challenge. Recent studies opened up some promising prospects to develop biocompatible microswimmers powered by in vivo-friendly means.22. A. I. Bunea and R. Taboryski, Micromachines 11, 1048 (2020). https://doi.org/10.3390/mi11121048 Microalgae were used as biodegradable carriers for drug delivery and environmental remediation.33. G. Santomauro, A. V. Singh, B. Park, M. Mohammadrahimi, P. Erkoc, E. Goering, G. Schütz, M. Sitti, and J. Bill, Adv. Biosyst. 2, 1800039 (2018). https://doi.org/10.1002/adbi.201800039 It was shown that the unicellular photosynthetic algae Chlamydomonas reinhardtii can transport microscale loads.44. D. B. Weibel, P. Garstecki, D. Ryan, W. R. DiLuzio, M. Mayer, J. E. Seto, and G. M. Whitesides, Proc. Natl. Acad. Sci. U.S.A. 102, 11963 (2005). https://doi.org/10.1073/pnas.0505481102 Living cells can also be used as actuators within artificial machines designed at small length scales.55. L. Ricotti, B. Trimmer, A. W. Feinberg, R. Raman, K. K. Parker, R. Bashir, M. Sitti, S. Martel, P. Dario, and A. Menciassi, Sci. Robot. 2, eaaq0495 (2017). https://doi.org/10.1126/scirobotics.aaq0495 In biomedicine, an accurate control mechanism is needed to transport the algal microrobots to the body cavities. It was demonstrated that living micromotors based on single algal cells can be used as living micromotors controlled by optical force for manipulation of biological targets and disruption of biological aggregates.66. H. Xin, N. Zhao, Y. Wang, X. Zhao, T. Pan, Y. Shi, and B. Li, Nano Lett. 20, 7177 (2020). https://doi.org/10.1021/acs.nanolett.0c02501 In biotechnology, conventional biomass harvesting, one of the key steps in the production of biofuels from non-feed stocks, is a complex and costly process (20%–30% of the total cost) due to the small size and low-density difference between the photosynthetic micro-organisms and their growth medium.77. A. I. Barros, A. L. Gonçalves, M. Simões, and J. C. M. Pires, Renewable Sustainable Energy Rev. 41, 1489 (2015). https://doi.org/10.1016/j.rser.2014.09.037 Novel low-cost techniques are, thus, required to substitute or improve the present downstream separation processes.Microfluidics offers an enticing alternative for particle separation and particle focusing. Microfluidic methods proposed for separation of cells and microparticles are broadly classified into two types: passive and active.88. P. Sajeesh and A. K. Sen, Microfluid Nanofluid 17, 1 (2014). https://doi.org/10.1007/s10404-013-1291-9 Passive techniques, such as membrane-microfiltration,99. L. Chen, M. E. Warkiani, H.-B. Liu, and H.-Q. Gong, J. Micromech. Microeng. 20, 075005 (2010). https://doi.org/10.1088/0960-1317/20/7/075005 pinched flow fractionation,1010. M. Yamada, M. Nakashima, and M. Seki, Anal. Chem. 76, 5465 (2004). https://doi.org/10.1021/ac049863r deterministic lateral displacement,1111. L. R. Huang, E. C. Cox, R. H. Austin, and J. C. Sturm, Science 304, 987 (2004). https://doi.org/10.1126/science.1094567 hydrodynamic filtration,12,1312. M. Yamada and M. Seki, Anal. Chem. 78, 1357 (2006). https://doi.org/10.1021/ac052008313. M. Kersaudy-Kerhoas, R. Dhariwal, M. P. Y. Desmulliez, and L. Jouvet, Microfluid Nanofluid 8, 105 (2010). https://doi.org/10.1007/s10404-009-0450-5 inertial separation,1414. M. E. Warkiani, A. K. P. Tay, G. Guan, and J. Han, Sci. Rep. 5, 11018 (2015). https://doi.org/10.1038/srep11018 and centrifugal microfluidics,1515. R. Martinez-Duarte, R. A. Gorkin III, K. Abi-Samra, and M. J. Madou, Lab Chip 10, 1030 (2010). https://doi.org/10.1039/b925456k are based on the geometrical effects of microchannels, hydrodynamic forces, and fluid–particle interactions. Inertial microfluidics is widely used due to its simplicity and accuracy.14,16,1714. M. E. Warkiani, A. K. P. Tay, G. Guan, and J. Han, Sci. Rep. 5, 11018 (2015). https://doi.org/10.1038/srep1101816. D. Lee, S. M. Nam, J. Kim, D. Di Carlo, and W. Lee, Anal. Chem. 90, 2902 (2018). https://doi.org/10.1021/acs.analchem.7b0514317. S. C. Hur, H. T. K. Tse, and D. Di Carlo, Lab Chip 10, 274 (2010). https://doi.org/10.1039/B919495A A competition between shear gradient lift force directing particles away from the channel center and wall lift force pushing the particles away from the wall vicinity determines the stable equilibrium position of particles. This method is effective when there is a large difference in cell size between species, especially to separate bacteria from microalgae1818. N. Godino, F. Jorde, D. Lawlor, M. Jaeger, and C. Duschl, J. Micromech. Microeng. 25, 084002 (2015). https://doi.org/10.1088/0960-1317/25/8/084002 and also for harvesting small cells from a culture medium.1919. L. Wang and D. S. Dandy, Algal Res. 26, 481 (2017). https://doi.org/10.1016/j.algal.2017.03.018 However, the method is inefficient when the cells are motile with a high swimming velocity such as the well-known model alga, Chlamydomonas reinhardtii. These swimmers cross the flow streamlines easily; thus, the equilibrium position mentioned above cannot be reached.Contrary to the passive methods, active techniques require the involvement of external fields. Acoustophoresis,2020. P. Li, Z. Mao, Z. Peng, L. Zhou, Y. Chen, P.-H. Huang, C. I. Truica, J. J. Drabick, W. S. El-Deiry, M. Dao, S. Suresh, and T. J. Huang, Proc. Natl. Acad. Sci. U.S.A. 112, 4970 (2015). https://doi.org/10.1073/pnas.1504484112 magnetophoresis,2121. S. Miltenyi, W. Müller, W. Weichel, and A. Radbruch, Cytometry 11, 231 (1990). https://doi.org/10.1002/cyto.990110203 optical tweezers,2222. D. G. Grier, Nature 424, 810 (2003). https://doi.org/10.1038/nature01935 and dielectrophoresis (DEP)2323. I.-F. Cheng, H.-C. Chang, D. Hou, and H.-C. Chang, Biomicrofluidics 1, 021503 (2007). https://doi.org/10.1063/1.2723669 are some examples of active methods. The last one (DEP), consisting of lateral movement of a dipole particle in a non-uniform electric field, has already been used to separate microalgae of a suspension based on their intracellular lipid content.24,2524. Y.-L. Deng, M.-Y. Kuo, and Y.-J. Juang, Biomicrofluidics 8, 064120 (2014). https://doi.org/10.1063/1.490394225. S.-I. Han, H. S. Kim, K.-H. Han, and A. Han, Lab Chip 19, 4128 (2019). https://doi.org/10.1039/C9LC00850K Aside from the device complexity, the main drawback is that both high-intensity electric field near the electrode edges and joule heating cause cell damages.Light has been used as an actuator for light-powered microrobots.11. A. I. Bunea, D. Martella, S. Nocentini, C. Parmeggiani, R. Taboryski, and D. S. Wiersma, Adv. Intell. Syst. 3, 2000256 (2021). https://doi.org/10.1002/aisy.202000256 Some motile micro-organisms are able to reorient their swimming direction toward or against a light source.26–3126. J. Dervaux, M. Capellazzi Resta, and P. Brunet, Nat. Phys. 13, 306 (2017). https://doi.org/10.1038/nphys392627. J. Arrieta, A. Barreira, M. Chioccioli, M. Polin, and I. Tuval, Sci. Rep. 7, 3447 (2017). https://doi.org/10.1038/s41598-017-03618-828. T. Vourc'h, J. Léopoldès, and H. Peerhossaini, J. Fluids Eng. 142, 031109 (2020). https://doi.org/10.1115/1.404595129. A. C. H. Tsang, A. T. Lam, and I. H. Riedel-Kruse, Nat. Phys. 14, 1216 (2018). https://doi.org/10.1038/s41567-018-0277-730. K. Drescher, R. E. Goldstein, and I. Tuval, Proc. Natl. Acad. Sci. U.S.A. 107, 11171 (2010). https://doi.org/10.1073/pnas.100090110731. H. de Maleprade, F. Moisy, T. Ishikawa, and R. E. Goldstein, Phys. Rev. E 101, 022416 (2020). https://doi.org/10.1103/PhysRevE.101.022416 This behavior, called phototaxis, has shown great potential for separation or focusing of microalgal cells. Kim et al.3232. J. Y. H. Kim, H. S. Kwak, Y. J. Sung, H. I. Choi, M. E. Hong, H. S. Lim, J.-H. Lee, S. Y. Lee, and S. J. Sim, Sci. Rep. 6, 21155 (2016). https://doi.org/10.1038/srep21155 proposed a microfluidic system using competitive phototaxis of Chlamydomonas reinhardtii to isolate strains with improved photosynthetic efficiencies. Kreis et al.3333. C. T. Kreis, M. Le Blay, C. Linne, M. M. Makowski, and O. Bäumchen, Nat. Phys. 14, 45 (2018). https://doi.org/10.1038/nphys4258 showed that Chlamydomonas reinhardtii's flagella provide light-switchable adhesive contacts with the surface. This reversible adhesiveness is a natural functionality of microalgae to regulate the transition between the planktonic and the surface-associated state to optimize the photosynthetic efficiency in combination with phototaxis. Lam et al.3434. A. T. Lam, K. G. Samuel-Gama, J. Griffin, M. Loeun, L. C. Gerber, Z. Hossain, N. J. Cira, S. A. Lee, and I. H. Riedel-Kruse, Lab Chip 17, 1442 (2017). https://doi.org/10.1039/C7LC00131B developed a hardware setup and a set of executable commands to control the motion of Euglena gracilis by applying spatiotemporal light stimuli. Garcia et al.3535. X. Garcia, S. Rafaï, and P. Peyla, Phys. Rev. Lett. 110, 138106 (2013). https://doi.org/10.1103/PhysRevLett.110.138106 reported that by coupling the effects of positive phototaxis and vorticity, the Chlamydomonas reinhardtii cells are accumulated near the center of a Poiseuille flow where the shear rate is at its lowest level (theoretically zero at the center) in the channel.While the flow regime in most of the separation techniques is steady, a few studies investigated the advantage of pulsatile regimes. Pulsatile flow was used to separate out different dilute species present in a carrier.3636. A. M. Thomas and R. Narayanan, Ann. N.Y. Acad. Sci. 974, 42 (2002). https://doi.org/10.1111/j.1749-6632.2002.tb05895.x A high removal efficiency, close to 100%, was achieved for a triple-channel separator working under a pulsatile regime at high frequency.3737. C. J. Lee, H. J. Sheen, H. C. Chu, C. J. Hsu, and T. H. Wu, J. Micromech. Microeng. 17, 439 (2007). https://doi.org/10.1088/0960-1317/17/3/004 Particles of multiple sizes were sorted in a microdevice operating under time series alternate flow at various actuating frequencies.3838. G. Su and R. M. Pidaparti, J. Nanotechnol. Eng. Med. 2, 021006 (2011). https://doi.org/10.1115/1.4003930 Oscillatory flow was also applied for separating species of different diffusion coefficients in rectangular channels and it was shown that the efficiency depends on the channel aspect ratio, the Schmidt number of the solutes, the Womersley number, and the dimensionless oscillation amplitude.3939. A. Hacioglu and R. Narayanan, Phys. Fluids 28, 073602 (2016). https://doi.org/10.1063/1.4954316 Moreover, when there is more than one inlet, the phase shift between entering flows plays a significant role in the process.4040. M. C. Nguyen, H. Peerhossaini, E. Pashmi, M. M. Salek, and M. Jarrahi, J. Fluids Eng. 142(8), 081208 (2020). https://doi.org/10.1115/1.4046851Studies on pulsating flow for separation applications have been limited to passive particles. Contrary to the results obtained for dead cells (passive particles), it has been recently reported that pulsation has no effect on the distribution of live (swimming) cells at the exit of a double Y-microchannel separator.4040. M. C. Nguyen, H. Peerhossaini, E. Pashmi, M. M. Salek, and M. Jarrahi, J. Fluids Eng. 142(8), 081208 (2020). https://doi.org/10.1115/1.4046851 The separation index remains around 50% and insensitive to pulsation parameters, implying that live cells choose an exit channel randomly due to their strong motility. In the present study, phototactic behavior of cells is coupled with pulsatile flow features, for the first time, to reveal the advantage of pulsation in the algae harvesting process. The underlying mechanism is as follows: during half of the pulsation cycle, when the flow rate is low, phototactic microswimmers are mainly redirected by the external stimulation (light); however, during the rest of the cycle, the flow effects become dominant and the microswimmers are driven toward the desired outlet. Although the experiments are conducted on the Chlamydomonas reinhardtii, a numerical simulation based on a simple model demonstrated that the idea can be extended to any other active particle stimulated by an attractive or repulsive external field. Thus, the potential applications can go beyond algae harvesting to control and improve separation, selection, or accumulation processes without using any mechanical component or chemical substance. For instance, in biomedicine, cells with different degrees of sensitivity to an external field can be efficiently sorted out or delivered to special zones by adjusting pulsation parameters. Furthermore, micro-organisms with different motility or phototactic behaviors, like cyanobacteria41–4341. H. Fadlallah, M. Jarrahi, E. Herbert, R. Ferrari, A. Mejean, and H. Peerhossaini, J. Appl. Fluid Mech. 13, 561 (2020). https://doi.org/10.29252/jafm.13.02.3013442. T. Vourc'h, J. Léopoldès, and H. Peerhossaini, Phys. Rev. E 101, 022612 (2020). https://doi.org/10.1103/PhysRevE.101.02261243. T. Vourc'h, H. Peerhossaini, J. Léopoldès, A. Méjean, F. Chauvat, and C. Cassier-Chauvat, Phys. Rev. E 97, 032407 (2018). https://doi.org/10.1103/PhysRevE.97.032407 and algae, can be separated in such a process.We first characterized the phototactic behavior of our microalgae strain as described in Sec. . This step was necessary since no data on the phototaxis behavior of this strain under our experimental conditions were reported in the literature. Then, we investigated the separation process of microalgae cells inside a double Y-microchannel under steady regime at different flow rates and pulsatile regime at different frequencies. For each flow regime, two types of experiments were carried out; with and without phototaxis. The results are presented and discussed in Sec. . Finally, a preliminary numerical simulation is performed in Sec. to emphasize the pertinence of the proposed method in other contexts.

II. MATERIALS AND METHODS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. MATERIALS AND METHODS <<III. SWIMMING BEHAVIOR OF...IV. MICROALGAE SEPARATION...V. A SIMPLE MODELVI. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCES

A. Microalga and cell cultivation

Chlamydomonas reinhardtii, widely used as a model micro-organism in biology and biophysics, is a motile oval unicellular green alga of about 10 μm diameter that uses two 10–12 μm long anterior flagella to swim in a breaststroke-like pulling motion, covering a distance of about ten times its body size per second.44,4544. E. H. Harris, The Chlamydomonas Sourcebook: A Comprehensive Guide to Biology and Laboratory Use (Academic Press, San Diego, CA, 1989).45. R. Jeanneret, M. Contino, and M. Polin, Eur. Phys. J. Spec. Top. 225, 2141 (2016). https://doi.org/10.1140/epjst/e2016-60065-3 The cell density is close to that of water and equal to ρcell = 1050 kg m−3. All experiments have been performed with wild-type Chlamydomonas reinhardtii strain SAG 34.89 purchased from the culture collection of algae at Goettingen University in Germany. The cell cultures were grown in liquid tris-acetate-phosphate (TAP) medium (reference number A13798-01, Thermo Fisher Scientific, USA) on a 12:12 h day-night cycle in a refrigerated and illuminated incubator. The temperature was kept at 22 °C. Cells were harvested for the experiments three days after inoculation in TAP medium. Before each experiment, the culture is diluted (using TAP medium) and kept in the dark for 30 min to make cells uniformly sensitive to light stimulus. Cell counting was performed using Cell Counter plugin in ImageJ/Fiji software after converting the images to 8-bit gray scale format and adjustment of the brightness and contrast to make the cells clearer. A bandpass filter was applied to filter the large (small) structures down (up) to 40 pixels (5 pixels). As a result, the average concentration of the suspension samples was found to be 13 800 ± 1400 cells/ml after dilution. This is equivalent to a volume fraction of αp = Vp/Vfluid ≈ 7.2 × 10−6, where Vp and Vfluid are the total volume of cells and the suspension volume, respectively.

B. Experimental setup

Images were acquired with a CCD camera (Edmund Optics) equipped with a Nikon TU Plant 10× objective (resolution = 1.6 pixels per micrometer). The acquisition frequency was 20 Hz. To avoid any undesired phototaxis, the channel was enclosed in a dark box and a red filter was placed on the path of the light that illuminates the observed area.

Two different microchannels were used. The one used in Sec. for characterization of the microalgae swimming in the flow with and without phototaxis is presented in Fig. 1(a). It is a 15 mm long microchannel of rectangular cross section (width = 500 μm, height = 85 μm) made of polydimethylsiloxane (PDMS). To trigger phototaxis in the suspension at a specific time, a blue light-emitting diode with a wavelength of 470 nm and a light intensity of 910 lx measured using an Amprobe LM-120 light meter was placed next to one of the lateral (XZ plane) walls of the channel. The second microchannel used in Sec. is shown in Fig. 1(b). It is a commercially available Y-Junction glass chip (Dolomite Ltd.)4646. Dolomite, Dolomite Ltd., Royston, UK (2020). that was used to study the cell separation at different flow conditions in steady and pulsatile regimes. The total length of the chip is 22.5 mm. The central straight channel is 12.5 mm long and both convergence and divergence angles are 90°. The form and dimensions of the cross section are constant all over the geometry [Fig. 1(b)]; the depth and width are, respectively, 100 and 205 μm. Two neighboring LEDs are placed immediately before one of the channel outlets, called A in Fig. 1(b).Steady and pulsatile flows were generated using a pressure-driven control system (ELVEFLOW OB1 MK3) connected to an external pressure source which was a high-pressure gas bottle. The device has two output channels; the exit pressure of each one drives the fluid (TAP liquid medium or algae suspension) from a small reservoir into the microchannel. The signal form (uniform or pulsatile) and pressure amplitude were adjusted (resolution = 0.1 mbar) via the device software (Elveflow ESI) in order to produce a desired flow rate at the microchannel inlet. Microfluidic thermal flow sensors (MFS2) are used to measure the flow rate at the microchannel inlets. For the experiments conducted in the first microchannel [Fig. 1(a)], only one channel of the pressure controller was active and one flow sensor was used. However, for the second microchannel [Fig. 1(b)] both pressure channels were active and two flow sensors were used, i.e., one per inlet. Typical time variations of the pressure and flow rate are shown in Fig. 2.The video recordings of the flow were processed using Manual Tracking plugin of ImageJ/Fiji software to obtain the trajectories of cells. The advantage of Manual Tracking compared to an automatic process (e.g., using a homemade code) is that the neighboring cells can be easily differentiated despite the high velocity of the algae. For the results presented in Sec. [Figs. 3(b), 4(c), 6(b), 6(d), and 6(e)], about 700–1000 cells were tracked during 1–2 s for each flow/light condition. To do this, 10 videos (each containing about 70–100 cells) were analyzed for each condition. To calculate the separation index in Sec. (Figs. 9–11), the cells passing through the outlets during 25 s (500 frames) were counted and tracked in ten videos for each flow/light condition and the counting was repeated five times. In this way, about 600–900 cells were tracked to calculate each value of the separation index.

III. SWIMMING BEHAVIOR OF THE MICROALGAE IN THE FLOW WITH AND WITHOUT PHOTOTAXIS

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. MATERIALS AND METHODSIII. SWIMMING BEHAVIOR OF... <<IV. MICROALGAE SEPARATION...V. A SIMPLE MODELVI. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCESNo complete data on the phototactic behavior of SAG 34.89 were found in the literature. Here, we describe the effect of phototaxis on reorientation of the algal cells swimming in quiescent, steady, and pulsatile flow conditions. The microchannel presented in Fig. 1(a) was used for the experiments presented in this section. For the steady flow, the flow rate was set to 0.5 μl/min corresponding to a mean flow velocity of Um = 200 μm/s in the channel. For the pulsatile flow, the following equation was used to express the instantaneous mean velocity of the flow: U(t)=Um(1+βsin(ωt)),(1)where β is the ratio of the peak oscillatory velocity component and the mean flow velocity (Um); ω = 2π/T is the angular frequency; T and t represent, respectively, the pulsation period and the time. The following conditions were applied in this part of study: Um = 200 μm/s, β = 1, and T = 1 s.The orientation of each cell trajectory, called θ, was defined as the angle between the flow direction and the cell trajectory [Fig. 3(a)]. Hereafter, θp represents the most probable value of θ obtained for a series of experiments.The distribution of θ in quiescent suspension and some typical trajectories are presented in Fig. 3. While there is no preferential orientation before activation of phototaxis, the majority of trajectories become perpendicular to the lateral walls, i.e., θp = 90°, when the light is on [Fig. 3(b)]. In the absence of light source, the cells swim in random directions [Fig. 3(c)]; however, after turning the light on, a negative phototaxis is observed: most of the cells run away from the light by swimming toward the opposite wall [Fig. 3(d)].The results obtained for the steady flow are shown in Fig. 4. When the light is off, the trajectories are mostly aligned with the flow direction [Fig. 4(a)]. After switching on the light, they are slightly oriented toward the wall which is far from the light source [Fig. 4(b)]. Distribution of θ shows that this small deviation due to negative phototaxis is less than 30° [Fig. 4(c)].To present the observations made on phototaxis in the pulsatile flow, each pulsation period was considered as a combination of two regimes called low flow, henceafter abbreviated as LF, and high flow, abbreviated as HF (Fig. 5). LF (HF) represents the half of period where the flow rate is less (higher) than the mean value. Figure 6(a) shows some trajectory samples obtained when the light is off. The segments traveled during LF and HF are colored in green and red, respectively. The distribution of θ in the absence of light [Fig. 6(b)] indicates that the cells show no preferential swimming direction during LF; however, they are roughly aligned (θp ≈ 0) with the flow streamlines during HF. This was expected since at low flow rates; the cells can freely swim in any direction; however, the advective effect of the flow becomes significant when the flow rate is high enough.When the light is turned on, the trajectories and accordingly the distribution of θ change as shown in Figs. 6(c) and 6(d). At low flow (LF) regime, the phototactic effect is dominant and the cells swim away from the light by swimming toward the opposite wall (θp ≈ 82°). However, at high flow (HF) regime, the flow effect becomes dominant and the cells reorient toward the flow direction with a θp equal to 30°. Another way to confirm this sharp change in the trajectories during a pulsation cycle is to follow the variations in the y-component of the cells velocity (Vy). Distributions of Vy in the LF and HF regimes are plotted in Fig. 6(e). It shows that the peaks of histograms shift from the right (∼110 μm/s) to the left (∼50 μm/s) when the flow regime changes from the LF to HF in a cycle. It should be noted that the histogram peak at the LF regime corresponds to the motility of the cells; i.e., the majority of the cells swim perpendicularly to the flow direction.In Sec. , we will show that this periodic reorientation of the trajectories (“cross” and “co-” flow directions) can be applied in a cell separation mechanism.

IV. MICROALGAE SEPARATION IN A DOUBLE Y-MICROCHANNEL

Section:

ChooseTop of pageABSTRACTI. INTRODUCTIONII. MATERIALS AND METHODSIII. SWIMMING BEHAVIOR OF...IV. MICROALGAE SEPARATION... <<V. A SIMPLE MODELVI. CONCLUSIONSSUPPLEMENTARY MATERIALREFERENCESCells orientation is influenced by the local vorticity and phototaxis.35,4735. X. Garcia, S. Rafaï, and P. Peyla, Phys. Rev. Lett. 110, 138106 (2013). https://doi.org/10.1103/PhysRevLett.110.13810647. M. Martin, A. Barzyk, E. Bertin, P. Peyla, and S. Rafai, Phys. Rev. E 93, 051101 (2016). https://doi.org/10.1103/PhysRevE.93.051101 Figure 7(a) shows schematically the microalgae swimming in a steady Poiseuille flow. Vorticity effect on the cells rotation is opposite above and below the centerline: vorticity makes the cells which swim above (blow) the centerline rotate in a (counter-) clockwise direction. Thus, swimming away from the light is easy (challenging) for the cells which are above (below) the centerline. In other words, negative phototaxis will not be able to drive easily the cells which are below the centerline from one wall to the other one if the flow is steady. However, if the flow is pulsatile, vorticity is weak enough during the low flow (LF) regime of each pulsation cycle and hence the effect of phototaxis dominates: most of the cells, independently from their position, will have the opportunity to swim across the channel during the LF regime [Fig. 7(b)]. It should be noted that the arguments provided in this paragraph are in agreement with the distributions of θ presented earlier in Figs. 4 and 6.We take advantage of this feature of swimming in a pulsatile flow in the presence of phototaxis to drive the algae entering from the inlet A of the double Y-microchannel [shown in Fig. 1(b)] to the opposite outlet (outlet B). Only TAP medium was injected from the inlet B. Hereafter, this manipulation of the trajectories is called separation and the separation index (SI) is defined as the ratio of the particles escaping from the outlet B to the total number of particles escaping from outlet A and outlet B together. Figures 7(c) and 7(d) show the scenarios expected in the steady and pulsatile flow conditions: more cells can escape to the outlet B in a pulsatile flow [Fig. 7(d)] compared to a steady flow [Fig. 7(c)].A series of experiments were then carried out to examine these scenarios. For the steady flow, the flow rate varied from 0.1 to 0.5 μl/min corresponding to a range of mean flow velocity between Um = 100 μm/s and Um = 500 μm/s at each inlet. For the pulsatile flow, four values of pulsation period T = 1, 2, 5, and 10 s were applied when Um = 200 μm/s and β = 1 at each inlet [see Eq. (1)].As is qualitatively shown in Fig. 8, the separation is not possible neither in the steady flow [Fig. 8(a)] nor in the pulsatile flow [Fig. 8(b)], when there is no phototaxis. Motile cells choose their exit from the microchannel randomly and the separation index remains around SI = 0.5 in both steady and pulsatile flows. Any variation of the ratio of flow rates at the inlets in the steady flow or of pulsation parameters (amplitude, frequency, phase shift) in the pulsatile flow does not change the separation efficiency. In this condition, there is no interest in applying pulsation to separate the motile cells.3030. K. Drescher, R. E. Goldstein, and I. Tuval, Proc. Natl. Acad. Sci. U.S.A. 107, 11171 (2010). https://doi.org/10.1073/pnas.1000901107 However, the experiments carried out in the presence of light stimulus show that the separation index is higher in the pulsatile flows compared to that obtained in the steady flows for similar mean velocities. This can be qualitatively seen in Figs. 8(c) and 8(d). Moreover, in both steady and pulsatile conditions, the separation is more significant than what was observed in the absence of phototaxis [compare Figs. 8(c) and 8(d) to Figs. 8(a) and 8(b), respectively].Variation of the separation index (SI) as a function of flow rate in the steady flow is shown in Fig. 9. For all the flow rates, SI in the presence of light stimulus is higher than the nearly constant value (0.5) obtained in the absence of phototaxis. Separation increases with flow rate until reaching its maximum, SI = 0.65, at 0.4 μl/min; then it decreases since at high flow rates, cells are strongly advected by the flow and the effect of phototaxis is no longer strong enough to deviate the cell trajectories. On the other hand, if the flow rate is very low (less than 0.15 μl/min), cells are not necessarily directed to the outlet B by phototaxis. Therefore, the advantage of phototaxis for separation in steady flows can be seen only in the range of intermediate values of flow rate. There is no interest to apply a light stimulus to improve the separation at very low or very high flow rates.For the pulsatile flow, the effect of pulsation period (T) on the separation was investigated. Figure 10 shows the results when the mean flow rate is in the range of intermediate values (here 0.2 μl/min) and β = 1. For all the pulsation periods, the presence of light stimulus enhances the separation and SI increases from SI = 0.67 for T = 1 s to SI = 0.75 for T > 1 s while its value is nearly constant (SI = 0.5) in the absence of phototaxis. Therefore, an enhancement of 34%–50% due to the phototaxis is achieved in the pulsatile regime. Furthermore, a comparison between Figs. 9 and 10 shows that for a similar mean flow rate (0.2 μl/min), the separation process in a pulsatile flow with any value of frequency is more efficient than that in a steady flow. It should be reminded that the presence of light stimulus is necessary; otherwise, both steady and pulsatile flows yield the same result (SI = 0.5).For T > 1 s, the separation index reaches a plateau and any increase in T does not change the separation efficiency. To interpret this observation, we define a dimensionless number, called P number, using two characteristic times which are the key parameters in the separation method proposed here, P=TransversemigrationtimeDurationoflowflowregimeinthepulsatileflow=(WVCR)(T2),(2)where W = 205 μm and VCR = 100 μm/s are the microchannel width [Fig. 1(b)] and the typical value of the cell motility, respectively. The transverse migration time is the time that a cell spends to travel from one wall to the opposite wall when the swimming direction is fully influenced by the phototaxis (θ = 90°). This can occur during the low flow (LF) regime that lasts for half of the pulsation period (T/2). When the P number is less than 1, the LF regime is long enough to allow the cells to travel across the channel and reach the opposite wall. Therefore, the highest level of separation is achieved when P T > 5 s) as shown in Fig. 10. On the other hand, when P > 1 (corresponding to T Question arises here as to the instantaneous state of separation during a process. To answer this question, the time evolutions of SI in both steady and pulsatile flows are plotted in Fig. 11. Dimensionless time, t*, is defined as t∗=TimeAdvectiontime=t−t0(Um,ChL),(3)where t0 = 60 s is the time at which the light is on; thereby the phototaxis is present only at positive values of t*. Advection time is calculated in the straight segment of the double Y-microchannel where the channel length is L = 12.5 mm [Fig. 1(b)] and the mean flow velocity in the channel is Um,Ch = 400 μm/s; thus, the advection time is equal to 31.25 s.It can be seen in Fig. 11 that before turning the light on, the separation index does not change with time, as was expected and explained earlier; SI remains constant for all the flow conditions. After turning the light, SI increases with a similar trend for all flow conditions until reaching a plateau at t* = 1. The values of the plateaus, which depend on the flow condition, are similar to those shown in Fig. 10. During the rising phase, SI in the pulsatile flows is always higher than that obtained in the steady flow. The practical aspect of this finding is that pulsation accelerates the separation process in addition to its enhancement.

Another observation is that the light stimulus should last at least for a period equal to the advection time (31.25 s in our case); otherwise, the maximum separation