Estudio de metodologías para el diagnóstico

Figure 4.3c,d show that CR are found preferably in the immediate vicinity of the chan- nel walls both in experiments and simulations. In experiments there is a 5-10µmarea close to the boundaries where we observe a 15-20% higher chance of finding an alga compared to the centre of the channel; this accumulation is also present in simulations although in a far more evident fashion, with a 100% higher probability of finding a cell in the immediate proximity of the wall (we use point like particles in simulations), where cells slide along the surface. In the simulations it is possible to observe a second peak in the particle distributions, in the area we defined as the interaction zone, where hy- drodynamic repulsion begins to act; this second peak is present also in the experiments but is far less pronounced, with a 5% higher concentration of CR. This is significantly different from the uniform distribution one would have for brownian particles, and it is a consequence of the swimmers motility, which has been previously observed in sim- ulations [173] for active matter, and observed experimentally for pusher-type microor- ganisms [144] but has been reported for puller-type swimmers only for concave surfaces [174]. In experiments the magnitude of the peaks do not vary appreciably as a function of the channel width, except for channels withw<50µm where the situation is qualita- tively different as the accumulation peaks relative to each side of the channel are close enough to overlap. The presence of a solid surface not only affects the concentration profile but also, more importantly, the swimming behaviour of the microorganisms: we observe in Figure 4.3a,c how the swimming direction is aligned with the channel axis for distances from the wallsr<35−40µmand how this alignment vanishes as we approach the channel centre. This effect is evident also in Figure 4.3d, where the 2D nematic order parameterOPw(d) for different channel widthswmeasured at different distances from

the closest walld, defined as<2 cos2(θsw(d))−1>, shows a maximum in the proximity

of walls decaying as the distance increases. The order parameterOPreach its maximum close to the wall,OPw(5µm)∼0.4 and decays asdincreases. The maximum value is al-

most constant for 100<w <400 while the minimum varies significantly as a function of the channel width: in thew =300, 400µm curves, OP reaches zero ford >80µm, while in thew=100µm curve, the minimum value observed isOP ∼0.2. It is worth noting howOP100(50µm)>OP400(50µm). In the two narrowest channels,w=50, 30µm

the maximum value of the order parameter is observed forw∼15µm. In the simula- tionsOPw goes to zero in almost every channel for distances greater than 30µm; this

Figure 4.3: Position and swimming direction in experiments and simulations forw: 30µm (ª), 50µm (ª), 100µm (ª), 150µm (ª), 200µm (ª),300µm (ª),400µm (ª). a,b) Distribution of CR position along the y axis in experiments (a), and simulations (b). c,d) 2D nematic order param- eterOPas a function of distance from the closest wall in experiments c) and simulations d).e,f ) Distribution of swimming angle respect to the x axis in 100µm (e) and 400µm (f ) wide channels in experiments (top) and simulations (bottom).

Figure 4.4: Distribution of incoming and outgoing angleθi n andθout in experiments and sim- ulations forw: 30µm (_ª), 50µm (_ª), 100µm (_ª), 150µm (_ª), 200µm (_ª),300µm (_ª),400µm (_ª). a) Distribution ofθi nfrom the experiments. b) Distribution ofθi nfrom the simulations. c) Distribution ofθoutfrom the experiments. d) Distribution ofθoutfrom the simulations.

discrepancy may be due to residual hydrodynamic interactions with walls, not present in the simulations model, the investigation of which goes beyond the purpose of this chapter. In Figure 4.4 the distribution of incoming and outgoing angles for experiments (left) and simulations (right) are shown: In every channel exceptw=30µm, we observe a peak placed aroundθout∼30◦in the outgoing angle distribution on top of a quasi uni-

form background. The situation for the 30µmchannel is significantly different, there is a much greater portion of events resulting in aθout>90o (random scattering) and the

peak for the incoming and outgoing angle are shifted down by 10o compared to other channels; we believe that for very narrow channels, the alga is subject to hydrodynamic forces exerted by both walls, which heavily affect the interaction behaviour of the CR. This is consistent with the results for the previous chapter, where we show evidences of interactions between CR and a solid pillar at distances up to 15µm, which is equal to the maximum distance from the walls inw =30µm channel. This effect has reper- cussions also on the dynamics of random scattering, as the distribution ofθout is not

uniformly distributed between 0 and 180◦_{but is peaked aroundθ}

out∼150◦. All the data

presented show how the CR proceed in straight line between collisions against the chan- nel walls and how this orientation is stronger as the collisions are more frequent. This is also confirmed by Figure 4.5a,b where we see how the time interval between collision against opposite walls consist of a sharp peak that gets broader as the distance between the sides increases. In this case results of simulations and experiments are qualitatively similar.