Dynamic control of active droplets using light-responsive chiral liquid crystal environment

Microscopic active droplets are of interest since they can be used to transport matter from one point to another. In this work, we demonstrate an approach to control the direction of active droplet propulsion by a photoresponsive cholesteric liquid crystal environment. The active droplet represents a water dispersion of bacterial Bacillus subtilis microswimmers. When placed in a cholesteric, a surfactant-stabilized active droplet distorts the local director field, producing a point defect-hedgehog, with fore-aft asymmetry, and allows for the chaotic motion of the bacteria inside the droplet to be rectified into directional motion. When the pitch of the cholesteric confined in a sandwich-like cell is altered by light irradiation, the droplet trajectory realigns along a new direction. The strategy allows for a non-contact dynamic control of active droplets trajectories and demonstrates the advantage of orientationally ordered media in control of active matter over their isotropic counterparts.


Introduction
2][3] One example is an emulsified spherical droplet that becomes motile due to interactions in the emulsion.Most self-propelled droplets in isotropic environments are driven into motion by the Marangoni effect.The mechanism of their propulsion is either by chemical reactions or solubilization at the surface of the droplet, both of which cause gradients in the surface tension of the dispersing medium and break the symmetry of the droplet, causing it to self-propel. 2,4,5Complex motion is generally observed in these systems, but ballistic motion is also achievable. 4 However, due to the inherent lack of ordering in isotropic media, the control of the direction of the flows of the droplets is a challenge, [6][7][8][9][10] which is why liquid crystals (LCs) are a convenient alternative. 11 active droplets emulsion in a LC could be, for example, a spherical water droplet containing a dispersion of swimming bacteria that is placed in a thermotropic nematic LC confined between two plates with planar molecular orientation.3][14] The director field of the droplet-HH pair is fore-aft asymmetric.We describe this asymmetry by a vector  directed from the droplet center towards the HH core.The flows created by the randomly swimming bacteria inside the droplet transfer through the interface into the nematic surrounding.The polar asymmetry of molecular orientations around the sphere-HH pair rectifies these chaotic flows into a directional flow of the nematic outside the droplet.As a result, the droplet propels unidirectionally along . 15 In addition to enabling and directing the locomotion of active droplet, the nematic environment adds a useful effect of levitation: the droplet is repelled from the top and bottom plates of a sandwich-like cell by the elastic response of the nematic to different anchoring conditions at the droplet's surface and at the plates.
As demonstrated previously, the trajectory of the active droplet could be controlled by surface patterning of the director, 15 by applying an electric field to realign the director, or by using a laser beam to locally melt the nematic into an isotropic phase. 16These methods of control are either static (as in the case of photopatterning 15 ) or require a complicated design (such as patterned electrodes or precise focusing of the laser beam 16 ).There is thus a need to develop a method to dynamically control the trajectories of active droplets with a simpler design that can be applied from a distance.We propose to address this challenge by using a light-responsive cholesteric (Ch) LC as the medium for the dispersed active droplets.
In a Ch, the director is arranged in a helical supramolecular structure, which is characterized by the pitch , defined as the distance over which the director twists by 360°.The pitch is sensitive to chemical composition.8][19][20] Imagine that an active droplet is placed in a Ch confined between two glass plates, one of which is rubbed to produce a unidirectional alignment along an axis .The second plate allows the director to glide on it.The thickness  of the cell is close to  or less than .The Ch helicoidal axis is perpendicular to the bounding plates.The equilibrium coordinate  ! of the droplet's center along the helicoidal axis is defined by the balance of gravity and elastic repulsion from the bounding plates. 21The dipole  is along the direction that makes an angle

A. Light-induced changes of the Ch pitch
The equilibrium pitch and the helicity of the Ch are determined by the -cell method. 22,23e -cell is used only for the pitch measurements and is not used for the experiments on controlled propulsion of active droplets.The -cell is formed by two parallel plates, the bottom one with planar anchoring and the top one with circular anchoring. 24,25The conflicting anchoring conditions lead to the formation of a disclination line.For a nematic, the disclination appears at 0° with respect to the rubbing direction.For a left-handed Ch, the disclination realigns clockwise (when viewed from the top plate side) towards the II and IV quadrants at an angle  < 0 measured with respect to the rubbing direction.For a right-handed Ch, the disclination realigns counterclockwise (when viewed from the top plate side) towards the I and III quadrants at  > 0. 22 The pitch  is determined as  = 2/, where  <  is the cell thickness. 22The measured pitch values of two Ch mixtures of BrDAB (Fig. 2b) in 5CB (Fig. 2a) are displayed in Table I.To ensure that the value of  corresponds to the equilibrium state, each measurement was performed after 10 min stabilization.The chiral dopant undergoes trans-to-cis isomerization on exposure to green 535 nm light, and the reversed process on exposure to blue 450 nm light. 17The trans configuration of BrDAB produces a left-handed Ch, while the cis configuration of BrDAB produces a right-handed Ch.The transition from one isomer to another requires an unwinding of the helix, passing through the nematic state, and twisting the helix in an opposite direction. 17Note that our experiments use two extreme guiding conditions, when only one wavelength is used at a time, to illustrate that the trajectories depend on the trans/cis content.One can also control the dynamics by two beams of different wavelength and variable intensities, to achieve smooth variations of the pitch.

B. Reorientation dynamics of active droplets by light irradiation in a Ch
The Ch cell induces planar anchoring of the director on the bottom plate  = 0 and azimuthally degenerate tangential anchoring on the top plate,  = , Figs.1d and 1e.
Degenerate tangential anchoring allows the material to adjust the pitch after every irradiation step.The anchoring at the bottom plate is set planar by unidirectional rubbing, so that when the pitch changes, the polar vector  of asymmetric director field around the droplet rotates.In the absence of planar anchoring, the director can glide at the bounding plate, which could prevent  from realignment.When a colloidal particle with homeotropic anchoring of the director is placed in a nematic cell, it causes the formation of topological defects in the surrounding LC: 12 a surface disclination loop, called a Saturn ring (SR), 26 or a point defect, called a hyperbolic hedgehog (HH). 12The SR configuration is of a quadrupolar symmetry and does not cause the propulsion of an active droplet. 151][32] High values of & '( ≫ 1 produce textures similar to that one of a nematic, Fig. 1a,b,c.For & '( ≪ 1, the appearance of HH is highly unlikely, since the strongly twisted planar Ch structure "flattens" the director lines to be parallel to the bounding plates.Instead, the condition disclination loop that encircles the sphere approximately 2/ times, being a twisted analog of the SR. 32,33As demonstrated experimentally and by numerical simulations 30 for /2 ≈ 1 − 2, the HH still forms in the equatorial plane of the spherical colloid, but in addition to it, there are also nonsingular disclination loops enclosing the top and bottom parts of the sphere.Since the director is continuous in these loops, they are hardly visible under the microscope. 30 is expected that since the ratio /2 controls the stability of the hedgehog defect, it should be important also in the efficiency of flow rectification around the active droplet. 1 is presented in Supplementary Fig. 2. In agreement with the prior results by Trivedi et al. 30 for a solid sphere of diameter ~10 µm, the Ch environment in all cases creates a dipolar structure with a hedgehog defect, suitable for the rectification of active flows and propulsion of the droplet, see Figs. 3,4 and Supplementary Fig. 1.Furthermore, fluorescence confocal microscopy of the vertical cross-section of the cells 34 shows that the active droplets levitate in the Ch bulk, Supplementary Fig. 3, as discussed for inanimate colloids by Pishnyak et al. 21,35 The equatorial plane of the large droplet, Supplementary Fig. 3a is close to the midplane of the cell,  = /2.The details of the propulsion and trajectory control, however, depend on the ratio |&| '( , which can be used as an optimization parameter depending on the tasks in the controlled steering of active droplets.We first describe the strongly twisted Ch with |&| '( ≈ 1.5, Fig. 3. The dipolar nature of the director field around the large active droplet, 2 = (134 ± 2) µm, is enhanced by a small satellite droplet trapped at the core of the HH, Fig. 3(a).The hedgehog point defect cores carry a large elastic energy of director distortions.In the presence of foreign particles, this energy can be reduced by attracting the particle to the core, thus removing the strongly distorted liquid crystal. 36In the present case, the hedgehog core attracts a small droplet which facilitates the observations and makes the polar axis  and the angle  it makes with the -axis clearly defined, Fig. 3a.
It is important to stress that the presence of the satellite droplet at the HH core is not the reason for the propulsion of the principal droplet.As explained in Discussion, the satellite droplet merely reduces the high core energy of the hedgehog.The principal active droplets show the same dynamic behavior even if there are no satellite droplets, as shown in Supplementary Figures 1 and 2 and Supplementary Movies 2 and 3.The propulsion is enabled by the fore-aft asymmetry of the director field around the principal droplet and this asymmetry persists regardless of the presence or absence of the satellite droplet, Fig. 1.The mechanism of propulsion is in the rectification of the chaotic bacteria-triggered flows by this fore-aft asymmetric director field.This mechanism is different from the nonreciprocal "predator-prey" interactions between two oil-in-water droplets which engage in oil exchange and Marangoni flows, as described by Meredith et al. 10 In addition, the polar axis  of the fore-aft asymmetry of the director field around the active droplet is controlled by the far-field director, which enables the control of the propulsion direction by this far field.
The situation is also different from the other LC-involving propulsion phenomenon described by Krüger et al., 5 which involves 5CB droplets dispersed in water with an ionic surfactant.The droplets dissolve with time since the concentration of the ionic surfactant is above the critical micelle concentration.In this dynamic regime, the 5CB droplets propel.Propulsion is observed when 5CB is in the isotropic phase and also in the nematic phase.The isotropic 5CB droplets move along rectilinear trajectories while the nematic 5CB droplets show a curling motion.In both cases, propulsion is caused by self-sustained gradients of the surfactant concentration at the droplets' surface, which produces Marangoni flows and drives the droplets; the coupling of the director inside the nematic droplets brings an additional symmetry-breaking mechanism that converts ballistic motion into a curled one.The phenomenon is different from the present case of bacterial active droplets.First, although our system does contain a surfactant (lecithin), its presence is not the reason for the propulsion.If the bacteria are deprived of oxygen for a long time and stop swimming, there is no propulsion of the droplets.Second, the environment in which the droplets propel in our case is a Ch liquid crystal, rather than isotropic water.This orientationally ordered environment produces director distortions around a surfactant-covered droplet which are of a polar symmetry, as specified by the vector P. If the liquid crystal environment is heated into the isotropic phase, the active droplets do not propel; 15 they experience a random Brownian motion.
Whenever the wavelength of light irradiation is changed, the Ch adjusts its pitch, while the droplet adjusts the angle  of the polar axis , Fig. 3a.The director field around the droplet experiences a strong reorganization, which involves shifts of the hedgehog core away from the droplet and transient appearance of nonsingular disclinations, Supplementary Movie 1.The readjustments are relatively slow, taking about 6-7 min, Fig. 3d,e, which is much longer than the characteristic time 75 s for the light-induced isomerization of BrDAB. 37ce the reorganization is complete, the direction of propulsion changes, as expected, Fig. 3b,c. rotates clockwise going from frames 1 to 2 and frames 3 to 4 when irradiation with 535 nm is switched to the 450 nm irradiation, Figure 3a and Supplementary Movie 1.The result is consistent with the clockwise twist described for the cis-to-trans transition caused by this irradiation change.The droplet rotates counterclockwise when the switch from 450 nm to 535 nm causes a trans-to-cis transition of the light-sensitive chiral BrDAB.
The propulsion of the active droplet is ballistic and uniform once the Ch structure readjusts to the new irradiation regime.In this steady regime, the velocity direction and magnitude d/d are constant, Fig. 3(b,c,d,e).Here,  is the distance by which the droplet progresses every 60 s.
Comparison of Fig. 3a to Fig. 3b also shows that the droplet propulsion direction is noticeably different from the direction of , in contrast to the case of a nematic environment, in which these two directions coincide. 15For example, the droplet moves along the azimuthal direction  ,,)*) ≈ 77° under 535 nm irradiation and along  ,,%)! ≈ −67° under 450 nm irradiation, Figs.3b,e.These values are different from the average orientation angles of  in the steady state, 〈 )*) 〉 = 44° and 〈 %)! 〉 = −46°, Fig. 3e.
Another important difference is that the propulsion speed of droplets with a diameter 2 ≈ 130 µm in a nematic environment is about 1 µm s $. , while the strongly twisted Ch with |&| '( ≈ 1.5, Fig. 3 and |&| '( ≈ 1.0, Supplementary Fig. 1, reduces the speed to about 0.2 µm s $. .The apparent reason for these differences between the Ch with |&| '( ≈ 1 and a nematic is a more complicated structure of the defects around the droplet in a Ch environment, which contains additional non-singular disclinations revealed by numerical simulations 30 and observed as weakly light-scattering strings in Supplementary Movies 1 and 2. The relatively strong structural twist and the presence of additional disclinations reduce the fore-aft asymmetry of the overall director configuration around the active droplet, which diminishes the efficiency of flow rectification and sets the direction of propulsion different from that of .The twist and disclinations also produce an additional viscous drag on the moving active droplet caused by the reconstruction of the director field.Hence, when    3b,e.These directions coincide with the direction of , Supplementary Movie 2. This behavior is the same as in the nematic environment. 15e higher ratio |&| '( yields a higher speed of active droplets.In Figure 4d, the speed of a droplet of the diameter 2 = (72 ± 4) µm fluctuates in the range (0.3 − 0.9 ) µm s $. , which is comparable to the speed 0.4 µm s $. of similarly sized droplets in the nematic environment 15 and noticeably faster than the speed 0.2 µm s $. of the larger droplet 2 = (134 ± 2) µm in the case |&| '( ≈ 1.5 in Fig. 3.The difference between the weakly and strongly twisted Ch is even more striking if one accounts for the fact that the large droplets move faster than the small ones in a nematic. 15he equilibrium value of the angle  at each wavelength of steady irradiation depends on both the droplet diameter and the pitch.The angular range of reorientations ∆ , =  ,,)*) −  ,,%)! , could be tuned by changing the concentration of the chiral dopant BrDAB.
At high concentrations, the director twists by a higher  for a given cell thickness, Eq. ( 1), which allows for larger degree of angular steering of an active droplet.In this respect, a strongly twisted Ch allows for a broader range of trajectory realignments, as clear from Fig. 3(b), in which ∆ , ≈ 180°.For a weakly twisted Ch, the trajectory realignment range is smaller, ∆ , ≈ 55°, Figure 4b.
If one uses Equation ( 1) for the droplet in the weakly twisted Ch, the expected values of  are  )*) = 48° and  %)! = −50°, so that ∆ , ≈ 100°, which is larger than the experimental ∆ , ≈ 55°.Equation ( 1) assumes that the ideal Ch helix is not distorted by the droplet and that the hedgehog geometry is the same as in nematics.However, previous studies [30][31][32] demonstrate that the director fields around a sphere with homeotropic anchoring in a Ch and a nematic are very different.Our data for the strongly twisted Ch also demonstrate that the direction of propulsion is not parallel to , Fig. 3b,e, which would make ∆ , different from the one expected on a simple argument of Equation (1).Furthermore, the value ∆ , calculated from Equation (1) assumes that the droplet is located at the exact same  !-level when irradiated with two different light beams.
However, since the cholesteric pitch is somewhat different in the two cases,  )*) = 273 µm and  %)! = −262 µm, the elastic interaction 21 of the droplet with the bounding plates and thus the  !-locations might be different in the two cases (also in the intermediate unwound nematic state), which would result in a different ∆ , .Other potential reasons such as distortions by viscous friction during self-propulsion, should not affect the spherical shape of the droplets much since the capillary number Ca = /0 1 is small.Here  and  are the viscosity and velocity of the moving droplet, and  is the interfacial tension between the two fluids.For the viscosity of DSCG 13%  ≈ 7 kg m $. s $. . 38and  = 0.6 µm s $. , assuming that  is in a very broad range from 1 to 100 mN m $. , the capillary number is in the range Ca = 10 $2 − 10 $3 , much smaller than 1.
The reorientation of the droplets in the weakly twisted Ch after subsequent changes in the wavelength of light irradiation is reproducible, as the equilibrium  )*) is the same in frames 1 and 3, and the equilibrium  %)! is the same in frames 2 and 4 in Fig. 4a.These values remain the same after two cycles of irradiation change.

Discussion
Propulsion and trajectory of active droplets in the Ch environment are controlled by a number of factors, such as the size of the droplet, the number of microswimmers in them, the cholesteric pitch, and the -coordinate of the droplet center.We discuss these parameters and associated limits below.
The droplet size is limited from below by three factors.The obvious requirement is that the droplet diameter is larger than the length of the bacterium, which in the case of B. subtilis places the lower limit at about 10 µm.Second, the droplets should be sufficiently large to maintain a perpendicular surface anchoring at the LC-Terrific Broth interface and strong fore-aft asymmetry of the director field around them, which defines the efficiency of flow rectification.The surface anchoring energy of a droplet scales approximately as  ' , where  is the anchoring coefficient, while the elastic energy of distortions around the droplet scales as . 39As a result, droplets smaller than  < / do not perturb much the uniform surrounding director field.For a typical  = 10 $2 J/m ' and  = 10 pN, the critical droplet radius is   ~  ~10 µm.Droplets of a radius smaller than   do not show a strong fore-aft asymmetry, do not rectify the chaotic flows induced by bacteria, and thus would not self-propel efficiently.Increasing  and decreasing  would make the limit   smaller.
It is important to stress that the scaling  ' of the surface anchoring energy and  of the elastic energy controls also the properties of the small satellite droplet that sometimes, Fig. 3, but not always, Fig. 4 and Supplementary Figs. 1 and 2, is found at the core of the hyperbolic hedgehog.This droplet is not needed to induce the self-propulsion of the prime The pitch of the cholesteric matrix could be independently adjusted to the requirements such as 2 < || by changing the composition, e.g., the molar fraction  8#9:8 of a chiral dopant, since || ∝  8#9:8 $.
. For example, the pitch changes from ≈270 µm when  8#9:8 = 4.9 × 10 $% , Fig. 4, to ≈140 µm when  8#9:8 = 12.1 × 10 $% , Supplementary Fig. S1.Since the bacterial active droplets capable of self-propulsion should be larger than about 30 µm, we conclude that the shortest pitch of interest should be about 30 µm.The upper limit on pitch is set by the desired steering angle ∆ , .If the steering angle for a droplet of a diameter ≈70 µm is desired to be about 55°, as in Fig. 4(b), then the pitch should be ≈270 µm or less.A smaller pitch would increase ∆ , but simultaneously decrease the speed of propulsion, compare Fig. 4 to Fig. 3.
Levitation of active droplets is an added benefit of using an LC environment instead of an isotropic fluid.The droplet levitates since gravity is counterbalanced by the elastic repulsion of the director distortions around the droplet from the bounding plates. 21,35In a nematic, the elastic repulsion force scales as  % .Since gravity force scales as  * , large droplets levitate better, which means that their equatorial plane is closer to the middle plane of the confinement cell.This effect is also relevant for the Ch environment, as confirmed by the fluorescence confocal microscopy textures 34 of the vertical crosssections of Ch in a  = 150 µm cell containing a large, 2 = 90 µm, and a small, 2 = 40 µm, active droplets, Supplementary Fig. 3.The large droplet levitates at a higher , close to the midplane of the cell,  = /2.
An enormous advantage of an LC environment is that its director controls the locomotion direction of active units in it.As already stated, the fore-aft director asymmetry enabling the active droplet's propulsion is caused by the surrounding far-field director of the liquid crystal medium.This far-field director can be designed as rectilinear or spatially and temporarily varied by several approaches, such as photopatterning of surface interactions, 40 application of the external electric field, 16 or by light irradiation, which allows one to control the propulsion direction.In the presented example, the photocontrol of the cholesteric pitch changes the in-plane direction of active droplet propulsion, so that the control can be called two-dimensional.However, the liquid crystal environment allows one to add dynamic control along the third dimension, perpendicular to the cell's plane.
For this purpose, one can use a liquid crystal medium with a negative dielectric anisotropy and apply a direct current (DC) field across the cell (by using two transparent electrode coatings at the bounding glass plates).As demonstrated by Lazo et al, 41 a colloidal particle in such an environment can be moved along the normal to the cell by linear electrophoresis, thus adding the third dimension to the control of propulsion.Such a control is hard to achieve with isotropic environment.

Conclusion
This work demonstrates that blanket light irradiation can be used to control the trajectories of active droplets.When suspended in a light-sensitive cholesteric, active droplets rotate counterclockwise or clockwise, depending on the wavelength of irradiation, which causes either trans-to-cis or cis-to-trans isomerization of the photosensitive chiral azobenzene additive.The isomerization causes reversal of the cholesteric handedness and changes the cholesteric pitch.As a result, the active droplet with dipolar asymmetry of the Ch director around it, realigns its polar axis  and moves in a new direction specified by the wavelength of irradiation.An important factor controlling the propulsion is the pitch-to diameter ratio |&| '( .Relatively small values |&| '( ≈ 1.5, corresponding to strongly twisted Ch, yield a higher range of trajectory realignment, which reaches about 180°.However, the propulsion speed and the transient regimes of structural reorganization are slow.In contrast, weakly twisted Ch with a higher |&| '( ≈ 3.7 − 3.8 offers a propulsion speed that is similar to the one in a nematic environment and reduces the reconstruction time of the director during irradiation to about 2 min.These features are related to a higher degree of polar asymmetry in the case of a higher |&| '( .
The presented approach allows one to dynamically control the trajectories of active droplets using light as a non-contact stimulus, with a simple experimental design.In this work, the driving force causing propulsion of active droplets is the activity of bacterial microswimmers.However, the approach to control the propulsion of the droplets by a cholesteric environment is not limited by bacteria: any interior or surface-active flows of droplets would produce similar propulsion and re-direction by the cholesteric environment if the director field outside the droplet is of a dipolar asymmetry.
Deionized water (Thermo Scientific Barnstead RO purifier, 18.2 MΩ-cm) is used for all aqueous solutions.The medium for bacteria growth is composed of terrific broth (TB) powder (Sigma-Aldrich) and glycerol (Sigma Life Science, >99%) in water.The surfactant L--phosphatidylcholine (lecithin) from egg yolk (Sigma Life Science, >99%) added to the LC imposes homeotropic anchoring of the director at the surface of the active droplets.
Disodium cromoglycate (DSCG) (Alfa Aesar, 98%) is added to the aqueous dispersion of bacteria to increase the viscosity of the medium for better momentum transfer through the droplet-LC interface. 15The solutions of dye Brilliant Yellow (BY) (Aldrich Chemistry,

C. Preparation of active droplets
Bacillus subtilis (strain 3280) is grown in lysogeny broth (LB) agar plates (Teknova) at 35 ℃ for 24 h.One colony of B. subtilis is subsequently grown in a TB medium (47.6 g/L TB powder, 8 mL L -1 glycerine, deionized water) at 35 ℃ for 9 h in a shaking incubator (Boekel Scientific).The bacteria are separated from their growth medium by centrifugation and suspended in the DSCG solution to achieve a final concentration of 2.4 × 10 .2 cells m -3 .Bacteria with the DSCG solution (2 L of this solution) are suspended in the light-sensitive Ch (50 L) and stirred in a vortex mixer to obtain a suspension of droplets of various sizes.

D. Ch cells assembly with active droplets
The active droplets emulsion is introduced into cells (of a thickness ℎ ≈ 150 m) with a rubbed polyimide (PI2555) coating on the bottom substrate and an unrubbed polystyrene coating on the top substrate, Fig. 2(a).The cell thickness was chosen to allow a wide range of droplet sizes to enter the cell, as big droplets move faster than small droplets. 15e unidirectionally rubbed polyimide PI2555 yields planar anchoring parallel to the axis. 42Unrubbed polystyrene yields an azimuthally degenerate tangential alignment. 43e polystyrene coating is produced by spin-coating (3000 rpm, 30 s) a solution of polystyrene beads in chloroform (Sigma-Aldrich, >99%) (5% by weight) over clean glass substrates and baking for 1 h at 90 ℃ to completely evaporate the solvent.The sides of the cells are sealed with epoxy glue after the filling.Experiments with active droplets are done within 2 h of sealing the cell.

E. Preparation of 𝜽-cell
3][24][25] BY is dissolved in DMF with constant stirring.The solution (0.5% by weight) is filtered, then spin-coated (3000 rpm, 30 s) over clean glass substrates and baked for 1 h at 90 ℃.The circular pattern of the dye in the coated substrate is achieved by a 10 min projection of a plasmonic metamask in a photopatterning setup. 44,45These substrates are used for the top of the cell.The bottom substrate is coated with a rubbed polyimide PI2555 layer.Cells of a thicknesses 18 µm are filled with the light-sensitive Ch by capillary action.The pitch dependence on the wavelength of irradiation is measured in the steady regime allowing 10 min of the pitch relaxation.

F. Optical microscopy
The dynamics of active droplets are studied under an inverted microscope (Nikon Eclipse TE2000-U) with a xenon light source (Asahi Spectra LAX-C100).Color filters are used to select the wavelength of light irradiation at wavelengths  = 535 nm (bandwidth 50 nm, Chroma Technology) and 450 nm (bandwidth 10 nm, Asahi Spectra).The intensity of the light source is set at its maximum before inserting the filters and yields values of intensity of 9.7 mW cm -2 and 1.4 mW cm -2 after inserting the 535 nm and 450 nm filters, respectively.The room temperature is 22 ℃.A level is used to check there is no tilt of the microscope stage.Videos and pictures are recorded with a camera (Emergent Vision Technologies HS-20000C) connected to the microscope; video and image analysis is done with the softwares ImageJ and Maplesoft.

G. Fluorescent confocal polarized microscopy (FCPM)
The -coordinates of the droplets are characterized by fluorescent confocal polarized microscopy (Olympus Fluoview) with an argon laser (wavelength 488 nm) light source (NEC Corporation, model GLG30808). 46The mixture for the FCPM observations is composed of DSCG droplets suspended in a low birefringence nematic MAT-03-382 doped with the fluorescent dye BTBP at 0.0025 % by weight and the chiral dopant S811 at 0.061% by weight (pitch ~150 µm).The cell (of thickness ℎ ≈ 150 m) has rubbed polyimide (PI2555) coating on the bottom substrate and an unrubbed polystyrene coating on the top substrate.Observations are made with the rubbing direction perpendicular to the polarizer axis of the FCPM.

FIG. 1 .
Figures 1b,c illustrate the concept of realignment of  for a droplet of a diameter 2 that is much smaller than the Ch pitch .The director field in the equatorial plane in this case

|&|'( 2 min, 4 ) 4 min, 4 )
FIG. 3. Active droplets trajectories by light irradiation in a strongly twisted Ch.(a) Optical microscope view of an active droplet with a diameter 2 = (134 ± 2) µm suspended in a Ch In a weakly twisted Ch with |&| '( ≈ 3.7 − 3.8, the clockwise and counterclockwise reorientations of the droplet upon changing the wavelength of light irradiation, Fig.4a, are faster than the reorientations in the strongly twisted Ch, Fig.4b,c,d,e.The uniform motion and constant speed of propulsion are recovered after 2 min of irradiation change; the change in the wavelength of irradiation does not cause the appearance of additional disclinations, Supplementary Movie 4, in contrast to the case with a smaller |&| '( ≈ 1.5 described above and |&| '( ≈ 1.0 in the Supplementary Movie 2. The droplet trajectory is along  ,,)*) ≈ 30° under 535 nm irradiation and along  ,,%)! ≈ −30° under 450 nm irradiation, Fig.

Table I .
Cholesteric pitch of 5CB + BrDAB mixtures at different wavelengths of steady irradiation.