We use rod-shaped swimming bacteria Bacillus subtilis (strain 1085) of a body length 5–7 μm and a diameter ∼0.7 μm. The bacteria are initially grown on Lysogeny broth (Miller composition from Teknova, Inc.) agar plates at 35°C for 12–24 h; then a colony is transferred to a Terrific Broth (TB) (Sigma Aldrich) liquid medium and grown in a shaking incubator at a temperature 35°C for 7–9 h. The concentration of bacteria during the growth stage is monitored by measuring the optical density. At the end of the exponential growth, the bacterial concentration is about c 0 = 0.8   × 10 15   cell / m 3 . At this stage, the bacteria are extracted from the liquid medium by centrifugation and added to a nematic lyotropic chromonic liquid crystal (LCLC) to achieve a concentration of 20   c 0 . The LCLC is a 13 wt% dispersion of disodium cromoglycate (DSCG) (Alfa Aesar), Figure 1A, in TB solution, doped with 0.5 wt% of egg-yolk lecithin (Sigma Aldrich) to stabilize the droplets and to set a perpendicular surface anchoring at the lyotropic-thermotropic nematic interface. Note that the nematic LCLC content of the active droplets is not critical for their propulsive ability. Droplets with bacteria dispersed in water without DSCG still propel in a thermotropic nematic environment and could be controlled by the electric field similarly to the experiments described below. As established previously [18], the LCLC interior produces higher speeds of propulsion, presumably because of a better match between the viscosities of the lyotropic nematic inside and the thermotropic nematic outside the droplet and thus a better momentum transfer.

A thermotropic nematic pentylcyanobiphenyl (5CB) (Merck) is used as the continuous medium, Figure 1B. The dielectric anisotropy of 5CB is positive, Δ ε =   ε ∥ − ε ⊥ = 10   ( 200   kHz ) [25], where ε ∥ and ε ⊥ are dielectric permittivities measured parallel and perpendicular to the director, respectively. Since Δ ε > 0 , the director prefers to align parallel to the external electric field. The bacteria-containing LCLC is dispersed in 5CB in a volume proportion of 1:50 and vortexed to achieve an emulsion with active droplets surrounded by 5CB.

The emulsion of active droplets in 5CB is filled into cells of a thickness d = 200   μ m , formed by two parallel glass plates with transparent indium tin oxide (ITO) electrodes at the inner surfaces. The plates are coated with polyisoprene (Sigma-Aldrich) that produces a nearly fully degenerate tangential surface anchoring of 5CB at the glass plates, with a vanishing azimuthal surface anchoring coefficient, W a < 3 × 10 − 10   J / m 2 [26, 27]. The substrates are prepared by spin coating of the solution of 3 wt% polyisoprene dissolved in methylcyclohexane (Acros Organics) and kept for 30 min at 45°C to evaporate the solvent [28]. All experiments were performed at room temperature within 40 min after preparation of the emulsion to make sure the droplets maintain their activity level during the experiment. No sign of degradation or change in the size of droplets was observed within several hours.

Two different geometries of the electrodes are designed to apply the electric field. 1) A segmented set of eight electrodes is used to apply an in-plane electric field along different directions, Figure 1E. We call this an “in-plane cell”. Four electrodes are located at each bounding plate and the separation distance between the opposite electrodes is l = 5   mm . The in-plane field is applied between electrodes located on the same plate. To understand the spatial distribution of the electric field, we performed a simulation using Ansys, a commercial finite element analysis modeling software. The simulation shows the electric field applied by two in-plane electrodes is uniform in the central part of the cell, Supplementary Figure S1 (Supplementary Information). The experiments are performed in this central area ( ∼ 2   mm 2 ). 2) The out-of-plane electric field is applied across a cell with a pair of transparent ITO electrodes on the glass plates. We call it “out-of-plane cell,” Figure 1F. A Siglent SDG1032X waveform generator and an amplifier Krohn-Hite 7602M are used to apply a sinusoidal alternate current (AC) electric field with a frequency f = 100–200 kHz to avoid electrohydrodynamic flows. The electric field is increased at a relatively slow rate ∼   1 − 3   V / s , in order to avoid strong backflows. Because of the degenerate azimuthal anchoring, the field realigns the 5CB director in the plane of the cell without hindrance or a memory effect from the substrates. The applied field does not affect the bacterial activity during the experiment time.

An Nd: YVO₄ laser (Coherent Verdi-V6) with the wavelength of 532 nm is used to change the director configuration near the active droplets. 5CB is doped with ∼ 1   w t % of azo-dye (E)-1-(4-bromo-2,6-difluorophenyl)-2′-(2′,6′-difluoro-4′-(hexyloxy)phenyl)diazene (BrOTFAzoO₆), Figure 1D, which experiences trans-cis isomerization under visible irradiation at 532 nm and thus enhances the sensitivity of 5CB to the laser beam [29]. A prolonged laser irradiation (>1 min) decreases the bacterial activity, thus in the reported experiments, the irradiation time is kept below 30 s.

The motion of active droplets is observed under an inverted Nikon TE2000 optical microscope equipped with a videocamera Emergent HS-20000C; the trajectories are tracked using the ImageJ software [30].

An in-plane electric field is applied to 5CB through the segmented electrodes illustrated in Figure 1E. The field realigns the overall director from the initial orientation n ^ 0 to a different direction n ^ e along the field. The active droplets redirect their trajectories to follow the newly-established n ^ e , Figures 2C–E. When the field is switched off, the direction n ^ e for both the overall 5CB director and the trajectory of the droplet remains intact because of the degeneracy of the azimuthal anchoring at the 5CB-polyisoprene interface.

Because of the sandwich geometry of the cell with two electrodes supplying an in-plane electric field, the actual value of the field is smaller than the simple relationship E = U / l would suggest [32]. Numerical simulation using Ansys software shows that the field in the central part of the cell is reduced by a factor β = 0.8 , i.e., E = β U / l , so that the applied voltage U = 70   V produces E ≈ 11   kV / m , Supplementary Figure S1 (Supplementary Information).

The active droplet redirection is defined by the field-induced director realignment. Figure 3 compares the time evolution of the angle φ d that the trajectory of the active droplet makes with the x -axis and the angle φ that the director makes with the same axis under the same applied field when the droplet is absent. The two dependencies are qualitatively the same and quantitatively similar. We first discuss the dynamics of the director in an applied electric field when the droplet is absent.

Since the azimuthal surface anchoring is negligibly small, the time evolution of φ can be obtained from the balance of the electric and viscose torques, γ 1 ∂ φ ∂ t ≈ −   ε 0 Δ ε   E 2 φ , which assumes director twist by a small angle φ , but no fluid flow. Here γ 1 is the rotational viscosity and ε 0 is the vacuum permittivity. Solving the equation with the initial conditions n ^ 0 = ( 1,0,0 ) and E 2,6 = E 2,6 ( 1,1,0 ) , results in φ ( t ) = π 4 ( 1 − e −   t τ ) (1) where τ = γ 1   ε 0 Δ ε   E 2,6 2 is the characteristic director realignment time. The dependency φ ( t ) can be determined experimentally by measuring the intensity of a monochromatic light (548 nm) passing through the cell and two crossed polarizers, polarized along the x- and y-axes: I / I 0 = sin 2 ( 2 φ ) , where I 0 is the maximum value of the intensity, achieved when the reorientation is complete, Supplementary Figure S2 in the Supplement. The experimentally determined φ ( t ) follows Eq. 1 with a fitted value τ = 18   s , as shown by the dashed line in Figure 3. The fitted value of τ compares well with the theoretically expected. The material properties of 5CB, Δ ε = 10 [25], γ 1 ≈ 0.14 P a . s [33], and E 2,6 ≈ 11   k V / m ( U = 70   V ), yield τ = γ 1 ε 0 Δ ε   E 2,6 2 ≈ 13 s . The difference between the experimental and theoretical values of τ could be due to the small-angle approximation in Eq. 1 and due to the difference in the exact temperatures at which the experiments were performed in our study and in characterization of material properties [25, 33].

The active droplet trajectory angle φ d follows closely the evolution of the director angle φ , Figure 3. The simple model of Eq. 1 thus captures well the essence of the field-controlled droplet redirection by the director realignment. Fitting the experimental dependence with Eq. 1 yields τ d = 22   s , a value slightly higher than τ = 18   s . The small difference between τ d and τ is expected, since Eq. 1 does not even account for the droplet’s presence. The presence of an active droplet leads to the following complications: 1) The swimmers’ activity inside the droplet creates flows of the surrounding liquid crystal [18]. 2) The electric field acting on the liquid crystal medium is different from the value E = β U / l , because of the high dielectric permittivity of the droplet comprised predominantly of water. 3) The droplet might experience a higher effective viscosity because of the proximity of the bounding plates [34]. Accounting for the activity-triggered flows, inhomogeneities of the electric field and effective viscosities presents the biggest challenge for further improvements of the theory.

The in-plane electric field could also control the speed of active droplets by changing the degree of director asymmetry, mainly through the transformation of HH into SR, Figures 4A–C. We quantify the asymmetry degree by the ratio r d / R , where r d is the distance from the center of the droplet to the plane of the disclination ring. We apply the field parallel to the propulsion direction where it causes no redirection. Increasing the voltage from 0 to U ∼   50   V yields a somewhat higher speed, Figures 4B,C ( t = 220   s ), apparently because partial director realignment along the field reduces the effective drag thanks to the viscous anisotropy: the nematic viscosity is smaller for motion parallel to the director. Stronger voltages, 50 V < U < 130 V, reduce the speed, Figures 4B,C ( t = 400 − 800   s ), possibly because the droplet-triggered flows in the surrounding nematic cannot overcome the director aligning action of the applied electric field. At high voltages, U > 130 V, the dielectric response of the nematic expands the HH into a disclination ring, Figure 4A ( t = 830 −   880   s ) [21]. During the opening of HH, the speed momentarily increases, as the shift of the opening disclination ring towards the equator means that the center of the droplet shifts in the opposite direction, Figure 4C ( t = 830 − 840   s ). Next, the speed decreases as the disclination ring gradually expands and the director asymmetry r d / R is diminished, Figures 4A–C ( t = 840 − 880   s ). Eventually, a quadrupolar structure forms, which is incapable of locomotion because of symmetry, Figures 4B,C ( t = 880 − 1200   s ) [18]. Once the electric field is switched off, the disclination ring shrinks to one side of the droplet and the droplet propels again, Figures 4A–C ( t = 1200 − 1590   s ). The direction of the ring’s shrinkage and thus the propulsion direction is left-right random with respect to the axis defined by the dipolar structure. The newly created HH could be switched back to the SR, Figures 4A–C ( t = 1590 − 2320   s ).

The speed of active droplets could also be controlled by the electric field applied across the cell, using transparent electrodes at the bounding plates, Figure 1F. The 5CB director tends to align parallel to the electric field, i.e., normally to the cell’s substrates. At small fields, the director far away from the drop remains in the xy plane because of the polar anchoring at the bounding substrates, Figures 5A,B. The director realignment around the droplet reduces the asymmetry of HH structure projected onto the xy plane and thus decreases the speed, Figures 5A–C. At higher voltages, U > 4 V , the far-field nematic reorients parallel to the field, and the droplet loses its in-plane asymmetry and stops, Figures 5A–C. When the field is reduced the overall director realigns towards the xy plane, and the droplet resumes its motion.

A laser beam can tune the motility and polarity of motion of active droplets. The speed relates to the degree of asymmetry of the director around the droplet. The polarity of motion depends on the location of the HH since the HH leads the droplet. One can establish the desired director configuration, either SR or HH, by locally melting 5CB near the sphere by a laser beam, Figure 6. The laser beam focused on one side of an SR droplet (left side in Figure 6A, t = 215 s ) causes local melting of the nematic [35, 36], thanks to light absorption enhanced by the dye molecules added to 5CB. When the light is switched off, the isotropic region relaxes back into the nematic state with a web of disclinations, Figure 6A ( t = 230 s ). The disclinations shrink and annihilate with each other until a HH forms on the side irradiated by the laser beam, Figure 6A ( t = 255 s ). Once the HH forms, the droplet starts to propel with the HH leading the way, Figures 6A,B ( t = 255 − 400 s ). One can stop the droplet by transforming the HH back to an SR, by applying the electric field, as described before, Figure 4 and Supplementary Figure S3 (Supplementary Information), or by focusing a laser beam, Figure 6A. The laser beam is focused at the HH and is moved around the droplet to melt the surrounding nematic, Figure 6A ( t = 400 s , 415 s , and 420 s ). When the laser is switched off, the isotropic area transforms to a nematic with multiple disclinations surrounding the droplet, Figure 6A ( t = 425 s ). The disclinations slowly shrink and eventually form a single loop in the form of an SR, Figure 6A ( t = 700 s ). The droplet trajectory fluctuates during the annihilation of the disclinations, Figure 6B ( t = 425 − 700 s ). When the SR of quadrupolar symmetry emerges, the droplet stops, Figure 6B ( t = 700 − 830 s ). To reverse the polarity of the motion to the opposite direction, the laser beam is pointed to the opposite side (right side in Figure 6A, t = 835 s ) of the droplet to form the HH on that side. When the HH is formed the droplet propels while the HH leads the way, Figures 6A,B ( t = 880 − 1000 s ).