Microscopic Engine Powered by Critical Demixing

We experimentally demonstrate a microscopic engine powered by the local reversible demixing of a critical mixture. We show that, when an absorbing microsphere is optically trapped by a focused laser beam in a subcritical mixture, it is set into rotation around the optical axis of the beam because of the emergence of diffusiophoretic propulsion. This behavior can be controlled by adjusting the optical power, the temperature, and the criticality of the mixture.

Figure 1

Critical engine working principle. (a) Phase diagram of the water–2,6-lutidine mixture featuring a lower critical point ($CP$) at the bottom of the coexistence line (black solid line). The system is prepared at the critical lutidine mass fraction $c_c=0.286$ and at a temperature $T_0$ significantly (some degrees) below the critical temperature $T_c\approx 34°\mathrm{C}$ (arrow). (b)–(d) An optically trapped microsphere experiences a harmonic restoring optical force that attracts it towards the center of the optical trap near the focal spot (red arrows). If the particle absorbs the illumination light, the temperature of the surrounding fluid increases generating an asymmetric temperature profile, which is hotter on the side of the particle closer to the focal spot. Because of the criticality of the mixture, the temperature gradient, in turn, generates a concentration gradient surrounding the particle and, eventually, a diffusiophoretic drift (green arrows). (b) When the particle is close to the focal spot, the diffusiophoretic drift dominates. (c) Instead, when the particle is far from the focal spot, the optical-force-induced drift dominates. (d) The equilibrium position along the radial direction lies where the optical and diffusiophoretic drifts balance each other and depends on the value of $T_0$ and on the light intensity; here the presence of small asymmetries in the temperature and demixing profile around the particle make the particle rotate around the optical axis (gray arrow).

Figure 2

Engine performance as a function of laser power. The ambient temperature of the sample is fixed at $T_0=26°\mathrm{C}$, while the laser power at the optical trap is (a)–(c) $P=0.6$, (d)–(f) 1.5, (g)–(i) 2.1, (j)–(l) 2.7, and (m)–(o) 3.2 mW. [(a),(d),(g),(j),(m)] Bright-field images of the particle with 0.6 s trajectories represented by white solid lines. [(b),(e),(h),(k),(n)] Velocity drift fields (white arrows) and particle position probability distributions (background color, brighter colors represent higher probability density). [(c),(f),(i),(l),(o)] Experimental (red symbols) and fitted (blue solid lines) differential cross-correlation functions ${\mathcal{D}}_{xy}$ in the $xy$ plane, from which the rotation rate of the particle ${\mathrm{\Omega }}_{xy}$ can be obtained as fit parameter (reported in the right column). The white bars in (m) and (n) correspond to $1\mu \mathrm{m}$. See also Supplemental Video 1 [17].

Figure 3

Simulation of a critical engine. (a) Particle (blue circle) with corresponding 0.6 s trajectory (black line). The black bar corresponds to $1\mu \mathrm{m}$. (b) Drift field (white arrows) and particle position distribution (background color, brighter colors represent higher probability density). The white bar corresponds to $1\mu \mathrm{m}$. (c) Differential cross-correlation function ${\mathcal{D}}_{xy}$ in the $xy$ plane, from which the rotation rate is estimated to be ${\mathrm{\Omega }}_{xy}=1200\mathrm{rpm}$.

Figure 4

Work dependence on laser power and ambient temperature. Work $W$ as a function of (a) laser power $P$ ($T_0=26°\mathrm{C}$) and (b) ambient temperature $T_0$ ($P=2.7\mathrm{mW}$). (c) Work as a function of $P$ and $T_0$. The circles represent the performed measurements. $W$ features a maximum for $P=2.7\mathrm{mW}$ and $T_0=26°\mathrm{C}$.