Fig. 5: Critical Casimir ratchet.
a A horizontal microdisk of diameter 2.4μm above a triangular pattern with 2μm base and 36μm height at T ≈ Tc moves towards the base of the triangle, where the overlap between the microdisk and the growing trapezoid is maximized and, therefore, the critical Casimir potential energy is minimized. b Trajectories of the microdisk above triangular patterns with the same base (2μm) but different heights (h = 18, 26, 30, 36μm, see Supplementary Video 5). c The depth \({U}_{\min }(x,y)\) of the interaction potential, calculated as a minimum of the potential with respect to the position of a microdisk above a triangular pattern with 2μm base and 36μm height at T ≈ Tc. d Corresponding mean theoretical trajectories above triangular patterns of different sizes, calculated by neglecting Brownian noise. For each h, the origin of time is chosen such as to match the position of the microdisk at t = 0 with that in the corresponding experiment (see panel (b)). The visible speedup is due to steeper changes of the potential close to the base (see panel (c)) because the particle gets closer to the surface. e Trajectory of a microdisk above a pattern constituted by a series of trapezoids each with a height of 18μm and short and wide bases of widths 1μm and 2μm. The temperature was cycled so that it was far from critical (ΔT = T − Tc ≈ − 1.30K) for the blue portions of the trajectory, where the microdisk tends to diffuse freely, and near critical (T ≈ Tc) for the red portions of the trajectory, where the critical Casimir force pulls the microdisk towards a trapezoid and, subsequently, towards the wide base (see Supplementary Video 6). f A similar trajectory above a curved trapezoidal bull-eye pattern, where the microdisk diffuses freely when the temperature is far from critical (blue portion of the trajectory) and follows the bend of the pattern when the temperature is near the critical one (red portion of the trajectory) (see Supplementary Video 7). In panels (a), (e), and (f), the cross and the circle indicate the trajectory starting and finishing points, respectively. Source data are provided as a Source Data file.
