Self-motion of an oil droplet. (a) Experimental setup and a typical self-motion path. The trajectory of the droplet intersects itself at several points. (b) Speed of droplet as a function of time, where is the time when the oil droplet was placed on the glass surface. The early stages of the time variation of (c) the magnitude of the droplet’s velocity and (d) direction ( and ). (e) The mean-square displacement of the droplet. This plot was obtained from the data shown in (b) using the range to . The condition was and the oil droplet was 40 μl.
The total path length, , of droplet motion and the concentration of the system. (a) The total path length, , is plotted against the concentration of iodine, , in the oil droplet. increased with an increase in . The concentration of surfactant, , in the aqueous phase was kept constant at . (b) is plotted against . decreases with an increase in . was kept constant at [open squares ] and [solid circles ]. The oil droplets were 30 μl.
(a) Schematic representation of the self-motion of an oil droplet. ions are represented by a circle and a line, which represent the hydrophilic and hydrophobic parts of the ion, respectively. The gray arrow represents the direction of droplet motion and the white arrow represents the flow of ions. (b) Schematic representation of the flow of ions.
(a) Actual morphology of the oil droplet during self-motion. (b) Approximate two-dimensional representation of the droplet. The direction of motion is taken to be in the -direction. The length of the droplet (in the direction) is denoted by , and the width of the droplet (in the direction) is denoted by . (c) Profile of the ion concentration in the direction.
(a) Velocity dependence of the driving force when . The ratio of the desorption rate to the adsorption rate is varied as shown in the figure. (b) dependence of . The solid curve represents , which is the limit of as . For large but finite , increases for small and decreases for large . Thus, there is an optimal value of for a traveling droplet. (c) The total force acting on droplet close to the bifurcation. Here, and . For , the total force acting on the droplet becomes positive (i.e., the droplet is propelled).
Motion of an oil droplet in quasi-one-dimensional conditions. The droplet underwent regular oscillatory motion. (a) The experimental setup, snapshot of the experiment (3 frames per second), and a spatio-temporal plot of oscillatory motion. (b) Time course of droplet velocity. (c) Distribution profile of droplet velocity. Data were obtained 30 times per second. The condition was and the oil droplet was 30 μl.
Motion of an oil droplet in an attractive centrifugal force field. The centrifugal force was generated by gravitational force, based on the greater relative density of the oil droplet than the aqueous phase. The droplet exhibited regular rotational motion. (a) Experimental setup, and a superimposed snapshot of droplet motion. (b) Time course of the droplet position ( : solid line; : dotted line). (c) Time course of the droplet velocity in the -direction. (d) Three-dimensional plot of the droplet position and velocity in the -direction. The condition was and the oil droplet was 70 μl.
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