Self-Running Droplet: Emergence of Regular Motion from Nonequilibrium Noise
Original entry: Tony Orth, APPHY 226, Spring 2009
Yutaka Sumino, Nobuyuki Magome, Tsutomu Hamada, and Kenichi Yoshikawa, PRL 94, 068301 (2005) 
"Spontaneous motion of an oil droplet driven by nonequilibrium chemical conditions is reported. It is shown that the droplet undergoes regular rhythmic motion under appropriately designed boundary conditions, whereas it exhibits random motion in an isotropic environment. This study is a novel manifestation on the direct energy transformation of chemical energy into regular spatial motion under isothermal conditions. A simple mathematical equation including noise reproduces the essential feature of the transition from irregularity into periodic regular motion. Our results will inspire the theoretical study on the mechanism of molecular motors in living matter, working under signiﬁcant inﬂuence of thermal ﬂuctuation."
Surface Tension Effects
Marangoni effects are concerned with the spontaneous change in a system which has a surface tension gradient associated with it. The surface tension gradient is usually due to temperature or chemical gradients. Here, the authors construct a system which has a chemical gradient leading to a spontaneous directed movement of a drop. This regular movement of the drop is also interesting because it is stable in nature and results in a periodic movement of the drop across a surface. The experiment consists of depositing an oil drop onto a glass slide, coated with Stearyl Trimethyl Ammonium ions (STA+) which renders the surface hydrophobic. The oil drop itself contains <math>I_3^-</math> ions which apparently encourage absorption of the STA+ into the drop. When the symmetry of the drops neighbourhood is broken, the drop will move towards the area of the glass slide with less STA+ coating. Once the drop moves in this direction, it is carried to a boundary of this low surface tension area. However, once its momentum carries it into an area of relatively high STA+ concentration, this excess STA+ is simply absorbed by the <math>I_3^-</math> ions in the drop. Thus, the drop is subjected to a directed motion. However, if the drop is free to move on an unconstrained geometry, the trajectory of the drop is seen to wander, though not with the same irregularity as one might expect from a purely random walk. Indeed, this walk is directed. Interestingly, when the authors constrained the geometry, periodic motion was observed. When the drop is placed on a strip of coated glass, the drop is prevented from running off the sides and so the directed propulsion is readily corrected, causing the drop to run back-and-forth to each side of the drop. Eventually, after the <math>I_3^-</math> ions in the drop are saturated with STA+, the drop motion ceases. It is also crucial that the STA+ ions are reabsorbed by the glass towards the rear of the drop where there is a smaller STA+ concentration. The authors simply state this mechanism, but don't delve into the physical process behind this. In any case this allows for the periodic motion by replenishing the chemical needed for the surface tension gradient, making it possible for the drop to cross its own path. Without this mechanism, the drop could not travel over an area it had already traversed. It may be interesting to consider the fully coupled chemical, interfacial energy along with viscous damping which defines the whole system to predict how long this drop might remain in motion for and to fully construct the energy pathway used for locomotion.