Simulation investigation of the spontaneous motion behaviors of underwater oil droplets on a conical surface

A conical surface can realize the spontaneous transportation of micro-sized oil droplets in an aqueous environment without energy input, exhibiting great potential for applications in microfluidics, chemical micro-reactors, water remediation, etc. However, the precise manipulation of an oil droplet on a cone is still very challenging because the dynamic behavior of a droplet on a cone is not fully understood. Herein, the dynamic behavior of oil droplets on a cone is quantitively studied via numerical simulations, and the effects of wettability, apex angle, and droplet size on the droplet's dynamic behavior are systematically analyzed. The results show that the moving velocity and transport distance of the droplet on the cone are highly related to the droplet shape on the cone. It was found that a clamshell-shaped droplet moves faster than a barrel-shaped droplet. Besides, the clamshell-shaped droplet with a larger size, on the cone with a smaller apex angle and smaller contact angle tends to obtain a faster moving speed and a longer transportation distance. The droplet shape adopted on the cone was determined by the cone wettability and the size of the droplet relative to the local curvature of the cone. It was found that the oil droplet tends to form a barrel shape on the cone with a highly oleophilic and small apex angle, and tends to form a clamshell shape on cones with a highly oleophobic and large apex angle. In addition, the droplet might transit from a barrel shape to a clamshell shape when it moves from the cone tip to the cone base, and the trigger time of the transit is negatively correlated with the contact angle and apex angle of the cone. This work provides a microscale understanding of the dynamic behavior of an underwater oil droplet on a cone, and also offers theoretical guidance for manipulating the behavior of a droplet on a cone and for the rational design of cone surfaces for spontaneous droplet transport and droplet collection.