Abstract
Plants and insects use slender conical structures to transport and collect small droplets, which are propelled along the conical structures due to capillary action. These droplets can deposit a fluid film during their motion, but despite its importance to many biological systems and industrial applications the properties of the deposited film are unknown. We characterise the film deposition by developing an asymptotic analysis together with experimental measurements and numerical simulations based on the lubrication equation. We show that the deposited film thickness depends significantly on both the fiber radius and the droplet size, highlighting that the coating is affected by finite size effects relevant to film deposition on fibres of any slender geometry. We demonstrate that by changing the droplet size, while the mean fiber radius and the Capillary number are fixed, the thickness of the deposited film can change by an order of magnitude or more. We show that self-propelled droplets have significant potential to create passively coated structures.
Highlights
Thin viscous films have been of great interest to mankind for centuries with a notable early application related to the invention of the wheel and axle and its need for lubricating films [1]
We study the dynamic wetting of a self-propelled viscous droplet using the time-dependent lubrication equation on a conical-shaped substrate for different cone radii, cone angles and slip lengths
Our results show that manipulating the droplet size, the cone angle and the slip length provides different schemes for guiding droplet motion and coating the substrate with a film
Summary
Thin viscous films have been of great interest to mankind for centuries with a notable early application related to the invention of the wheel and axle and its need for lubricating films [1]. The motion of an elastic sheet supported by a thin layer of viscous fluid is a phenomenon that manifests itself in processes spanning wide ranges of time and length scales, from, e.g., magmatic intrusion in the Earth’s crust [1,2], to fracturing and crack formation in glaciers [3], to pumping in the digestive and arterial systems [4–6], or the construction of two-dimensional (2D) crystals for electronic engineering [7]. Elastohydrodynamic flows have been studied in model geometries in order to understand their generic features and the inherent coupling between the driving force from the elastic deformations of the material and the viscous friction force resisting motion [8–16]. If the supporting film is instead of nanoscopic thickness, elastic bending generates a restoring force trying to oppose the van der Waals force that pulls the plate towards the wall and can lead to an elastohydrodynamic touchdown [24] similar to the dewetting of a liquid film [25]. Not much is known about how elastohydrodynamic flows are affected by the ratio between the geometric parameters that characterize the system as it undergoes large changes while the driving force remain the same
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