Abstract
Abstract
Highlights
Coating a film onto a substrate as a liquid is forced to move along it is a technique used in painting and industrial applications such as lithography, which has been studied since the early twentieth century (Quéré 1999)
At t = 0.89, a nearly uniform pressure distribution is achieved in the bulk of the droplet, but a large pressure gradient is created at the two edges of the droplet, which are commonly referred to as the ‘contact line regions’, see figure 2(b) for the pressure distribution at t = 256
The directional spreading of a viscous droplet on a conical fibre due to capillarity is investigated for small cone angles and for a wide range of slip lengths by using the lubrication equation on a cone
Summary
Coating a film onto a substrate as a liquid is forced to move along it is a technique used in painting and industrial applications such as lithography, which has been studied since the early twentieth century (Quéré 1999). By using the method of asymptotic matching, the thickness of the film hf , denoted as the Landau–Levich–Derjaguin (LLD) film, is shown to have a universal scaling with respect to the plate velocity U as hf / c ∼ Ca2/3, where the capillary number Ca ≡ ηU/γ is the ratio between the viscous and the surface tension forces This Ca2/3 power law has been demonstrated to be a robust relation in many different systems when a fluid film is deposited. When a droplet with a size smaller than the capillary length comes in contact with a conical fibre, it moves spontaneously from the tip to the base of the cone due to capillarity (Lorenceau & Quéré 2004; Li & Thoroddsen 2013) In nature, this self-propelled mechanism has been exploited by plants (Liu et al 2015) and animals (Zheng et al 2010; Wang et al 2015) to facilitate water transport at small scales. The approach of MD simulations has previously been implemented to study the wetting dynamics at the nanoscale (Nakamura et al 2013), the slip condition at a contact line region (Qian, Wang & Sheng 2003), the frictional force on a sliding droplet (Koplik 2019) and the influence of physico-chemistry of the water/substrate interface on the droplet dynamics (Johansson, Carlson & Hess 2015)
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