Film deposition and dynamics of a self-propelled wetting droplet on a conical fibre

Abstract

Abstract

Multiple droplets on a conical fiber: formation, motion, and droplet mergers

“…The axisymmetric liquid-air interface profile is given by ĥ = ĥ(z,t), defined as the distance between the interface and the substrate, as a function of the distance from the vertex of the cone z and time t. We note that z measures along the surface of the cone and is related to the experimentally measured z as z = z cos(a) and for small angles z E z. The evolution of the liquid-air This journal is © The Royal Society of Chemistry 2022 interface is described by the thin film equation and driven by the capillary pressure gradients qp/qz which reads, 20,43 @ ĥ…”

“…20,43 Eqn ( 1) and ( 3) are discretized by linear elements and numerically solved with a Newton solver by using the open source finite element code FEniCS, 44 additional details about the numerical approach are found in. 43 The initial condition is a droplet smoothly connected to a pre-wet film of thickness e. At the two boundaries (dO) of the numerical domain we impose ĥ(dO,t) = e and p(dO,t) = g/[R(dO) +e], where R(dO) is the radius of the cone at the boundaries. We note that only the droplet volume V is important and the initial droplet shape does not affect the results.…”

Multiple droplets on a conical fiber: formation, motion, and droplet mergers

“…The axisymmetric liquid-air interface profile is given by h = h(ζ, t), defined as the distance between the interface and the substrate, as a function of the distance from the vertex of the cone ζ and time t. We note that ζ measures along the surface of the cone and is related to the experimentally measured z as z = ζcos(α) and for small angles ζ ≈ z. The evolution of the liquid-air interface is described by the thin film equation and driven by the capillary pressure gradients ∂p/∂ζ which reads [20,44],…”

“…Eq. ( 1) and ( 3) are discretized by linear elements and numerically solved with a Newton solver by using the open source finite element code FEniCS [45], additional details about the numerical approach are found in [44]. The initial condition is a droplet smoothly connected to a pre-wet film of thickness .…”

Static wetting of a barrel-shaped droplet on a soft-layer-coated fiber

“…1,2 The shape of deformation has been explored extensively in the last few decades; however, those studies have mainly focussed on situations of a droplet on a planar substrate. 1–25 Although there have been numerous studies of droplets on rigid fibers, 26–31 wetting on a rigid fiber coated with a soft layer has been far less investigated. 32 How this geometry modifies the deformation of the coated elastic layer remains unclear, which is the focus of this study.…”