Abstract
Inspired by the antiwetting property of pitcher plants, specialists have designed different functional material with slippery surfaces, and a directional slippery surface has been fabricated. This paper considers a gravity-driven liquid film coating the interior surface of a vertical tube, and different slippery lengths in the azimuthal direction and the axial direction are taken into account. The evolution equation of coating flow is derived using the thin film model, and time responses for two dimensional flow are calculated. Linear stability analysis (LSA) is given based on the traveling wave solutions, demonstrating that the axial slippery effect suppresses the flow instability and causes a larger traveling wave speed. Simultaneously, the azimuthal slippery effect plays a destabilizing role for perturbations with small wavenumbers and it is stabilizing for large wavenumbers. Direct simulations of the fingering flow patterns agree well with the linear stability analysis. Our results offer insight into the influence of wall slippage on the flow stability of liquid in petroleum engineering.
Highlights
Thin film flowing and droplet spreading are commonly encountered in chemical engineering, nuclear industry and materials sciences
We investigated the fingering instability of a coating flow down a vertical tube with dynamic contact line, and the influence of the directional slippery substrate on the flow instability was analyzed
Based on the thin film theory, the governing equation for the thin film flow was derived, the time responses for the axisymmetry model for different parameters were simulated, including the precursor thicknesses, the axial slippery length and the radius of the tube
Summary
Thin film flowing and droplet spreading are commonly encountered in chemical engineering, nuclear industry and materials sciences. In the modeling of the liquid film, assumption of a small averaged thickness is crucial [7,8] These modeling methods were applied in dynamical contact line problems [9,10,11,12]. The spreading and falling of the liquid films on different substrates have been received much attention. It was found the curvature and property of the substrate played important roles in the film flows [20,21,22,23,24]. This paper mainly focuses on the influence of the anisotropic slippery length on the surface instability of thin films flowing down a vertical tube.
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