Numerical validation of analytical formulas for channel flows over liquid-infused surfaces

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Engineering Mathematics Pub Date : 2024-01-17 DOI:10.1007/s10665-023-10314-2

Hiroyuki Miyoshi, Henry Rodriguez-Broadbent, Darren G. Crowdy

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Abstract

This paper provides numerical validation of some new explicit, asymptotically exact, analytical formulas describing channel flows over liquid-infused surfaces, an important class of surfaces of current interest in surface engineering. The new asymptotic formulas, reproduced here, were derived in a recent companion paper by the authors. The numerical validation is done by presenting a novel computational method for calculating longitudinal flow in a periodic channel involving finite-length closed liquid-filled grooves with a flat two-fluid interface, a challenging problem given the two-fluid nature of the flow. The formulas are asymptotically exact for wide channels where the grooves on the lower wall of the channel are well separated; the numerical method devised here, however, is subject to no such restrictions. Significantly, it is shown here that the asymptotic formulas remain good global approximants for the flow over a wide range of flow geometries, including those well outside the asymptotic parameter range for which they were derived. It is found that the formulas are more reliable for liquid-infused surfaces than for superhydrophobic surfaces.

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液体注入表面上的通道流分析公式的数值验证

本文对一些新的明确、渐近精确的分析公式进行了数值验证，这些公式描述了液体注入表面上的通道流，这是表面工程领域目前关注的一类重要表面。本文转载的新渐近公式是作者在最近的一篇论文中推导出来的。数值验证是通过提出一种新颖的计算方法来完成的，该方法用于计算周期性通道中的纵向流动，该通道涉及有限长度的封闭液体填充凹槽，凹槽具有平坦的双流体界面，鉴于流动的双流体性质，这是一个具有挑战性的问题。对于通道下壁的凹槽分离良好的宽通道，公式是渐进精确的；而本文设计的数值方法则不受这些限制。值得注意的是，本文显示，渐近公式在广泛的流动几何形状中，包括在其推导的渐近参数范围之外的流动几何形状中，仍然是良好的全局近似值。研究发现，与超疏水表面相比，这些公式对于液体注入表面更为可靠。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Engineering Mathematics 工程技术-工程：综合

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： The aim of this journal is to promote the application of mathematics to problems from engineering and the applied sciences. It also aims to emphasize the intrinsic unity, through mathematics, of the fundamental problems of applied and engineering science. The scope of the journal includes the following: • Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional−analytic methods, Numerical analysis, Computational methods. • Applied Fields: Continuum mechanics, Stability theory, Wave propagation, Diffusion, Heat and mass transfer, Free−boundary problems; Fluid mechanics: Aero− and hydrodynamics, Boundary layers, Shock waves, Fluid machinery, Fluid−structure interactions, Convection, Combustion, Acoustics, Multi−phase flows, Transition and turbulence, Creeping flow, Rheology, Porous−media flows, Ocean engineering, Atmospheric engineering, Non-Newtonian flows, Ship hydrodynamics; Solid mechanics: Elasticity, Classical mechanics, Nonlinear mechanics, Vibrations, Plates and shells, Fracture mechanics; Biomedical engineering, Geophysical engineering, Reaction−diffusion problems; and related areas. The Journal also publishes occasional invited ''Perspectives'' articles by distinguished researchers reviewing and bringing their authoritative overview to recent developments in topics of current interest in their area of expertise. Authors wishing to suggest topics for such articles should contact the Editors-in-Chief directly. Prospective authors are encouraged to consult recent issues of the journal in order to judge whether or not their manuscript is consistent with the style and content of published papers.