Droplet impact onto a porous substrate: a Wagner theory for early-stage spreading

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Engineering Mathematics Pub Date : 2024-04-17 DOI:10.1007/s10665-024-10352-4

Gavin Moreton, Richard Purvis, Mark J. Cooker

引用次数: 0

Abstract

An analytical model for droplet impact onto a porous substrate is presented, based on Wagner theory. An idealised substrate boundary condition is introduced, mimicking the effect of fluid entry into a genuinely porous substrate. The asymptotic analysis yields a solution for a small porous correction with free-surfaces and pressures compared with the impermeable case. On a global scale, it is found that the impact region on the substrate grows more slowly with porosity included due to loss of mass into the substrate. The spatial distribution of liquid volume flux into the substrate is also described. Locally near the turn-over regions, the expected jetting along the surface is calculated with the same volume flux but the jet is found to be slower and thicker than for an impermeable substrate.

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液滴撞击多孔基质：瓦格纳早期扩散理论

以瓦格纳理论为基础，介绍了液滴撞击多孔基底的分析模型。模型引入了理想化的基底边界条件，模拟了流体进入真正多孔基底的效果。通过渐近分析，得出了与不渗透情况相比，具有自由表面和压力的小型多孔校正解。研究发现，在全局范围内，由于基底的质量损失，基底上的撞击区域随着多孔性的加入而增长更慢。此外，还描述了进入基底的液体体积流量的空间分布。在翻转区域附近的局部，在相同体积流量的情况下，计算出了沿表面的预期喷射，但发现喷射比不渗透基底的喷射更慢、更厚。

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.