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Liquid film on a hydrophobic radome or roof top in rain

Published online by Cambridge University Press:  16 May 2019

Xiaoyu Guo  and
Chiang C. Mei Open the ORCID record for Chiang C. Mei [Opens in a new window]
Xiaoyu Guo
Affiliation:
Department of Engineering Mechanics, Key Laboratory of Hydrodynamics, Shanghai Jiaotong University, Shanghai, China
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
*
†Email address for correspondence: [email protected]
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Abstract

The water film due to rain falling on a radome surface causes severe losses in radio wave transmission. Hydrophobic coatings have been applied as a remedy to reduce the film thickness and to minimize the losses. However, quantitative accounts of the wave scattering are mostly based on empirical estimates of the film thickness. We describe a fluid-mechanical theory for the film under steady rain falling on a textured surface formed by a square array of pillars. Assuming the water surface on top of the pillars to be in the Cassie–Baxter state, the analysis is carried out by making use of the sharp contrast of length scales between the film thickness and the radome radius. The textured surface is viewed as a periodic array of cells around pillars. The macro-scale flow is simple and linear but the micro-scale flow in a typical lattice period is fully nonlinear. These two problems are coupled and are solved iteratively to obtain the slip length and the spatial variation of the film thickness. Numerical results are presented to show the effect of solid fraction on local flow field, the slip length and the non-uniform reduction of the film thickness. To examine the influence of the macro-scale geometry on film formation, the theory is also modified for a hydrophobic roof top formed by two inclined planes.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 1158 - 1174
Copyright
© 2019 Cambridge University Press 

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