Longitudinal Shear Flow over a Superhydrophobic Grating with Partially Invaded Grooves and Curved Menisci

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Ehud Yariv
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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1186-1203, June 2024.
Abstract. We consider longitudinal shear flows over a superhydrophobic grating made up of a periodic array of grooves separated by infinitely thin slats, addressing the case where the liquid partially invades the grooves. We allow for curved menisci, specified via a depression angle at the contact line. We focus on the limit of small solid fractions where the length of the wetted portion of the slat is small compared with the period. Following an earlier analysis of the comparable flow over noninvaded grooves [O. Schnitzer, J. Fluid Mech., 820 (2017), pp. 580–603], this singular limit is treated using matched asymptotic expansions, with an outer region on the scale of a single period and an inner region on the scale of the wetted portion of the slat. The flow problem in both regions is solved using conformal mappings. Asymptotic matching yields a closed-form approximation for the slip length as a function of the solid fraction and depression angle.
带有部分内陷凹槽和弯曲半月板的超疏水光栅上的纵向剪切流
SIAM 应用数学杂志》第 84 卷第 3 期第 1186-1203 页,2024 年 6 月。 摘要。我们考虑了超疏水性光栅上的纵向剪切流,该光栅由无限薄的板条隔开的周期性凹槽阵列组成,解决了液体部分侵入凹槽的情况。我们允许通过接触线的凹陷角来指定弯曲的半月板。我们将重点放在固体分数较小的极限上,即板条润湿部分的长度与周期相比较小。根据早先对非侵蚀沟槽上可比流动的分析[O. Schnitzer, J. Fluid Mech., 820 (2017), pp.这两个区域的流动问题均采用保角映射法求解。渐近匹配得出了滑移长度作为固体分数和凹陷角函数的闭式近似值。
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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