On the shape and size of liquid droplets on flat solid surfaces

Mestechkin M
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引用次数: 2

Abstract

This article introduces two dimensionless positive geometric parameters that characterize the shape of a liquid droplet on a flat solid surface, which formed by the surface tension. The first parameter, “shape coefficient” K, is defined by the ratio of volume to surface and is always >3 (3 is the space dimension). The second parameter, “holding limit” κ0, is defined by the fraction of osculating surface and K and is <1. The ratio of the surface tension energy of a droplet attached to a substrate in zero gravity to the energy of the same droplet floating in zero gravity is presented through these parameters as 1-(K-3)(κ0-κ)/3(1-κ0), where the material parameter κ (which appears in the Young equation κ=cosθ) indicates the decrease in liquid surface tension by the solid The relative energy of the surface tension, K and κ0, are explicitly expressed for a droplet of an elliptical rounded segment (ERS) shape through its eccentricity e, relative height χ, and relative rounding radius η. It is shown that the Young equation is a self-consistent (i.e., leading to η=0) minimum condition of the energy only in the spherical (e=0) case. The rounding, either inner or outer, is specified by the legs of a triangle with zero angles and the median as a slope line. The main result obtained is the proof that the outer rounded ERS weighty droplets with inflection points, due to weight and hydrostatic forces, cannot exist if their radii larger than 2-4 capillary length. This proscription is absent in zero gravity.
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在平坦的固体表面上液滴的形状和大小
本文介绍了表征平面固体表面上液滴形状的两个无量纲正几何参数,它们是由表面张力形成的。第一个参数“形状系数”K,由体积与表面的比值定义,且总是>3(3为空间维度)。第二个参数“保持极限”κ0,由接触面与K的分数定义,且<1。在失重状态下附着在衬底上的液滴的表面张力能与在失重状态下漂浮的液滴的表面张力能之比通过这些参数表示为1-(K-3)(κ0-κ)/3(1-κ0),其中材料参数κ(出现在Young方程κ= cost θ中)表示固体对液体表面张力的降低。通过偏心率e、相对高度χ和相对圆弧半径η来明确表示椭圆圆弧段(ERS)形状的液滴。结果表明,只有在e=0的球形情况下,Young方程是能量的自洽(即导致η=0)最小条件。内部或外部的舍入由三角形的腿指定,三角形的角为零,中间为斜线。得到的主要结果是证明了具有拐点的外圆形ERS重液滴,由于重量和流体静力的作用,当其半径大于2-4毛细长度时,不可能存在。这种禁止在零重力下是不存在的。
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