On the capillary bridge between spherical particles of unequal size: analytical and experimental approaches

Nguyen, Hien Nho Gia; Millet, Olivier; Gagneux, Gérard

doi:10.1007/s00161-018-0658-2

Cited by 22 publications

(21 citation statements)

References 21 publications

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“…This principle corresponds to the realization of the bridge of free surface of minimal area under various constraints, including that of an imposed liquid volume. The associated analytical calculations have been validated by experimental measurements using an imageprocessing technique, for capillary bridges between two identical spherical particles [17], or even between particles of different radii [18,19]. This method is proven to be very efficient and therefore will be extended in this article to capillary bridges between a sphere and a planar surface.…”

Section: Introductionmentioning

confidence: 92%

Liquid bridges between a sphere and a plane - Classification of meniscus profiles for unknown capillary pressure

Nguyen

Millet

Gagneux

2019

Mathematics and Mechanics of Solids

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The motivation for this study results from the following practical observation: for the experimenter, the value of the capillary pressure is a priori an unknown of the problem, it corresponds to a spontaneous value resulting a posteriori from a static equilibrium. A general classification of axisymmetric capillary bridge profiles for unknown capillary pressure between a sphere and a plane is addressed in this article. The meridian of the liquid bridge is classified into convex or concave profiles as portions of nodoid or unduloid surfaces based on measured geometrical data with special limit cases as catenoid, cylinder, or sphere. The theoretical work is then validated by an image-processing technique applied to images of real capillary bridges from experiments for small water volumes and small sphere–plate separation distances. The laboratory tests show very good agreement between the theoretical calculations and the associated classification proposed. Even the transition case of a catenoid can be observed.

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Section: Introductionmentioning

confidence: 92%

Liquid bridges between a sphere and a plane - Classification of meniscus profiles for unknown capillary pressure

Nguyen

Millet

Gagneux

2019

Mathematics and Mechanics of Solids

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“…The pressure difference of a symmetric capillary bridge can be derived by the Young–Laplace equation. Various works have shown experimentally that the Young–Laplace equation describes the properties of capillary bridges accurately without the gravity effect [ 24 ]. To simplify the calculation of the capillary bridge profile, a dimensionless Young–Laplace equation is written as follows:

where

, and

is the dimensionless pressure difference.…”

Section: Modeling the Capillary Bridge And Capillary Forcementioning

confidence: 99%

Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping

et al. 2021

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The capillary action between two solid surfaces has drawn significant attention in micro-objects manipulation. The axisymmetric capillary bridges and capillary forces between a spherical concave gripper and a spherical particle are investigated in the present study. A numerical procedure based on a shooting method, which consists of double iterative loops, was employed to obtain the capillary bridge profile and bring the capillary force subject to a constant volume condition. Capillary bridge rupture was characterized using the parameters of the neck radius, pressure difference, half-filling angle, and capillary force. The effects of various parameters, such as the contact angle of the spherical concave gripper, the radius ratio, and the liquid bridge volume on the dimensionless capillary force, are discussed. The results show that the radius ratio has a significant influence on the dimensionless capillary force for the dimensionless liquid bridge volumes of 0.01, 0.05, and 0.1 when the radius ratio value is smaller than 10. The effectiveness of the theorical approach was verified using simulation model and experiments.

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“…И, наконец, на рис. 4 приведены четыре различных профиля боковой поверхности жидкого моста между сферами, соответствующие одному значению высоты моста h 0 = 0.9 и четырем различным значениям параметра M. Заметим, что график (a), соответствующий варианту (+ +), согласуется с фотографиями, полученными в ходе эксперимента и приведенными в работе [6], в то время как остальные три графика отражают другие теоретически возможные профили.…”

Section: пример расчета жидкого моста между сферамиunclassified

“…В работе [4] построена асимптотика формы поверхности горизонтального жидкого моста между двумя вертикальными твердыми плоскостями при малых числах Бонда. Оригинальный подход к нахождению формы жидкого моста между сферами, основанный на решении обратной задачи, используется в [5,6]. В первой из этих работ дается классификация форм мостов, а во второйприводятся их фотографии, полученные в эксперименте.…”

Section: Introductionunclassified

Решение Задачи О Форме Вертикального Жидкого Моста Между Выпуклыми Поверхностями С Учетом Силы Тяжести

Галактионов¹,

Галактионова²,

Тропп³

2021

Журнал Технической Физики

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The solution to the problem on the shape of the lateral surface of a vertical three-dimensional catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the axisymmetric case, taking into account the action of gravity, is presented. A variational formulation of the original problem has given. The solution has found by the iteration method under the assumption that the Bond number has been small. The algorithm of iterative process has proposed. The parameters change areas for which there is no uniqueness of the solution to the problem have discovered. It has been established that the maximum number of different profiles of the liquid bridge lateral surface corresponding the single selected set of parameters has equal to four. As an example, the liquid bridge shape problem between two spheres was solved.

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On the capillary bridge between spherical particles of unequal size: analytical and experimental approaches

Cited by 22 publications

References 21 publications

Liquid bridges between a sphere and a plane - Classification of meniscus profiles for unknown capillary pressure

Liquid bridges between a sphere and a plane - Classification of meniscus profiles for unknown capillary pressure

Capillary Forces between Concave Gripper and Spherical Particle for Micro-Objects Gripping

Решение Задачи О Форме Вертикального Жидкого Моста Между Выпуклыми Поверхностями С Учетом Силы Тяжести

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