Exact identities for sessile drops

Hajirahimi, Maryam; Mokhtari, Fatemeh; Fatollahi, Amir H.

doi:10.1007/s10483-015-1916-6

Cited by 3 publications

(3 citation statements)

References 22 publications

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“…This pressure, with the use of the Young–Laplace equation, can also be written in terms of the mean-curvature H 0 at point o

2

with γ as the surface tension of liquid. Altogether the force balance ( 2.18 ) reads

22

or, after dividing by

2

The above is a direct generalization of eqn (12) of [ 14 , 15 , 19 ] for a horizontal substrate ( α = 0).…”

Section: Identities By Force Balancementioning

confidence: 99%

“…An early example of these identities is the one by [12] between the volume, curvature at apex, height and contact radius of axi-symmetric drops on a flat horizontal surface (see also [13,14]). For axi-symmetric drops on curved surfaces the very same identities are derived in [15]. For droplets under the combined tangential and normal body forces the dynamical relations between shape parameters have been presented in a linear approximation recently [16].…”

Section: Introductionmentioning

confidence: 95%

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Identities for droplets with circular footprint on tilted surfaces

et al. 2020

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Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young–Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

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“…This pressure, with the use of the Young–Laplace equation, can also be written in terms of the mean-curvature H 0 at point o

2

with γ as the surface tension of liquid. Altogether the force balance ( 2.18 ) reads

22

or, after dividing by

2

The above is a direct generalization of eqn (12) of [ 14 , 15 , 19 ] for a horizontal substrate ( α = 0).…”

Section: Identities By Force Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Identities for droplets with circular footprint on tilted surfaces

et al. 2020

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“…However, the ellipsoidal models keep in agreement with practical situations only when

. M. Hajirahimi [ 13 ] used the direct integration of the Laplace equation to gain the profiles and ACAs of an axisymmetric heavy droplet on smooth spherical surfaces in 2015. Based on Matlab’s “fmin” function, Jian Dong [ 14 ] used the direct discretion of the droplet profile to gain the profiles and ACAs of an axisymmetric heavy droplet on rough horizontal surfaces in 2017.…”

Section: Introductionmentioning

confidence: 99%

Predictions of the Wettable Parameters of an Axisymmetric Large-Volume Droplet on a Microstructured Surface in Gravity

Jian

Zhang

et al. 2023

Micromachines

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In this study, a numerical model was developed to predict the wettable parameters of an axisymmetric large-volume droplet on a microstructured surface in gravity. We defined a droplet with the Bond number Bo>0.1 as a large-volume droplet. Bo was calculated by using the equation Bo=ρlgγlv(3V4π)23 where ρl is the density of liquid, γlv is the liquid-vapor interfacial tension, g is the gravity acceleration and V is the droplet volume. The volume of a large-volume water droplet was larger than 2.7 uL. By using the total energy minimization and the arc differential method of the Bashforth–Adams equation, we got the profile, the apparent contact angle and the contact circle diameter of an axisymmetric large-volume droplet in gravity on a microstructured horizontal plane and the external spherical surface. The predictions of our model have a less than 3% error rate when compared to experiments. Our model is much more accurate than previous ellipsoidal models. In addition, our model calculates much more quickly than previous models because of the use of the arc differential method of the Bashforth–Adams equation. It shows promise for use in the design and fabrication of microfluidic devices.

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