Analysis of the Equilibrium Droplet Shape Based on an Ellipsoidal Droplet Model

Lubarda, Vlado A.; Talke, Kurt

doi:10.1021/la202077w

Cited by 141 publications

(94 citation statements)

References 51 publications

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“…A widely used approach to calculate a minimum energy surface is by means of the Surface Evolver program. 42 But several other approaches, both theoretical and numerical, have been used for studying the fluid-fluid interface shape in different physical problems, e.g., menisci shapes and capillary interactions, [43][44][45][46][47][48][49][50][51][52] droplet shapes, [53][54][55][56][57] diffuse interfaces, [58][59][60] or fluid-fluid interfaces in contact with deformable solids. [61][62][63] In this article, we introduce a new numerical method to obtain the minimum-energy shape of a fluid-fluid interface.…”

Section: Introductionmentioning

confidence: 99%

The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations

Soligno

Dijkstra

Roij

2014

The Journal of Chemical Physics

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Articles you may be interested inMany physical problems require explicit knowledge of the equilibrium shape of the interface between two fluid phases. Here, we present a new numerical method which is simply implementable and easily adaptable for a wide range of problems involving capillary deformations of fluid-fluid interfaces. We apply a simulated annealing algorithm to find the interface shape that minimizes the thermodynamic potential of the system. First, for completeness, we provide an analytical proof that minimizing this potential is equivalent to solving the Young-Laplace equation and the Young law. Then, we illustrate our numerical method showing two-dimensional results for fluid-fluid menisci between vertical or inclined walls and curved surfaces, capillary interactions between vertical walls, equilibrium shapes of sessile heavy droplets on a flat horizontal solid surface, and of droplets pending from flat or curved solid surfaces. Finally, we show illustrative three-dimensional results to point out the applicability of the method to micro-or nano-particles adsorbed at a fluid-fluid interface. C 2014 AIP Publishing LLC.[http://dx

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Section: Introductionmentioning

confidence: 99%

The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations

Soligno

Dijkstra

Roij

2014

The Journal of Chemical Physics

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“…Two cases of spheroidal caps (http://keisan.casio.com/exec/system/1223382199; http://keisan.casio.com/exec/system/13581717527) 40,41 must be differentiated to calculate the values of the solid–liquid Ω SL and the liquid–air Ω L interfacial areas: a * = 0 and a * < 0.…”

Section: Theoretical Basis Of the Methodsmentioning

confidence: 99%

The measurement of the surface energy of solids using a laboratory drop tower

Calvimontes

2017

npj Microgravity

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This work presents a technique for the study and measurement of the interfacial energies of solid–liquid–gas systems. The instrument and the evaluation method for the measurements obtained by it, allow the analysis of the energy changes of sessile drops submitted to microgravity. A mathematical model based on the thermodynamic of wetting is applied to evaluate the interfacial energies as a function of the drop shape changes due to the effect of the release of gravitation during the experiment. The presented model bases on the thermodynamic equilibrium of the interfaces and not on the balance of bi-dimensional tensors on the contour line. For this reason, the model does not follow Young’s equation as the current surface wetting characterization techniques usually do.

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“…where β = g pR 0 2 /γ is the Bond number, 25 θ is the tangential angle, as shown in Fig. 1, ρ is the difference in the densities of the two bulk phases, and g is the gravitational acceleration.…”

Section: Validation Of the Accuracy Of Water Drop Profiles Generamentioning

confidence: 99%

“…As the water drop volume increases, the water drop profile gradually approaches that of part of an ellipse. 25 The ellipse-fitting algorithm 24,27 is more suitable for larger contact angles and drop volumes. However, static contact angle measurements on a superhydrophobic surface will introduce significant errors.…”

Section: Introductionmentioning

confidence: 99%

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis

Zhi-niu

2014

Review of Scientific Instruments

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In this study, an error analysis is performed to study real water drop images and the corresponding numerically generated water drop profiles for three widely used static contact angle algorithms: the circle- and ellipse-fitting algorithms and the axisymmetric drop shape analysis-profile (ADSA-P) algorithm. The results demonstrate the accuracy of the numerically generated drop profiles based on the Laplace equation. A significant number of water drop profiles with different volumes, contact angles, and noise levels are generated, and the influences of the three factors on the accuracies of the three algorithms are systematically investigated. The results reveal that the above-mentioned three algorithms are complementary. In fact, the circle- and ellipse-fitting algorithms show low errors and are highly resistant to noise for water drops with small/medium volumes and contact angles, while for water drop with large volumes and contact angles just the ADSA-P algorithm can meet accuracy requirement. However, this algorithm introduces significant errors in the case of small volumes and contact angles because of its high sensitivity to noise. The critical water drop volumes of the circle- and ellipse-fitting algorithms corresponding to a certain contact angle error are obtained through a significant amount of computation. To improve the precision of the static contact angle measurement, a more accurate algorithm based on a combination of the three algorithms is proposed. Following a systematic investigation, the algorithm selection rule is described in detail, while maintaining the advantages of the three algorithms and overcoming their deficiencies. In general, static contact angles over the entire hydrophobicity range can be accurately evaluated using the proposed algorithm. The ease of erroneous judgment in static contact angle measurements is avoided. The proposed algorithm is validated by a static contact angle evaluation of real and numerically generated water drop images with different hydrophobicity values and volumes.

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Analysis of the Equilibrium Droplet Shape Based on an Ellipsoidal Droplet Model

Cited by 141 publications

References 51 publications

The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations

The equilibrium shape of fluid-fluid interfaces: Derivation and a new numerical method for Young’s and Young-Laplace equations

The measurement of the surface energy of solids using a laboratory drop tower

An algorithm for selecting the most accurate protocol for contact angle measurement by drop shape analysis

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