On the Validity of Antonoff's Rule.

Antonoff, George

doi:10.1021/j150418a009

Cited by 30 publications

(16 citation statements)

References 1 publication

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“…From the modeling point of view, the droplet formation can be described as

where:

is the level set function and the

and

are numerical stabilization parameters, u is the velocity (m/s), t is the time (s), µ is the dynamic viscosity (Pa·s) and the p is the pressure (Pa). The F st is the surface tension force (N/m) and can be approximated using Antonoff’s [ 63 ] rule as

where

is the surface tension of water and

is the surface tension of oil phase measured in the contact with air.…”

Section: Simulation Of Droplet Formationmentioning

confidence: 99%

Micro Droplet Formation towards Continuous Nanoparticles Synthesis

et al. 2018

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In this paper, micro droplets are generated in a microfluidic focusing contactor and then they move sequentially in a free-flowing mode (no wall contact). For this purpose, two different micro-flow glass devices (hydrophobic and hydrophilic) were used. During the study, the influence of the flow rate of the water phase and the oil phase on the droplet size and size distribution was investigated. Moreover, the influence of the oil phase viscosity on the droplet size was analyzed. It was found that the size and size distribution of the droplets can be controlled simply by the aqueous phase flow rate. Additionally, 2D simulations to determine the droplet size were performed and compared with the experiment.

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“…From the modeling point of view, the droplet formation can be described as

where:

is the level set function and the

and

where

is the surface tension of water and

is the surface tension of oil phase measured in the contact with air.…”

Section: Simulation Of Droplet Formationmentioning

confidence: 99%

Micro Droplet Formation towards Continuous Nanoparticles Synthesis

et al. 2018

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“…The simplest method for relating the interfacial tension between two substances with their respective surface energies is the Antonoff method 18,19 given as follows:…”

Section: Estimation Of the Surface Energy Of Hpeso Polysoapsmentioning

confidence: 99%

Investigation of the surface properties of polymeric soaps obtained by ring‐opening polymerization of epoxidized soybean oil

Biresaw

Liu

Erhan

2008

J of Applied Polymer Sci

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Epoxidized soybean oil (ESO) was converted to a polysoap (PESO) via a two-step synthetic procedure of catalytic ring-opening polymerization, followed by hydrolysis (HPESO) with a base. Various molecular weights of PESO and HPESO were prepared by varying the reaction temperature and/or catalyst concentration. In addition, the counter ion chemistry was varied by changing the base used for saponification. The PESO and HPESO products were carefully characterized and identified using a combination of FTIR, 1 H-NMR, solid state 13 C-NMR, and GPC. The effect of HPESO polysoaps on the surface tension of water and the interfacial tension of water-hexadecane was investigated as a function of HPESO concentration, molecular weight, and counter ion chemistry. HPESO polysoaps were effective at lowering the surface tension of water and the interfacial tension of water-hexadecane and displayed minimum values in the range of 20-24 and 12-17 dyn/cm, respectively, at concentration of 200-250 lM. Water-hexadecane interfacial tension was also calculated from measured surface tension data using the Antonoff, harmonic mean (HM), and geometric mean (GM) methods. Measured values agreed well with those calculated using the HM and GM methods, but not the Antonoff method.

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“…Antonoff claimed in 1942 that the validity of the rule "cannot be disputed, since it is a law of equilibrium, it is bound to be a precise law"; however, one should be careful in defining the surface tensions σa and σb [14]. According to Antonoff [14], the words "when exposed to air" were absent from his original definition of the rule [6], and this later addition by other scientist "places the whole principle in contradiction with the laws of thermodynamics. "…”

Section: Antonow's Equationmentioning

confidence: 99%

Geometric Interpretation of Surface Tension Equilibrium in Superhydrophobic Systems

Nosonovsky

Ramachandran

2015

Entropy

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Surface tension and surface energy are closely related, although not identical concepts. Surface tension is a generalized force; unlike a conventional mechanical force, it is not applied to any particular body or point. Using this notion, we suggest a simple geometric interpretation of the Young, Wenzel, Cassie, Antonoff and Girifalco-Good equations for the equilibrium during wetting. This approach extends the traditional concept of Neumann's triangle. Substances are presented as points, while tensions are vectors connecting the points, and the equations and inequalities of wetting equilibrium obtain simple geometric meaning with the surface roughness effect interpreted as stretching of corresponding vectors; surface heterogeneity is their linear combination, and contact angle hysteresis is rotation. We discuss energy dissipation mechanisms during wetting due to contact angle hysteresis, the superhydrophobicity and the possible entropic nature of the surface tension.

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On the Validity of Antonoff's Rule.

Cited by 30 publications

References 1 publication

Micro Droplet Formation towards Continuous Nanoparticles Synthesis

Micro Droplet Formation towards Continuous Nanoparticles Synthesis

Investigation of the surface properties of polymeric soaps obtained by ring‐opening polymerization of epoxidized soybean oil

Geometric Interpretation of Surface Tension Equilibrium in Superhydrophobic Systems

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