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Related Concept Videos

Surface Tension and Surface Energy01:16

Surface Tension and Surface Energy

When a paint brush is immersed in water, the bristles wave freely inside the water. When it is taken out, the bristles stick together. The reason behind this effect is surface tension.
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Surface Tension01:24

Surface Tension

Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
Surface Tension, Capillary Action, and Viscosity02:57

Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
Surface Tension of Fluid01:22

Surface Tension of Fluid

Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies with...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
Surface Integrals01:28

Surface Integrals

A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...

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Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
07:57

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

Published on: August 30, 2019

Calculation of surface tension via area sampling.

Jeffrey R Errington1, David A Kofke

  • 1Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA. jerring@buffalo.edu

The Journal of Chemical Physics
|November 13, 2007
PubMed
Summary

Molecular simulation techniques for calculating surface tension were evaluated. Bennett and expanded ensemble methods offer the best accuracy and precision for thermodynamic surface tension calculations.

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Area of Science:

  • Thermodynamics
  • Computational Chemistry
  • Materials Science

Background:

  • Surface tension is a critical property in fluid mechanics and materials science.
  • Accurate calculation of surface tension using molecular simulations is essential for understanding interfacial phenomena.
  • Several computational techniques exist, but their performance varies depending on the system and parameters.

Purpose of the Study:

  • To evaluate and compare the performance of different molecular simulation techniques for calculating surface tension.
  • To identify the most accurate and precise methods for thermodynamic surface tension evaluation.
  • To understand the limitations and underlying reasons for inaccuracies in certain simulation approaches.

Main Methods:

  • Calculated surface tension via the thermodynamic definition, approximating Helmholtz free energy changes.
  • Simulated liquid slabs under constant particle number, volume, and temperature conditions.
  • Explored free-energy perturbation, Bennett acceptance-ratio, and expanded ensemble techniques for truncated Lennard-Jones and square-well fluids.

Main Results:

  • Bennett and expanded ensemble methods demonstrated superior accuracy and precision.
  • All methods yielded equivalent results for the Lennard-Jones fluid with small area perturbations.
  • Single-stage perturbation methods showed inconsistencies for the square-well fluid and large perturbations for the Lennard-Jones fluid, explained by phase-space overlap analysis.

Conclusions:

  • Bennett and expanded ensemble techniques are recommended for reliable thermodynamic surface tension calculations.
  • Inaccuracies in single-stage perturbation methods stem from phase-space overlap issues, particularly with larger perturbations or specific potentials like the square-well fluid.
  • Method performance is sensitive to adjustable parameters, necessitating careful selection and analysis.