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Basic Equation for Pressure Field

Basic Equation for Pressure Field

The basic equation for a pressure field in fluid mechanics captures the balance of forces within any segment of fluid, providing a foundational understanding of how pressure changes within fluids under various forces. Generally, two main types of forces act on any part of a fluid: surface forces and body forces. Surface forces arise from pressure differences across points within the fluid, which result in net forces that can vary depending on the local pressure gradient. Body forces, on the...

The Van der Waals Equation

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...

Van der Waals Equation

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...

Concept of Pressure at a Point

Concept of Pressure at a Point

The concept of pressure at a point in a fluid establishes that pressure within a fluid is uniform in all directions at a specific location. This uniformity occurs because fluid molecules exert force evenly across any point due to their random motion and continuous collisions within the fluid. Pressure at a point is determined by the surrounding fluid molecules and is influenced by factors like depth and density, rather than by shape or orientation.
In a fluid at rest, pressure acts equally in...

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.

Pressure Variation in a Fluid at Rest

Pressure Variation in a Fluid at Rest

In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
When measuring pressure at two different levels within the fluid, the difference in pressure...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems.

Takenobu Nakamura¹, Wataru Shinoda, Tamio Ikeshoji

¹Nanosystem Research Institute (NRI), National Institute of Advanced Industrial Science and Technology (AIST), Central-2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan. takenobu.nakamura@aist.go.jp

The Journal of Chemical Physics

|September 15, 2011

Summary

We developed a new method to precisely calculate the radial pressure tensor in spherical molecular systems. This approach enhances numerical stability and reduces computational cost for molecular simulations.

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Area of Science:

Computational chemistry
Molecular dynamics
Statistical mechanics

Background:

Accurate calculation of pressure tensor is crucial for understanding molecular systems.
Existing methods can suffer from numerical instability and high computational cost.
Spherical symmetry in molecular systems offers opportunities for simplification.

Purpose of the Study:

To introduce a novel, numerically stable, and computationally efficient method for calculating the radial pressure tensor.
To derive simplified expressions for local pressure in common molecular force fields.
To address and overcome issues of numerical singularity in pressure tensor calculations.

Main Methods:

Utilizing slice-averaged pressure for improved numerical stability and precision.
Deriving simplified local pressure expressions for non-bond, bond, angle, and torsion interactions.
Implementing an algorithm to circumvent numerical singularity.

Main Results:

The proposed method significantly enhances numerical stability and precision.
Simplified expressions lead to reduced computational cost.
Successful application to diverse systems: water droplet, micelle, and liposome.

Conclusions:

The novel method provides a robust and efficient approach for radial pressure tensor computation.
The technique is validated across various spherical molecular systems.
This work offers a valuable tool for molecular simulations requiring accurate pressure tensor analysis.