A New Microscopic Look into Pressure Fields and Local Buoyancy

TL;DR

This paper introduces a microscopic definition of local pressure in classical fluids using a local barometer potential within the Hamiltonian, enabling detailed analysis of buoyancy and pressure fields.

Contribution

It provides a novel microscopic framework for defining local pressure and derives a generalized buoyancy principle within this context.

Findings

Microscopic pressure definition via ensemble average of radial force.

Derivation of a generalized Archimedes's buoyancy principle.

Application to various external fields demonstrating the framework's versatility.

Abstract

The concept of local pressure is pivotal to describe many important physical phenomena, such as buoyancy or atmospheric phenomena, which always require the consideration of space-varying pressure fields. These fields have precise definitions within the phenomenology of hydro-thermodynamics, but a simple and pedagogical microscopic description based on Statistical Mechanical is still lacking in present literature. In this paper, we propose a new microscopic definition of the local pressure field inside a classical fluid, relying on a local barometer potential that is built into the many-particle Hamiltonian. Such a setup allows the pressure to be locally defined, at an arbitrary point inside the fluid, simply by doing a standard ensemble average of the radial force exerted by the barometer potential on the gas' particles. This setup is further used to give a microscopic derivation of the generalized Archimedes's buoyancy principle, in the presence of an arbitrary external field. As instructive examples, buoyancy force fields are calculated for ideal fluids in the presence of: i) a uniform force field, ii) a spherically symmetric harmonic confinement field, and iii) a centrifugal rotating frame.