Speed of sound in liquids at high pressure

TL;DR

This paper introduces a new general formula for the speed of sound in liquids under high pressure, validated against experimental data for triolein, and proposes phenomenological approximate formulas derived from this new expression.

Contribution

It presents a novel general formula for sound speed in liquids at high pressure, linking it to density and internal energy, and develops phenomenological models based on this formula.

Findings

New formula accurately predicts sound speed up to 450 MPa

Phenomenological formulas with 2 and 3 parameters fit experimental data

Analytical expressions derived through heuristic modeling

Abstract

In this paper, a new general formula for the sound speed in adiabatic conditions ( S = const ) has been established. The sound speed depends on the mass density {\rho} (p,T ) and the internal energy per unit mass E(p,T ), both expressed as functions of the pressure p and the temperature T . This formula has been compared with experimental data on the example of triolein over the pressure range up to 450 MPa. For experimental data, phenomenological approximate formulas have been proposed. Those formulas have two versions, depending on the 2 and 3 parameters. Both versions have been developed with the help of the new expression (Eq.8) for the sound speed. The explicit form of both approximate curves can be regarded as the result of purely phenomenological modeling. However, in this paper, these new analytical expressions have been obtained by applying the heuristic procedure described in Appendix.