Fluid mechanics in fluids at rest

Area of Science:

• Fluid mechanics
• Continuum mechanics
• Chemical engineering

Background:

• Conventional fluid mechanics assumes a single fluid velocity, applicable to both compressible and incompressible flows.
• Current experimental techniques using tracers like dyes or particles often assume they measure the same local fluid velocity.
• The perception of liquids as incompressible can obscure the need for distinct velocity measures in non-isothermal flows.

Purpose of the Study:

• To challenge the assumption of single fluid velocity measurements in compressible flows.
• To demonstrate that different tracers measure fundamentally different fluid velocities in compressible flows.
• To introduce the concept of bivelocity hydrodynamics for a more accurate modeling of fluid behavior.

Main Methods:

• Analysis of experimental thermophoretic particle-velocity data.
• Theoretical examination of tracer behavior in compressible and incompressible fluid flows.
• Comparison of dye-tracer (mass velocity) and particle-tracer (volume velocity) measurements.

Main Results:

• Tracer-velocity equality holds only for incompressible flows.
• In compressible fluids, dye tracers measure mass velocity (v), while inert particles measure volume velocity (v(v)).
• Compressibility effects include pressure and temperature influences on fluid density.

Conclusions:

• Contemporary fluid mechanics, including Navier-Stokes-Fourier equations, is limited to incompressible flows.
• A new bipartite theory, bivelocity hydrodynamics, is required for accurate modeling of compressible fluid dynamics.
• This new framework is applicable to both liquids and gases, unifying their fluid mechanical descriptions.