Continuum equations for magnetic and dielectric fluids with internal rotations

Area of Science:

• * Physics, Fluid Dynamics, Electromagnetism

Background:

• * Previous attempts to derive equations for polar fluid motion with internal rotations have met with limited success.
• * Polar fluids in a state of polarization disequilibrium require a comprehensive set of governing equations.

Purpose of the Study:

• * To develop a complete set of governing equations for the motion of polar fluids with internal rotations.
• * To incorporate electromagnetic momentum and stress-energy contributions into the fluid dynamics framework.
• * To refine and extend previous analyses of such systems.

Main Methods:

• * Derivation based on dynamic balance relationships and thermodynamic considerations for the dissipation function.
• * Determination of the magnetization relaxation equation from the requirement of positive entropy production.
• * Inclusion of antisymmetric terms in the total stress tensor and use of the Minkowski expression for electromagnetic momentum.
• * Analysis to first order in the ratio of fluid velocity to light speed.

Main Results:

• * A complete set of constitutive laws for polar fluids, including antisymmetric stress tensor components, has been established.
• * The contribution of electromagnetic stress and velocity to energy balance is integrated.
• * The derived equations provide a refined model for polar fluid dynamics under electromagnetic influence.

Conclusions:

• * The developed equations offer a more complete and accurate description of polar fluid motion with internal rotations.
• * This work advances the understanding of electromagnetic-fluid interactions in complex fluid systems.