Rotational Inertial Physics in Non-Classical Thermoviscous Fluent Continua Incorporating Internal Rotation Rates

In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.

NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

Observation of tiny polarization rotation rate in total internal reflection via weak measurements

In this paper,we examine the tiny polarization rotation effect in total internal reflection due to the spin–orbit interaction of light.We find that the tiny polarization rotation rate will induce a geometric phase gradient,which can be regarded as the physical origin of photonic spin Hall effect.We demonstrate that the spin-dependent splitting in position space is related to the polarization rotation in momentum space,while the spin-dependent splitting in momentum space is attributed to the polarization rotation in position space.Furthermore,we introduce a quantum weak measurement to determine the tiny polarization rotation rate.The rotation rate in momentum space is obtained with 118 nm,which manifests itself as a spatial shift,and the rotation rate in position space is achieved with 38 μrad∕λ,which manifests itself as an angular shift.The investigation of the polarization rotation characteristics will provide insights into the photonic spin Hall effect and will enable us to better understand the spin–orbit interaction of light.