Hydrodynamics and Collective Angular-Momentum Fluctuations in Molecular Fluids

Abstract

expansion and evaluated leading terms for the phonon frequency and damping which were not available before.The rather sizable reduction in algebraic complexity using our method seen s to indicate that the next order, i. e. , the two-ring terms, is not out of reach. The study of two-ring diagrams will be much more than just a mathematical exercise. It will be a critical examination of the so-called "four-phonon process" and it will indicate the role of close-range interactions. The numerical results (5. 38)-(5.40) are not expected to be too useful in fitting the pho-non dispersion data of superfluid helium. Of course, useful numerical coefficients are not the objective of our calculation. We hope the above analysis has demonstrated a more novel method of calculation as well as given a clearer physical picture. Rev. 174, 227 (1968).The scattering length alone is not sufficient to deter-mine the interaction potential. Therefore, our model, which will assume a point interaction, will not illuminate effects pertaining to the detailed form of the potential. %'e shall keep the formalism here to a minimum. For a more detailed dielectric-constant formulation, see Ref. 5, Sec. II. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N. Y. )~34 291 (1965).OThe Hugenholtz-Pines theorem is usually stated in terms of the full self-energy. However, it is trivial to show that only the irreducible part contributes.'~The rules of the standard finite-temperature perturbation theory can be found in many texts, for example, A. A. Abrikosov et al.Generalized hydrodynamics for classical fluids composed of structured molecules is discussed from a fundamental microscopic viewpoint. The analysis is concentrated on collective fluctuations of the intrinsic molecular angular momentum, and their coupling to the conserved densities of particle number, linear momentum, and energy. It is found from symmetry that the transverse components of linear and angular momentum are dynamically coupled, while the longitudinal angular momentum density moves independently of the other variables. By using the Zwanzig-Mori projection-operator technique, we derive closed and rigorous equations of motion for the set of fluctuations considered. For the case where the intrinsic angular momentum is not far from being separately conserved, approximations can be motivated which reduce these equations to simple relaxation equations, valid for small k and long times. General, Kubo-type expressions for the relaxation coefficients are given. Finally, sum-rule considerations are presented from which these coefficients can be approximately calculated.

Nematic-isotropic interfaces under shear: A molecular-dynamics simulation

“…In fact, Ω cannot be strictly zero in the isotropic phase, since general considerations show that it should be one half the local shear rate. 68 In our system, however, the local shear rate in the isotropic slab wasγ ≈ 0.00025 (cf. Fig.…”

Continuum Nanofluidics

“…In real space the non-local description amounts to a convolution of the viscosity kernel and the strain rate distribution, Eq. (26). In the homogeneous situation where the fluid undergoes a steady shear in the x-direction with varying amplitude in the z-direction we have one non-zero shear component in the pressure tensor, namely, the P xz component.…”

Nanoflow hydrodynamics

“…The extension of the Navier-Stokes equation to deal with the coupling between the hydrodynamic flow degree of freedom u(r,t) and the microscopic molecular spin angular velocity degree of freedom (r,t) was developed long ago [12][13][14]. If I is 1/3 of the trace of the inertia tensor per unit mass, in the absence of torque and pressure gradients the extended NavierStokes equations [14,15] read for a divergence-free flow…”