Generalized extended Navier-Stokes theory: Correlations in molecular fluids with intrinsic angular momentum

Abstract

The extended Navier-Stokes theory accounts for the coupling between the translational and rotational molecular degrees of freedom. In this paper, we generalize this theory to non-zero frequencies and wavevectors, which enables a new study of spatio-temporal correlation phenomena present in molecular fluids. To discuss these phenomena in detail, molecular dynamics simulations of molecular chlorine are performed for three different state points. In general, the theory captures the behavior for small wavevector and frequencies as expected. For example, in the hydrodynamic regime and for molecular fluids with small moment of inertia like chlorine, the theory predicts that the longitudinal and transverse intrinsic angular velocity correlation functions are almost identical, which is also seen in the molecular dynamics simulations. However, the theory fails at large wavevector and frequencies. To account for the correlations at these scales, we derive a phenomenological expression for the frequency dependent rotational viscosity and wavevector and frequency dependent longitudinal spin viscosity. From this we observe a significant coupling enhancement between the molecular angular velocity and translational velocity for large frequencies in the gas phase; this is not observed for the supercritical fluid and liquid state points.

Continuum Nanofluidics

“…From MD simulations one can calculate the LAVACF (as shown above) and from there find the kernels. For dense fluids ζ is characterized by a sharp peak around zero wave vector [42] IV. NANOFLOWS…”

Automated, contour-based tracking and analysis of cell behaviour over long time scales in environments of varying complexity and cell density

“…For example, the movement of individual elements (particles or cells) can be used to calculate ensemble-averaged functions such as the MSD [61] or velocity autocorrelation. Differences in collective migration driven by gradients in mechanical properties or cell-cell interactions can be quantified using scalar quantities derived from these functions, including diffusion or time relaxation constants [62]. Finally, statistical physics metrics are particularly well suited to capture changes in the behaviour of groups of cells as a function of cell density, which could be important for understanding cell behaviour in vivo.…”

Continuum simulations of water flow in carbon nanotube membranes

“…Our results on flow rates are within the error bars of the values obtained with MD simulations. We note that recently it has been reported [21,22] that in highly confined nanoscale channels an extended Navier-Stokes equation coupled to the microscopic molecular spin angular velocity describes the water flow better than the standard Navier-Stokes equation. According to our results the standard Navier-Stokes equation still gives the correct description of flow in highly confined channels when the slip length is large.…”