acta physica slovaca
Acta Physica Slovaca 61, No.4, 391-482 (2011) (91 pages)
NONLOCAL TRANSPORT AND THE GLASS TRANSITION
Ruslan M. Puscasu
Swinburne University of Technology, Melbourne, Victoria, 3122, Australia
Full text: ::pdf :: (Received 5 September 2011, accepted 6 September 2011)
Abstract: The paper gives a review of recent advances in theory and simulation of nonlocal transport in nanoflows. The aim is to show how to computationally model and simulate the nonlocal viscous transport in atomic and molecular fluids. The ultimate goal is to provide nanofluidics and other disciplines with methodologies capable to give exact descriptions of flow at the nanoscale by using nonlocal constitutive relations which involve nonlocal transport kernels. Nanomaterials have properties that can be substantially different from those of the corresponding bulk phases. In particular, fluid flows in pores or channels of nanoscale dimension can deviate strongly from macroscopic expectations. When such structures approach the size regime corresponding to molecular scaling lengths, new physical constraints are placed on the behavior of the fluid. These physical constraints induce regions of the fluid to exhibit new properties (e.g. vastly increased viscosity near the pore wall) and they may affect changes in thermodynamic properties and may also alter the chemical reactivity of species at the fluidsolid interface. Consequently, many classical theories break down and are no longer valid at such small length and time scales. The development of models that go beyond classical (Navier-Stokes-Fourier) hydrodynamics would be very helpful for the prediction and understanding of flows in highly confined geometries (typically 1-100 nm). While such nanoscale systems can be very difficult to probe experimentally, they can be easily approached in a very strict manner by molecular modelling, providing theory and simulation an opportunity for the discovery of new phenomena. We therefore review in this article the advances within the framework of generalized hydrodynamics and present the latest theoretical developments and modelling results that can ultimately lead to suitable predictive tools capable of accurate prediction of the key physical properties of fluids under nano-confined geometries.
We start with an overview on the nonlocal constitutive relation and the microscopic definitions of the key properties such as momentum density autocorrelation function, stress autocorrelation function and the wavevector dependent viscosity. Then we demonstrate how the nonlocal viscosity kernel can be computed via equilibrium molecular dynamics. Firstly, we showcase the spatially nonlocal viscosity kernel for simple monatomic and diatomic fluids over a wide range of wavevectors, state points and potential energy functions. Further we consider more complex fluids; in particular, we report results for alkanes and polymer melts. Secondly, we study glass-forming liquids and therefore extend the temperature range and report the nonlocal viscosities of polymer melts cooled towards their glassy state. The results reveal the nonlocal nature of the viscous transport and we give evidence that the slow dynamics in supercooled liquids is governed by a dynamic critical point at which time and length scales diverge and link it to the dynamic heterogeneity. It follows that the response of polymer melts to a velocity gradient near the glass transition temperature is highly nonlocal. In systems where the strain rate varies significantly over the width of the real space kernels, the generalized nonlocal viscosity must be used in order to correctly compute the velocity profile of molecular fluids via use of generalized hydrodynamics and thus the nonlocal behaviour of the transport must be integrated into methodologies developed to describe the multi-scale physics of nanoflows.
PACS: 61.20.Ja, 61.25.H-, 61.25.Em, 61.25.hk, 64.70.pj, 66.20.Ej, 66.20.Gd, 66.20.-d, 66.20.Cy
Keywords: Computational nanofluidics, Molecular dynamics, Nonlocal transport, Viscosity, Polymers, Glass transition
ISSN 1336-040X (online)
ISSN 0323-0465 (printed)
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