%0 Book Section %1 statphys23_0064 %A Hansen, J.S. %A Todd, B.D. %A Daivis, P.J. %A Travis, K.P. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K confined dynamics fluids hydrodynamics molecular nonequilibrium statphys23 topic-6 transport viscosity %T Computing the viscosity kernel for highly confined fluids %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=64 %X A key problem in the prediction of the flow properties of highly confined (nano-scale) fluids is that the classical Navier-Stokes equations of hydrodynamics catastrophically break down at this length scale. This has been demonstrated in a number of simulation studies in the past, in which the predicted classical velocity profiles for nonequilibrium fluids do not match the profiles generated via molecular dynamics simulation 1, 2. The problem is more complicated than merely including explicit density dependence in the hydrodynamic equations, since it has also been demonstrated that the viscosity of such nonequilibrium fluids cannot be computed by a local approximation 2-5. A non-local viscosity needs to be computed before accurate flow predictions can be made 6. In this presentation we demonstrate how to compute a non-local viscosity kernel from either equilibrium or nonequilibrium molecular dynamics simulations of a homogeneous fluid at equivalent state points corresponding to those of an inhomogeneous fluid. The kernels are computed first in momentum space and then inverse Fourier transformed into real space. The momentum space kernels can be reasonably well represented by several functional forms. Based on the full inhomogeneous non-local viscosity profile we are able to predict the velocity profiles for arbitrary flows and do so for the specific example of highly confined planar Poiseuille flow. Our formalism paves the way for a generalised approach to hydrodynamics at the nano-scale. 1 I. Bitsanis, J.J. Magda, M. Tirell and H.T. Davis, J. Chem. Phys. 87, 1733 (1987); I. Bitsanis, T.K. Vanderlick, M. Tirell and, J. Chem. Phys. 89, 3152 (1988); I. Bitsanis, S.A. Somers, H.T. Davis and M. Tirell, J. Chem. Phys. 93, 3427 (1990). 2 K.P. Travis, B.D. Todd and D.J. Evans, Phys. Rev. E 55, 4288 (1997). 3 K. P. Travis and K. E. Gubbins, J. Chem. Phys. 112, 1984 (2000). 4 J. Zhang, B.D. Todd and K.P. Travis, J. Chem. Phys. 121, 10778 (2004); J. Chem. Phys. 122, 219901 (2005). 5 L.A. Pozhar, Phys. Rev. E 61, 1432 (2000). 6 B.D. Todd, Mol. Simul. 31, 411 (2005).

@incollection{statphys23_0064, abstract = {A key problem in the prediction of the flow properties of highly confined (nano-scale) fluids is that the classical Navier-Stokes equations of hydrodynamics catastrophically break down at this length scale. This has been demonstrated in a number of simulation studies in the past, in which the predicted classical velocity profiles for nonequilibrium fluids do not match the profiles generated via molecular dynamics simulation [1, 2]. The problem is more complicated than merely including explicit density dependence in the hydrodynamic equations, since it has also been demonstrated that the viscosity of such nonequilibrium fluids cannot be computed by a local approximation [2-5]. A non-local viscosity needs to be computed before accurate flow predictions can be made [6]. In this presentation we demonstrate how to compute a non-local viscosity kernel from either equilibrium or nonequilibrium molecular dynamics simulations of a homogeneous fluid at equivalent state points corresponding to those of an inhomogeneous fluid. The kernels are computed first in momentum space and then inverse Fourier transformed into real space. The momentum space kernels can be reasonably well represented by several functional forms. Based on the full inhomogeneous non-local viscosity profile we are able to predict the velocity profiles for arbitrary flows and do so for the specific example of highly confined planar Poiseuille flow. Our formalism paves the way for a generalised approach to hydrodynamics at the nano-scale. [1] I. Bitsanis, J.J. Magda, M. Tirell and H.T. Davis, J. Chem. Phys. 87, 1733 (1987); I. Bitsanis, T.K. Vanderlick, M. Tirell and, J. Chem. Phys. 89, 3152 (1988); I. Bitsanis, S.A. Somers, H.T. Davis and M. Tirell, J. Chem. Phys. 93, 3427 (1990). [2] K.P. Travis, B.D. Todd and D.J. Evans, Phys. Rev. E 55, 4288 (1997). [3] K. P. Travis and K. E. Gubbins, J. Chem. Phys. 112, 1984 (2000). [4] J. Zhang, B.D. Todd and K.P. Travis, J. Chem. Phys. 121, 10778 (2004); J. Chem. Phys. 122, 219901 (2005). [5] L.A. Pozhar, Phys. Rev. E 61, 1432 (2000). [6] B.D. Todd, Mol. Simul. 31, 411 (2005).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Hansen, J.S. and Todd, B.D. and Daivis, P.J. and Travis, K.P.}, biburl = {https://www.bibsonomy.org/bibtex/2ff9ed2c3c28f0be66eaba8f6461395dd/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {d9ecbc6c5830675f148c2b323c2873fe}, intrahash = {ff9ed2c3c28f0be66eaba8f6461395dd}, keywords = {confined dynamics fluids hydrodynamics molecular nonequilibrium statphys23 topic-6 transport viscosity}, month = {9-13 July}, timestamp = {2007-06-20T10:16:10.000+0200}, title = {Computing the viscosity kernel for highly confined fluids}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=64}, year = 2007 }