IJPAM: Volume 43, No. 1 (2008)


Eugen Grycko$^1$, Jens Rentmeister$^2$
$^1$Faculty of Mathematics and Computer Science
University of Hagen
Lützowstrasse 125, Hagen, D-58094, GERMANY
e-mail: eugen.grycko@fernuni-hagen.de
Thingslindestrasse 90, Kierspe, D-58566, GERMANY
e-mail: support@omegaspace.de

Abstract.$N$ hard disks are injected into a 2-dimensional virtual pipe. The initial positions of the disks are generated according to the uniform distribution and the initial velocities according to a centered normal distribution. The Newtonian dynamics is imposed on the system (fluid) entailing a viscous fluid flow through the pipe. Since the flow velocity profiles can be assessed statistically during the computational process imitating the motion of the disks, computer experimental data carrying information about the dependence of viscosity on the thermodynamic conditions of the virtual fluid can be sampled. The statistical evaluation of these data leads to the establishment of a formula for the viscosity of the hard disk fluid. As an application, a possibility of the quantitative prediction of laboratory measurements of the viscosity of water as function of temperature is discussed.

Received: December 7, 2007

AMS Subject Classification: 74A25, 76A99, 62G08

Key Words and Phrases: molecular dynamics, fluid flow, velocity profiles, Nadaraya-Watson estimator

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 1