Rheol Acta (2009) 48:1017–1030 DOI 10.1007/s00397-009-0385-5 ORIGINAL CONTRIBUTION Predictions of the excess pressure drop of Boger fluids through a 2:1:2 contraction–expansion geometry using non-equilibrium molecular dynamics G. González González · J. Castillo Tejas · J. P. Aguayo Vallejo · Juan F. J. Alvarado · O. Manero Received: 20 January 2009 / Accepted: 2 September 2009 / Published online: 15 September 2009 © Springer-Verlag 2009 Abstract Non-equilibrium molecular dynamics are used to generate the flow of polymer solutions, specifically of Boger fluids, through a planar 2:1:2 contraction–expansion geometry. The solvent mole- cules are represented by Lennard–Jones particles, while linear molecules are described by spring- monomers with a finite extensible non-linear elastic spring potential. The equations for Poiseuille flow are solved using a multiple time-scale algorithm ex- tended to non-equilibrium situations. Simulations are performed at constant temperature using Nose–Hoover dynamics. At simulation conditions, changes in con- centration show no significant effect on molecular conformation, velocity profiles, and stress fields, while variations in the Deborah number have a strong influ- ence on fluid response. Increasing the magnitude of the Deborah number (De), larger deformation rates are developed in the flow region. For a Deborah number of one, the non-dimensional pressure drop presents values lower than the correspondent Newtonian case. How- ever, for large Deborah numbers, the pressure drop G. G. González · J. C. Tejas (B ) · J. P. A. Vallejo Facultad de Ciencias Básicas, Ingeniería y Tecnología, Universidad Autónoma de Tlaxcala, Calzada Apizaquito S/N, Apizaco, Tlaxcala, 90300, México e-mail: j_castillo_tejas@hotmail.com J. F. J. Alvarado Departamento de Ingeniería Química, Instituto Tecnológico de Celaya, Avenida Tecnológico y García Cubas S/N, Celaya, Guanajuato, 38010, México O. Manero Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F., 04510, México increases above the Newtonian reference. An effective excess pressure drop above the Newtonian value is predicted for Boger fluids along this geometry. Keywords Non equilibrium molecular-dynamics · Pressure drop · Contraction–expansion flow Introduction Boger fluids are formed by polymer chains dissolved in a viscous solvent. These fluids exhibit a constant shear viscosity η and non-Newtonian effects, such as high extensional viscosities or non-zero normal-stress differences. When Boger fluids flow through a cylindri- cal contraction or in contraction–expansion geometries, the pressure drop measured is generally larger than the one observed for Newtonian fluids with the same shear viscosity. This is the so-called excess pressure drop (epd). Numerical simulations intended to predict the excess pressure drops in these geometries represent a benchmark problem and a challenging issue. Nigen and Walters (2002) measured the pressure drop through contraction geometries  2 ≤ ˆ β ≤ 32  , in planar and axisymmetric configurations, with short and long exit dies. In their experiments, they used aspect ratios (AR = contraction gap/channel width) of 20 or larger, to produce a two-dimensional flow through a slit. Experiments were carried out for two Newtonian liquids and two Boger fluids, and the results show no difference between Newtonian and Boger fluids (with similar viscosity) for planar configurations. In the axisymmetric contraction, however, larger pressure drops were obtained for Boger fluids. In addition, large