Prediction of excess pressure drop in contraction–expansion flow by molecular dynamics: Axisymmetric and planar configurations

Abstract In this paper, non-equilibrium molecular dynamics is used to simulate the flow of a dilute solution of linear molecules (Boger fluid) and a simple fluid (Lennard-Jones) through axisymmetric and planar contraction–expansion geometries. The pressure flow condition is generated by adding an external force field F e to the equation of motion for the velocity, which is coupled to Nose–Hoover dynamics to keep the temperature constant. According to the monomer-spring model of Kremer and Grest, linear molecules are represented; and the simple fluid consists of spherical particles, which interact by means of a Lennard-Jones potential. The rheological response of the fluids indicates that the Boger fluid and the simple fluid exhibit constant viscosity in the interval ( 0.002 ⩽ γ ⩽ 0.5 ); additionally, the Boger fluid presents elastic effects under shear (first normal stress difference, N 1 ) which are quadratic at low shear rates. In pressure flow through the expansion–contraction, results indicate that when both fluids have the same viscosity, pressure profiles P ( x 1 ) in the axisymmetric geometry reveal a higher pressure drop (Δ P ) in the Boger fluid, while in the planar geometry Δ P was the same for both fluids. Results also reveal that Δ P is closely related to the extensional strain rate ( e ) experienced by the fluid at the contraction entrance. The pressure drop is higher in the axisymmetric geometry because the change in the molecular conformation, as measured by the mean-square mass distribution tensor 〈 I 2 2 〉 , is 80% higher than in the planar case, resulting in an increase in the energy required to deform the molecule and the loss of mechanical energy. In the planar geometry, under the same extensional strain rate, the conformational change of the molecules in the Boger fluid at the contraction is then lower than in the axisymmetric geometry.