Rheology of several hundred rigid bodies
Dlugogorski, B.Z., Grmela, M., Carreau, P.J. and Lebon, G. (1994) Rheology of several hundred rigid bodies. Journal of Non-Newtonian Fluid Mechanics, 53 . pp. 25-64.
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A novel nonequilibrium molecular dynamics, originating in mesoscopic theory of suspensions, is introduced to investigate the behavior of model polymeric fluids consisting of several hundred ellipsoids of revolution (spheroids) that interact via the Gay-Berne potential. This dynamics is used to generate new microstructural, thermodynamic and rheological data. The microcanonical equtions of motion for the translational and angular momenta as well as for mass-centers and orientational unit vectors are derived from a Hamiltonian. These expresssions are then augmented by SLLOD-like and Gaussian thermostat terms added consistently to equations for both the rotational and translational degrees of freedom; the role of Gaussian thermostat is to maintain constant kinetic temperature of the assembly of spheroids. The thermodynamic results are calculated along one isotherm (nondimensional temperature T maintained at unity). Rheology is investigated for two state points (namely for particle number density p equal to 0.25, 0.4 and T set to 1), that lie well inside the isotropic phase if no external flow is applied. A state point is defined by the fluid's temperature T,. and the concentration of particles per unit volume p. As indicated by snapshots of molecular configurations, at the intermediate shear rates (nondimensional shear rate approximately 1–2), ellipsoids become aligned to the direction of flow and the stress tensor begins to be nonsymmetric. At even higher shear rates, this configuration breaks down leading to the formation of a transitory isotropic-type fluid, and then to the build-up of a highly ordered structure exhibiting global orientation of particles in the direction of the vorticity axis.
For ϱ = 0.4, the first (N1) and the second (N2) normal stress differences are positive and negative respectively, but at low densities (ϱ = 0.25), n1 becomes slightly negative. In addition to the stress tensor, we compute the conformation tensor, the order parameter and the components of the pair radial distribution function. At high shear rates the radial distribution functions become significantly anisotropic. Furthermore, we investigate the phenomenon of the stress overshoot at the inception of the simple shear flow from a molecular perspective, and study the evolution of the distribution of translational velocities as a function of the shear rate.
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|Copyright:||© 1994 Published by Elsevier B.V.|
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