Abstract
In an earlier work (Litvinov et al., Phys.Rev.E 77, 066703 (2008)), a model for a polymer molecule in solution based on the smoothed dissipative particle dynamics method (SDPD) has been presented. In the present paper, we show that the model can be extended to three-dimensional situations and simulate effectively diluted and concentrated polymer solutions. For an isolated suspended polymer, calculated static and dynamic properties agree well with previous numerical studies and theoretical predictions based on the Zimm model. This implies that hydrodynamic interactions are fully developed and correctly reproduced under the current simulated conditions. Simulations of polymer solutions and melts are also performed using a reverse Poiseuille flow setup. The resulting steady rheological properties (viscosity, normal stress coefficients) are extracted from the simulations and the results are compared with the previous numerical studies, showing good results.
Highlights
The simulation of polymer dynamics represents a long-standing problem in computational rheology
Experiments have confirmed that, under diluted conditions, polymer dynamics is best described by the Zimm model [2], where the effects of hydrodynamic interaction (HI) are taken into account by using the Oseen tensor formulation, and the solvent is assumed to behave as an incompressible Stokes flow
+ Fi,i dt hydro where mi is the mass of the bead i, Fi is the total sum of the resulting smoothed dissipative particle dynamics method (SDPD) forces acting on particle i given in Equations (2)–(4), and i1, i2 are the two neighboring beads of i in the polymer chain which interact via the non-hydrodynamic forces derived by the potential Equation (6), i.e., FijFENE =
Summary
The simulation of polymer dynamics represents a long-standing problem in computational rheology. A new type of DPD method, called smoothed dissipative particles dynamics (SDPD) [27,28,29], is used to investigate the static and dynamic behavior of polymers This model is a mesoscopic extension of a popular particle-based method applied to continuum flow, i.e., smoothed particle hydrodynamics (SPH) [30]. Thermal fluctuations can be included in a physically consistent way, that is, in agreement with a fluctuation-dissipation theorem (FDT) and with basic properties of statistical mechanics where fluctuations of hydrodynamic variables increase naturally by reducing the size of the problem down to the mesoscopic scale [29] These properties of SDPD make it a suitable tool to simulate physically relevant length and time scales as seen in experiments.
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