Multiscale Modeling for Polymeric Flow: Particle-Fluid Bridging Scale Methods

Abstract

Multiscale simulation methods have been developed based on the local stress sampling strategy and applied to three flow problems with different difficulty levels: (a) general flow problems of simple fluids, (b) parallel (one-dimensional) flow problems of polymeric liquids, and (c) general (two-or three-dimensional) flow problems of polymeric liquids. In our multiscale methods, the local stress of each fluid element is calculated directly by performing microscopic or mesoscopic simulations according to the local flow quantities instead of using any constitutive relations. For simple fluids (a), such as the Lenard-Jones liquid, a multiscale method combining molecular dynamics (MD) and computational fluid dynamics (CFD) simulations is developed rather straightforwardly based on the local stationarity assumption without memories of the flow history. For polymeric liquids in parallel flows (b), the multiscale method is extended to take into account the memory effects that arise in hydrodynamic stress due to the slow relaxation of polymer-chain conformations. The memory of polymer dynamics on each fluid element is thus resolved by performing MD simulations in which cells are fixed at the mesh nodes of the CFD simulations. The complicated viscoelastic flow behaviors of a polymeric liquid confined between oscillating plates are simulated using the multiscale method. For general (two-or three-dimensional) flow problems of polymeric liquids (c), it is necessary to trace the history of microscopic information such as polymer-chain conformation, which carries the memories of past flow history, along the streamline of each fluid element. A Lagrangian-based CFD is thus implemented to correctly advect the polymerchain conformation consistently with the flow. On each fluid element, coarse-grained polymer simulations are carried out to consider the dynamics of entangled polymer chains that show extremely slow relaxation compared to microscopic time scales. This method is successfully applied to simulate a flow around a cylindrical obstacle.

Multiscale Simulation of Polymer Melt Spinning by Using the Dumbbell Model

“…By comparing the velocity and cross section area profiles with the end-point distribution for the dumbbell connective vectors, for dumbbells located in Lagrangian particles along typical places along the spinning line, we show that our multiscale simulation method successfully bridges the microscopic state of the system with its simultaneous macroscopic flow behavior. It is also confirmed that the present schemes gives good agreements two parallel plates 33,35,36,[41][42][43][44][45][46][47]50) , flows around an infinitely long cylinder 37,40,48,49) , flows in between eccentric rotating cylinders 38,39) and so forth. As far as we know, no one has ever 28,29) or NAPLES 26) , among many others.…”

“…So far, for flow problems of polymeric fluids a limited number of this type of multiscale simulations have been performed. [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] Actually, the MSS method has…”

Synchronized molecular-dynamics simulation for the thermal lubrication of a polymeric liquid between parallel plates

“…The multiscale method was first developed for simple fluids [19] and subsequently extended to polymeric liquids with the memory effect. [20,21,22,23] Recently, we proposed the synchronized molecular dynamics (SMD) method in which the multiscale method was extended to treat the coupled heat and momentum transfer of complex liquids. [24] In the previous study, the SMD method was applied to the polymer lubrication generating the viscous heating between parallel plates.…”

Synchronized Molecular-Dynamics Simulation via Macroscopic Heat and Momentum Transfer: An Application to Polymer Lubrication

“…We have also developed a multiscale simulation of MD and computational fluid dynamics. The multiscale method was first developed for simple fluids [19] and subsequently extended to polymeric liquids with the memory effect [20][21][22][23].…”