The properties of semidilute polymer solutions are investigated at equilibrium and under shear flow by mesoscale simulations, which combine molecular dynamics simulations and the multiparticle collision dynamics approach. In semidilute solution, intermolecular hydrodynamic and excluded volume interactions become increasingly important due to the presence of polymer overlap. At equilibrium, the dependence of the radius of gyration, the structure factor, and the zero-shear viscosity on the polymer concentration is determined and found to be in good agreement with scaling predictions. In shear flow, the polymer alignment and deformation are calculated as a function of concentration. Shear thinning, which is related to flow alignment and finite polymer extensibility, is characterized by the shear viscosity and the normal stress coefficients

The emergent fluctuating hydrodynamics of the multiparticle collision dynamics (MPC) approach, a particlebased mesoscale simulation technique for fluid dynamics, is analyzed theoretically and numerically. We focus on the stochastic rotation dynamics implementation of the MPC method. The fluid is characterized by its longitudinal and transverse velocity correlation functions in Fourier space and velocity autocorrelation functions in real space. Particular attention is paid to the role of sound, which leads to piecewise negative correlation functions. Moreover, finite system-size effects are addressed with an emphasis on the role of sound. Analytical expressions are provided for the transverse and longitudinal velocity correlations, which are derived from the linearized Landau-Lifshitz Navier-Stokes equation adopted for an isothermal MPC fluid. The comparison of the analytical results with simulations shows excellent agreement above a minimal length scale. The simulations indicate a breakdown in hydrodynamics on length scales smaller than this minimal length. This demonstrates that we have an excellent analytical description and understanding of the MPC method and its limitations in terms of time and length scales.

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The tumbling dynamics of individual polymers in semidilute solution is studied by large-scale non-equilibrium mesoscale hydrodynamic simulations. We find that the tumbling time is equal to the non-equilibrium relaxation time of the polymer end-to-end distance along the flow direction and strongly depends on concentration. In addition, the normalized tumbling frequency as well as the widths of the alignment distribution functions for a given concentration dependent Weissenberg number exhibit a weak concentration dependence in the cross-over regime from a dilute to a semidilute solution. For semidilute solutions a universal behavior is obtained. This is a consequence of screening of hydrodynamic interactions at polymer concentrations exceeding the overlap concentration.

Stress tensors are derived for the multiparticle collision dynamics algorithm, a particle-based mesoscale simulation method for fluctuating fluids, resembling those of atomistic or molecular systems. Systems with periodic boundary conditions as well as fluids confined in a slit are considered. For every case, two equivalent expressions for the tensor are provided, the internal stress tensor, which involves all degrees of freedom of a system, and the external stress, which only includes the interactions with the confining surfaces. In addition, stress tensors for a system with embedded particles are determined. Based on the derived stress tensors, analytical expressions are calculated for the shear viscosity. Simulations illustrate the difference in fluctuations between the various derived expressions and yield very good agreement between the numerical results and the analytically derived expression for the viscosity.