Accelerated Stokesian dynamics: Development and application to sheared non-Brownian suspensions.

摘要

A new implementation of the conventional Stokesian Dynamics (SD) algorithm, called Accelerated Stokesian Dynamics (ASD), is presented. The equations governing the motion of N particles suspended in a viscous fluid at low particle Reynolds number are solved accurately and efficiently, including all hydrodynamic interactions, but with a significantly lower computational cost of O(N ln N). The main differences from the conventional SD method lie in the calculation of the many-body long-range interactions, where the Ewald-summed wave-space contribution is calculated as a Fourier Transform sum, and in the iterative inversion of the now sparse resistance matrix. The new method is applied to the study of sheared non-Brownian suspensions.; The rheological behavior of a monodisperse suspension of non-Brownian particles in simple shear flow in the presence of a weak interparticle force is studied first. The suspension viscosity, first and second normal stress differences and the particle pressure are accurately determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the microstructure is correlated with the suspension non-Newtonian behavior. Volume fractions above the equilibrium freezing volume fraction (&phis; ≈ 0.494) are also studied, and it is found that the system exhibits a strong tendency to order under flow for volume fractions below the hard-sphere glass transition; limited results for &phis; = 0.60, however, show that the system is again disordered under shear.; Self-diffusion is subsequently studied and accurate results for the complete tensor of the shear-induced self-diffusivities are determined. The finite, and oftentimes large, autocorrelation time requires the mean-square displacement curves to be followed for longer times than was previously thought necessary. Results determined from either the mean-square displacement or the velocity autocorrelation function are in excellent agreement. The self-diffusivity in the flow direction is also determined as a function of the volume fraction, and it is shown that the finite autocorrelation time introduces an additional coupled term to its value, a term which previous theoretical and numerical results omitted.