Rapid calculation of hydrodynamic and transport properties in concentrated solutions of colloidal particles and macromolecules

Abstract

A new method for calculating the resistance tensors of arbitrarily shaped particles and the translational and rotational self-diffusivity in suspensions of such particles is developed. This approach can be harnessed to efficiently and accurately predict the hydrodynamic and transport properties of large macromolecules such as antibodies in solution. Particles are modeled as a rigid composite of spherical beads, and the continuum equations for low Reynolds number fluid mechanics are used to calculate the drag on the composite or its diffusivity in a solution of other composites. The hydrodynamic calculations are driven by a graphics processing unit (GPU) implementation of the particle-mesh-Ewald technique which offers log-linear scaling with respect to the complexity of the composite-bead particles modeled as well as high speed execution leveraging the hyper-parallelization of the GPU. Matrix-free expressions for the hydrodynamic resistance and translational and rotational diffusivity of composite bead particles are developed, which exhibit substantial improvements in computational complexity over existing approaches. The effectiveness of these methods is demonstrated through a series of calculations for composite-bead particles having a spherical geometry, and the results are compared to exact solutions for spheres. Included in the supplementary material is an implementation of the proposed algorithm which functions as a plug-in for the GPU molecular dynamics suite HOOMD-blue (http://codeblue.umich.edu/hoomd-blue) [J. A. Anderson, C. D. Lorenz, and A. Travesset, “General purpose molecular dynamics simulations fully implemented on graphics processing units,” J. Comput. Phys. 227(10), 5342–5359 (2008) and Glaser et al., “Strong scaling of general-purpose molecular dynamics simulations on GPUs,” Comput. Phys. Commun. 192, 97–107 (2015)].