Velocity relaxation of a porous sphere immersed in a viscous incompressible fluid

Adhesion of a polymer-grafted nanoparticle to cells explored using generalized Langevin dynamics

We model a polymer-grafted stealth nanoparticle (SNP) as a composite system consisting of a spherical core coated with a porous polymeric brush with end-ligands. Adjacent to target cells, the near-wall hydrodynamics, thermal fluctuations, and thermodynamic adhesive interactions simultaneously impact the transient motion of the SNP. Employing both the Langevin framework for the effective hard sphere dynamics and the coupled generalized Langevin framework for the nanoparticle-polymer dynamics, we comprehensively investigate the velocity and position temporal relaxations of the SNP in the absence and presence of end-to-end distance fluctuations for the tethered polymer. We demonstrate that polymer structural relaxations substantially impact the SNP adhesive dynamics, especially when the grafted polymer is more flexible. Moreover, a long-time tail with t-3/2 scaling due to polymer chain-length fluctuations is observed in the velocity autocorrelation for a bound SNP. Finally, the thermodynamic effects of membrane morphology on SNP adhesion are explored by modifying the membrane-mediated binding potential of mean force.

The raspberry model for hydrodynamic interactions revisited. I. Periodic arrays of spheres and dumbbells

The so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates.