Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle

Abstract

.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E 91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.

Multiscale modeling: foundations, historical milestones, current status, and future prospects

“…The fourth term on the right-hand side is the force from other thermodynamic potentials, same as F(S) in (Eq. 7), and the fifth term is the random force term with colored noise to be consistent with the fluctuation-dissipation theorem for composite GLE [129,130].…”

“…The equation of stochastic motion for each component of the velocity of a nanoparticle immersed in a fluid in bounded and unbounded domains takes the form of a generalized Langevin equation (GLE) of the form of (Eq. 9); to account for hydrodynamic interaction, a composite GLE was introduced [129,130].…”

“…Effect of molecular forces is introduced as forcing functions in the GLE [129] and the effect of multiple particles including multiparticle HI can be introduced via density functional theory-based treatments [82,83] to define F(S) from hydrodynamic and colloidal effects in addition to the specific contributions from molecular forces. If the memory functions are unknown, they can be obtained via deterministic approaches by solving the continuum hydrodynamic equations numerically [46,128].…”

A survey of multiscale modeling: Foundations, historical milestones, current status, and future prospects

“…Memory function approach to coarse‐graining with HIs: In the description of the dynamics of nanosized Brownian particles in an bounded and unbounded fluid domains the memory functions decay with algebraic correlations as enumerated by theoretical and computational studies 71,116,158 . The equation of stochastic motion for each component of the velocity of a nanoparticle immersed in a fluid in bounded and unbounded domains takes the form of a GLE of the form of Equation ); to account for HI, a composite GLE was introduced 159,160 …”

“…Effect of molecular forces is introduced as forcing functions in the GLE 159 and the effect of multiple particles including multiparticle HI can be introduced via DFT‐based treatments 110,111 to define F ( S ) from hydrodynamic and colloidal effects in addition to the specific contributions from molecular forces. If the memory functions are unknown, they can be obtained via deterministic approaches by solving the continuum hydrodynamic equations numerically 71,158 .…”