Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

Abstract

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation–dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible – an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

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

“…Umbrella sampling 57 Multiple time step molecular dynamics 96 Parallel tempering 24 Multigrid PDE solvers 71,97 Metadynamics 98 Dual resolution 46 Path sampling 99 Equation free methods 100,101 Coarse graining methods 102,103 Concurrent multiscale methods Classical density functional theory 110,111 Particle to field passing 112 Polymer field theory 113 Loosely coupled process flow 114,115 Memory-function approach to hydrodynamics 116 just some of the more foundational methods below. There is an entire journal dedicated to MSM, Multiscale Modeling and Simulation (https:// www.siam.org/journals/mms.php).…”

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

“…The fluctuating hydrodynamic equations discretized in terms of finite element shape functions based on the Delaunay triangulation satisfy the fluctuation-dissipation theorem. The numerical schemes for implementing the thermal fluctuations in the FHD equations are delicate to implement, and obtaining accurate numerical results is a challenging endeavor [46].…”

“…5.5.1 Memory function approach to coarse-graining with hydrodynamic interactions: 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 [46,85,128]. 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.…”

“…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]. These disparate hydrodynamic fields and molecular forces can be integrated into a single GLE to realize a unified description of particle dynamics under the influence of molecular and hydrodynamic forces [85].…”

Nanofluid Dynamics of Flexible Polymeric Nanoparticles Under Wall Confinement

“…In general, NPs can be classified into nondeformable (or rigid) and deformable (or flexible) categories. While theoretical and computational works have extensively analyzed for the impact of size and shape of rigid NPs on their targeting efficiency [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], the role of carriers' flexibility on enhanced drug delivery has been explored to a far lesser extent, and the potential benefits of tuning nanoparticle elasticity are not clear. As such, similar treatment of flexible NPs offers a lot of exciting challenges and opportunities and recent research efforts have focused on how flexibility can be leveraged to tune the biological function and fate of nanoparticles.…”