Modeling of a Nanoparticle Motion in a Newtonian Fluid: A Comparison Between Fluctuating Hydrodynamics and Generalized Langevin Procedures

Abstract

A direct numerical simulation adopting an arbitrary Lagrangian-Eulerian based finite element method is employed to simulate the motion of a nanocarrier in a quiescent fluid contained in a cylindrical tube. The nanocarrier is treated as a solid sphere. Thermal fluctuations are implemented using two different approaches: (1) fluctuating hydrodynamics; (2) generalized Langevin dynamics (Mittag-Leffler noise). At thermal equilibrium, the numerical predictions for temperature of the nanoparticle, velocity distribution of the particle, decay of the velocity autocorrelation function, diffusivity of the particle and particle-wall interactions are evaluated and compared with analytical results, where available. For a neutrally buoyant nanoparticle of 200 nm radius, the comparisons between the results obtained from the fluctuating hydrodynamics and the generalized Langevin dynamics approaches are provided. Results for particle diffusivity predicted by the fluctuating hydrodynamics approach compare very well with analytical predictions. Ease of computation of the thermostat is obtained with the Langevin approach although the dynamics gets altered.

Nanocarrier Hydrodynamics and Binding in Targeted Drug Delivery: Challenges in Numerical Modeling and Experimental Validation

“…Furthermore, with these particles the drug release rate for a specific purpose can be adjusted by varying the ratio of PLA (increased hydrophobicity) to PGA (increased hydrophilicity). [51,54,[56][57][58][59]. The treatments of the resistance of the glycocalyx and adhesion interactions mediated by multivalent antigen-antibody binding/unbinding events using molecular dynamics have been bridged with the macroscopic regime so evaluated [1,29,51,66,82,85], see Fig.…”

“…This bridging procedure for F cell-NC and F NCÀNC can be described here (see below) but the bridging for F adhesive that is associated with binding can be discussed later. To solve the above set of equations with specified boundary conditions at the inlet, outlet, closed boundaries of the wall and the moving particles, an arbitrary Lagrangian-Eulerian based finite element method may be employed to solve the fluid equation [51,53,54,[57][58][59]. Such a numerical approach should also be able to capture arbitrary flow fields and flow geometries (including boundary conditions), the noncontinuum nature of the stress because in this formalism an allowance has been made for the stress to fluctuate in the fluid domain.…”

“…Such a numerical approach should also be able to capture arbitrary flow fields and flow geometries (including boundary conditions), the noncontinuum nature of the stress because in this formalism an allowance has been made for the stress to fluctuate in the fluid domain. Moreover, with this formalism, the equations of motions incorporate temporal memory in NC dynamics [51,53,54,[56][57][58][59], adhesive force from ligandreceptor bonds [56,58], cell-NC, cell-cell, and NC-NC interaction forces [99]. The dominant factors in nonspecific NC-NC, NC-cell, and cell-cell (this term occurs in the equations of motion of the cells, not provided in this article for the sake of brevity) interactions in this model will be the fluid-mediated hydrodynamic interactions.…”

“…These include (i) molecular and geometric parameters surrounding receptor-ligand interactions and NCs [13,[31][32][33]; (ii) lack of accurate characterization of hydrodynamics and (iii) physicochemical barriers for NC uptake/arrest [34][35][36][37]; (iv) incomplete characterization of nanoparticle-cell membrane force interactions and their influence on particle trafficking [38]; (v) extreme complexity and variability of targeting environment in vivo [39][40][41] and (vi) incomplete tracking of transported cargo delivery and losses in transit. Among the factors impacting the design of nanocarriers and therapeutic agents are: (a) binding affinity [42,43]; (b) multivalency or the average number of receptor-ligand bonds per bound NC and their spatial orientation [43][44][45][46][47]; (c) in vivo targeting, measured as percentage of injected dose accumulated after intravenous injection [48][49][50], and (d) hemodynamics [51][52][53][54][55][56][57][58][59][60].…”

“…Multiscale modeling must complement experimental technologies. Novel computational methods [1,29,52,[54][55][56][57][58][82][83][84][85] may be combined with in vivo and in vitro experiments [14,46,47,55] to model NC motion and adhesion. Brownian motion and hydrodynamic interactions are both important.…”