Phase-Space Diffusion Equations for Single Brownian Particle Motion Near Surfaces

Peters, Michael; Ying, Ruoxian

doi:10.1080/00986449108910957

Cited by 11 publications

(5 citation statements)

References 32 publications

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“…The dilute assumption neglects interactions between aqueous cells, and this assumption will not be valid when there are significant cell interactions such as those encountered in cell clumping and quorum sensing [125]. Approaches that invoke the interactions among cells have not yet been developed; however, such effects have been rigorously incorporated in the description of the transport of simple colloids [89,90]. A similar analysis for representing the interactions among microorganisms represents a significant challenge, and is an open area for continuing research.…”

Section: Conceptual and Mathematical Representation Of Subsurface Biomentioning

confidence: 99%

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Processes in microbial transport in the natural subsurface

Ginn

Wood

Nelson

et al. 2002

Advances in Water Resources

262

131

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Section: Conceptual and Mathematical Representation Of Subsurface Biomentioning

confidence: 99%

“…From a statistical-mechanical analysis [89,90,103], one can show that for incompressible flows the relevant transport equation takes the form:…”

Section: Combining Physical Chemical Electrostatic and Biological mentioning

confidence: 99%

Processes in microbial transport in the natural subsurface

Ginn

Wood

Nelson

et al. 2002

Advances in Water Resources

262

131

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“…19 Nonequilibrium local fluid distribution functions have also been included, such as those due to bulk fluid flow or external forces. 35,36 Note that the equilibrium fluid force acting on the B-particles can often be broken down into different contributions depending on the nature of the interaction potential. For example, an electrostatic force interaction between a polar solvent, such as water, and the B-particles leads to the local dielectric behavior of the fluid in the configuration space of the B-particles, and the accompanying nonpolar force interactions, such as van der Waals and Born force interactions, lead to the so-called hydrophobic effect.…”

Section: Fokker-planck Equationmentioning

confidence: 99%

Langevin dynamics for the transport of flexible biological macromolecules in confined geometries

Peters

2011

The Journal of Chemical Physics

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The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an α-helix protein through a carbon nanotube is simulated.

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“…1 .I describes the Stokes' drag on a single isolated particle with c, representing the Cunningham correction factor (Tien, 1989). The use of this form for the force indicates that we are ignoring particle-particle interactions and the fluid mechanical complications that arise when a particle approaches a solid surface (Peters and Ying, 1991). These effects should certainly be taken into account; however, in this initial study it is our attention to keep the analysis as simple as possible.…”

Section: Particle Motionmentioning

confidence: 99%

“…This correction to the Smoluchowski equation has been used by Yeh and Liu (1974), Banks and Kurowski (1983), and others for the study of particle transport in the filtration process, and derivations are available from de la Mora and Rosner (198 1,1982) and from Peters and Ying (1991) in addition to the references cited above. Equation 1.8 represents the frst smoothing process in the hierarchy of averaging processes illustrated in Figure 1.…”

Section: In the Y -Phasementioning

confidence: 99%

Particle filtration: An analysis using the method of volume averaging

Quintard

Whitaker

1994

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The process of filtration of non-charged, submicron particles is analyzed using the method of volume averaging. The particle continuity equation is represented in terms of thefirst correction to the Smoluchowski equation that takes into account particle inertia effects for small Stokes numbers. This leads to a cellular efficiency that contains a minimum in the efficiency as a h c t i o n of the particle size, and this allows us to identifjr the mostpenetratingparticle size. Comparison of the theory with results fiom Brownian dynamics indicates that the first correction to the Smoluchowski equation gives reasonable results in terms of both the cellular efficiency and the most penetrating particle size. However, the results for larger particles clearly indicate the need to extend the Smoluchowski equation to include higher order corrections. Comparison of the theory with laboratory experiments, in the absence of adjustable parameters, provides interesting agreement for particle diameters that are equal to or less than the diameter of the most penetrating particle.

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Phase-Space Diffusion Equations for Single Brownian Particle Motion Near Surfaces

Cited by 11 publications

References 32 publications

Processes in microbial transport in the natural subsurface

Processes in microbial transport in the natural subsurface

Langevin dynamics for the transport of flexible biological macromolecules in confined geometries

Particle filtration: An analysis using the method of volume averaging

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