Brownian motion in confined geometries

Bezrukov, Sergey M.; Schimansky‐Geier, Lutz; Schmid, Gerhard

doi:10.1140/epjst/e2014-02316-6

Cited by 16 publications

(6 citation statements)

References 42 publications

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“…2, B and C). The mathematical properties of the model are discussed in (20)(21)(22)(23)(24)26,29,30). This homogenization yields to an isotropic system for diffusing particles.…”

Section: Methodsmentioning

confidence: 99%

A Model for the Transient Subdiffusive Behavior of Particles in Mucus

Ernst¹,

John

Guenther³

et al. 2017

Biophysical Journal

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In this study we have applied a model to explain the reported subdiffusion of particles in mucus, based on the measured mean squared displacements (MSD). The model considers Brownian diffusion of particles in a confined geometry, made from permeable membranes. The applied model predicts a normal diffusive behavior at very short and long time lags, as observed in several experiments. In between these timescales, we find that the ''subdiffusive'' regime is only a transient effect, MSDft a ; a < 1. The only parameters in the model are the diffusion-coefficients at the limits of very short and long times, and the distance between the permeable membranes L. Our numerical results are in agreement with published experimental data for realistic assumptions of these parameters. Finally, we show that only particles with a diameter less than 40 nm are able to pass through a mucus layer by passive Brownian motion.

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“…2, B and C). The mathematical properties of the model are discussed in (20)(21)(22)(23)(24)26,29,30). This homogenization yields to an isotropic system for diffusing particles.…”

Section: Methodsmentioning

confidence: 99%

A Model for the Transient Subdiffusive Behavior of Particles in Mucus

Ernst¹,

John

Guenther³

et al. 2017

Biophysical Journal

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“…The latter two properties have deep and non trivial implications whenever a stochastic equation of motion, in the form of Equation ( 3) is considered, due to the highly singular nature of the Wiener description of the thermal/hydrodynamic fluctuations. For the sake of completeness, it should be also mentioned that a position dependent effective diffusivity arises in modeling solute transport in microchannels with undulated walls, in the case the transport problem is referred exclusively to the channel axial coordinate [43,44]. This is referred to as the Fick-Jacobs approximation and it is essentially a geometrical effect within an approximate transport model unrelated to any hydrodynamic interactions.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modeling of Particle Transport in Confined Geometries: Problems and Peculiarities

Procopio

Giona

2022

Fluids

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The equivalence between parabolic transport equations for solute concentrations and stochastic dynamics for solute particle motion represents one of the most fertile correspondences in statistical physics originating from the work by Einstein on Brownian motion. In this article, we analyze the problems and the peculiarities of the stochastic equations of motion in microfluidic confined systems. The presence of solid boundaries leads to tensorial hydrodynamic coefficients (hydrodynamic resistance matrix) that depend also on the particle position. Singularity issues, originating from the non-integrable divergence of the entries of the resistance matrix near a solid no-slip boundary, determine some mass-transport paradoxes whenever surface phenomena, such as surface chemical reactions at the walls, are considered. These problems can be overcome by considering the occurrence of non vanishing slippage. Added-mass effects and the influence of fluid inertia in confined geometries are also briefly addressed.

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“…On the other hand, when the particles diffuse in a confined geometry, their motion is highly controlled by the structure of the geometry [16][17][18][19][20][21][22], e.g., ion channels [23], zeolites [24], microfluidic devices [25], ratchets [26][27][28][29][30] and artificial channels [31]. The irregular shape of the structure gives rise to entropic barriers which play a prominent role in the diffusive behavior of the particles [32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Confined diffusion in a random Lorentz gas environment

Khatri

Burada

2020

Phys. Rev. E

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We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacles density η and the scaling parameter f , which is the ratio of work done to the particles to available thermal energy. We show that, when the thermal fluctuations dominate over the external force, i.e., small f regime, particles get trapped in the given environment when the system percolates at the critical obstacles density η c ≈ 1.2. However, as f increases, we observe that particles trapping occurs prior to η c. In particular, we find a relation between η and f which provides an estimate of the minimum η up to a critical scaling parameter f c beyond which the Fick-Jacobs description is invalid. Prominent transport features like nonmonotonic behavior of the nonlinear mobility, anomalous diffusion, and greatly enhanced effective diffusion coefficient are explained for various strengths of f and η. Also, it is interesting to observe that particles exhibit different kinds of diffusive behaviors, i.e., subdiffusion, normal diffusion, and superdiffusion. These findings, which are genuine to the confined and random Lorentz gas environment, can be useful to understand the transport of small particles or molecules in systems such as molecular sieves and porous media which have a complex heterogeneous environment of the freezing obstacles.

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Brownian motion in confined geometries

Cited by 16 publications

References 42 publications

A Model for the Transient Subdiffusive Behavior of Particles in Mucus

A Model for the Transient Subdiffusive Behavior of Particles in Mucus

Stochastic Modeling of Particle Transport in Confined Geometries: Problems and Peculiarities

Confined diffusion in a random Lorentz gas environment

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