Diffusion in inhomogeneous media

doi:10.1016/0022-3697(88)90199-0

Journal of Physics and Chemistry of Solids

Volume 49, Issue 6, 1988, Pages 673-677

https://doi.org/10.1016/0022-3697(88)90199-0 Get rights and content

Abstract

The correct form of the diffusion equation in the case of an inhomogeneous medium, whose temperature may also vary in space, has been the subject of some debate. As no universal answer has been found, we have studied special models of three types: (1) Landauer's model of a Knudsen gas in a narrow pipe; (2) transfer by hopping or random walk; (3) Brownian motion and a generalization thereof. On comparing the results one recognizes enough common features to formulate a general scheme for establishing the correct diffusion equation, provided that the diffusing particles are independent of each other.

References (22)

M. Büttiker et al.
Nonlinear Phenomena of Phase Transitions and Instabilities
R. Landauer
Helv. Phys. Acta
(1983)
R.E. Mortensen
J. statist. Phys.
(1969)
N.G. van Kampen
J. statist. Phys.
(1981)
U. Geigenmüller et al.
Physica
(1983)
U. Geigenmüller et al.
Physica
(1983)
U. Geigenmüller et al.
Physica
(1983)
C.W. Gardiner
Handbook of Stochastic Methods
M. Planck
Sitzungsber. Preuss. Akad. Wissens.
(1917)
N.G. van Kampen
Phys. Lett.
(1977)
N.G. van Kampen
Stochastic Processes in Physics and Chemistry
(1981)
H.A. Kramers
Physica
(1940)
U.M. Titulaer
Physica
(1978)
U.M. Titulaer
Physica
(1980)
U.M. Titulaer
Physica
(1980)
R. Landauer
Phys. Rev.
(1975)

R. Stratton

Phys. Rev.

(1962)

R. Stratton

J. appl. Phys.

(1969)

R. Stratton

IEEE Trans. Electron. Devices

(1972)

Cited by (93)

Beyond microtubules: The cellular environment at the endoplasmic reticulum attracts proteins to the nucleus, enabling nuclear transport
2024, iScience
All proteins are translated in the cytoplasm, yet many, including transcription factors, play vital roles in the nucleus. While previous research has concentrated on molecular motors for the transport of these proteins to the nucleus, recent observations reveal perinuclear accumulation even in the absence of an energy source, hinting at alternative mechanisms. Here, we propose that structural properties of the cellular environment, specifically the endoplasmic reticulum (ER), can promote molecular transport to the perinucleus without requiring additional energy expenditure. Specifically, physical interaction between proteins and the ER impedes their diffusion and leads to their accumulation near the nucleus. This result explains why larger proteins, more frequently interacting with the ER membrane, tend to accumulate at the perinucleus. Interestingly, such diffusion in a heterogeneous environment follows Chapman’s law rather than the popular Fick’s law. Our findings suggest a novel protein transport mechanism arising solely from characteristics of the intracellular environment.
Inverse thermodiffusion of active matter in temperature gradient systems
2024, Physica A: Statistical Mechanics and its Applications
We have revealed an inverse thermodiffusion phenomenon for active particles under temperature gradient in one-species systems. This counterintuitive behavior is supported by numerical calculations as well as theoretical analyses. It is presented that the active particles flow from high-temperature to low-temperature regions when the self-driving force is small. On the contrary, the active particles can flow from low-temperature to high-temperature regions as long as the self-driving force is large enough. The mass current reversal phenomenon can be explained analytically from the special swimming pressures of the active particles. The P é clet numbers defined in our work indicate a potential application in separating the particles with different activities. The findings may bring a new understanding of the physical properties of active matter and provide enlightenment for the study of the non-equilibrium collective transport of active particles.
The space between us: Modeling spatial heterogeneity in synthetic microbial consortia dynamics
2022, Biophysical Reports
Citation Excerpt :
However, the well-mixed compartment models do not allow for the explicit incorporation of strain patterns, and agent-based modeling frameworks are computationally expensive for larger systems (31). To address this gap in the literature, we borrow from previous research focused on modeling diffusion in heterogeneous media (32,33,34) and develop a piecewise-defined reaction-diffusion equation framework for modeling spatiotemporal consortium dynamics. Here, we show that this modeling framework allows for the explicit incorporation of consortium spatial organization while remaining computationally tractable for larger systems.
A central endeavor in bioengineering concerns the construction of multistrain microbial consortia with desired properties. Typically, a gene network is partitioned between strains, and strains communicate via quorum sensing, allowing for complex behaviors. Yet a fundamental question of how emergent spatiotemporal patterning in multistrain microbial consortia affects consortial dynamics is not understood well. Here, we propose a computationally tractable and straightforward modeling framework that explicitly allows linking spatiotemporal patterning to consortial dynamics. We validate our model against previously published results and make predictions of how spatial heterogeneity impacts interstrain communication. By enabling the investigation of spatial patterns effects on microbial dynamics, our modeling framework informs experimentalists, helps advance the understanding of complex microbial systems, and supports the development of applications involving them.
Polymer Concentration Regimes from Fractional Microrheology
2024, arXiv
A Mode-Coupling Model of Colloid Thermophoresis in Aqueous Systems: Temperature and Size Dependencies of the Soret Coefficient
2024, Nano Letters
DIFFUSION LAWS SELECT BOUNDARY CONDITIONS
2023, arXiv

View all citing articles on Scopus

View full text

Diffusion in inhomogeneous media

Abstract

Helv. Phys. Acta

J. statist. Phys.

J. statist. Phys.

Physica

Physica

Physica

Sitzungsber. Preuss. Akad. Wissens.

Phys. Lett.

Physica

Physica

Physica

Physica

Phys. Rev.

Phys. Rev.

J. appl. Phys.

IEEE Trans. Electron. Devices