Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTracer diffusion in crowded narrow channels. Topical review
373
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels -- single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. We also present a survey of different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.
rate research
Read More
Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically out-of-equilibrium due to the energy-dissipating active processes underlying their mechanical and dynamical features. The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms indeed differs significantly from Brownian motion, manifest in a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. While such characteristic features have been extensively observed in experiments, there is so far no comprehensive theory explaining how they emerge from the microscopic active dynamics. Here we present a theoretical framework of the enhanced tracer diffusion in an active medium from its microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The tracer is shown to follow a non-Markovian coloured Poisson process that accounts quantitatively for all empirical observations. The theory predicts in particular a long-lived Levy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, thus suggesting that the optimal foraging strategy of swimming microorganisms might crucially depend on the density in order to exploit the Levy flights of nutrients. Our framework provides the first validation of the celebrated Levy flight model from a physical microscopic dynamics.
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it at the mesoscopic level and this is shown to lead to non-linear cross diffusion terms that modify the conventional Fickean picture. After reviewing the derivation of the model, the experiments carried out to test the model are described. It is found that it can adequately explain the dynamics of two dense ink drops simultaneously evolving in a container filled with water. The experiment shows that molecular crowding results in the formation of a dynamical barrier that prevents the mixing of the drops. This phenomenon is successfully captured by the model. This suggests that the proposed model can be justifiably viewed as a generalization of standard diffusion to a multispecies setting, where crowding and steric interferences are taken into account.
We study by extensive numerical simulations the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder - frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour $sim t^{4/3}$, $t$ being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position $X$ along the $x$-axis. Our analysis evidences that in absence of the lattice gas particles the latter has a Gaussian central part $sim exp(- u^2)$, where $u = X/t^{2/3}$, and exhibits slower-than-Gaussian tails $sim exp(-|u|^{4/3})$ for sufficiently large $t$ and $u$. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.
We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials, considering an attractive substrate potential at the bottom, confining side walls, and hard-core repulsive fluid-fluid interactions. Using kinetic Monte Carlo simulations we find a diffusive behavior. The corresponding diffusion coefficient depends on the density and is bounded from below by the free one-dimensional diffusion coefficient, valid for an inert bottom wall. These numerical results are rationalized within the corresponding continuum limit.
Diffusion of impenetrable particles in a crowded one-dimensional channel is referred as the single file diffusion. The particles do not pass each other and the displacement of each individual particle is sub-diffusive. We analyse a simple realization of this single file diffusion problem where one dimensional Brownian point particles interact only by hard-core repulsion. We show that the large deviation function which characterizes the displacement of a tracer at large time can be computed via a mapping to a problem of non-interacting Brownian particles. We confirm recently obtained results of the one time distribution of the displacement and show how to extend them to the multi-time correlations. The probability distribution of the tracer position depends on whether we take annealed or quenched averages. In the quenched case we notice an exact relation between the distribution of the tracer and the distribution of the current. This relation is in fact much more general and would be valid for arbitrary single file diffusion. It allows in particular to get the full statistics of the tracer position for the symmetric simple exclusion process (SSEP) at density 1/2 in the quenched case.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
