Modelling and asymptotic analysis of the concentration difference in a nanoregion between an influx andoutflux diffusion acrossnarrow windows

When a flux of Brownian particles is injected in a narrow window located on the surface of a bounded domain, these particles diffuse and can eventually escape through a cluster of narrow windows. At steady state, we compute asymptotically the distribution of concentration between the different windows. The solution is obtained by solving Laplace’s equation using Green’s function techniques and second-order asymptotic analysis, and depends on the influx amplitude, the diffusion properties, as well as the geometrical organization of all the windows, such as their distances and the mean curvature. We explore the range of validity of the present asymptotic expansions using numerical simulations of the mixed boundary value problem. Finally, we introduce a length scale to estimate how deep inside a domain a local diffusion current can spread.

Focusing of Brownian Particles in a Fluid Induced by the Temperature Difference

In this work the Brownian motion of particles in a two-dimensional channel was numerically studied through a fluctuating-lattice Boltzmann method. The effects of the fluid temperature difference on the biased Brownian motion of particles were examined. It is shown that the particles are likely to move towards and stay at the low temperature zone. More importantly, the focusing of Brownian particles may be realized if the temperature difference is large enough. This paper also provides a quantitative analysis on this issue.