Blocker Effect on Diffusion Resistance of a Membrane Channel: Dependence on the Blocker Geometry.

Being motivated by recent progress in nanopore sensing, we develop a theory of the effect of large analytes, or blockers, trapped within the nanopore confines, on diffusion flow of small solutes. The focus is on the nanopore diffusion resistance which is the ratio of the solute concentration difference in the reservoirs connected by the nanopore to the solute flux driven by this difference. Analytical expressions for the diffusion resistance are derived for a cylindrically symmetric blocker whose axis coincides with the axis of a cylindrical nanopore in two limiting cases where the blocker radius changes either smoothly or abruptly. Comparison of our theoretical predictions with the results obtained from Brownian dynamics simulations shows good agreement between the two.

Trapping of diffusing particles by striped cylindrical surfaces. Boundary homogenization approach.

We study trapping of diffusing particles by a cylindrical surface formed by rolling a flat surface, containing alternating absorbing and reflecting stripes, into a tube. For an arbitrary stripe orientation with respect to the tube axis, this problem is intractable analytically because it requires dealing with non-uniform boundary conditions. To bypass this difficulty, we use a boundary homogenization approach which replaces non-uniform boundary conditions on the tube wall by an effective uniform partially absorbing boundary condition with properly chosen effective trapping rate. We demonstrate that the exact solution for the effective trapping rate, known for a flat, striped surface, works very well when this surface is rolled into a cylindrical tube. This is shown for both internal and external problems, where the particles diffuse inside and outside the striped tube, at three orientations of the stripe direction with respect to the tube axis: (a) perpendicular to the axis, (b) parallel to the axis, and

Aris-Taylor dispersion in tubes with dead ends.

This paper deals with transport of point Brownian particles in a cylindrical tube with dead ends in the presence of laminar flow of viscous fluid in the cylindrical part of the tube (Poiseuille flow). It is assumed that the dead ends are identical and are formed by spherical cavities connected to the cylindrical part of the tube by narrow necks. The focus is on the effective velocity and diffusivity of the particles as functions of the mean flow velocity and geometric parameter of the tube. Entering a dead end, the particle interrupts its propagation along the tube axis. Later it returns, and the axial motion continues. From the axial propagation point of view, the particle entry into a dead end and its successive return to the flow is equivalent to the particle reversible binding to the tube wall. The effect of reversible binding on the transport parameters has been previously studied assuming that the particle survival probability in the bound state decays as a single exponential. However, this is not the case when the particle enters a dead end, since escape from the dead end is a non-Markovian process. Our analysis of the problem consists of two steps: First, we derive expressions for the effective transport parameters in the general case of non-Markovian binding. Second, we find the effective velocity and diffusivity by substituting into these expressions known results for the moments of the particle lifetime in the dead end [L. Dagdug, A. M. Berezhkovskii, Yu. A. Makhnovskii, and V. Yu. Zitserman, J. Chem. Phys. 127, 224712 (2007)]. To check the accuracy of our theory, we compare its predictions with the values of the effective velocity and diffusivity obtained from Brownian dynamics simulations. The comparison shows excellent agreement between the theoretical predictions and numerical results.