Related Experiment Video
Updated: Mar 16, 2026

Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
Published on: May 20, 2014
On the description of Brownian particles in confinement on a non-Cartesian coordinates basis
Leonardo Dagdug1, Angel A García-Chung1, Guillermo Chacón-Acosta2
1Physics Department, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, México D. F. 09340, Mexico.
Abstract:
We developed a theoretical framework to study the diffusion of Brownian point-like particles in bounded geometries in two and three dimensions. We use the Frenet-Serret moving frame as the coordinate system. For narrow tubes and channels, we use an effective one-dimensional description reducing the diffusion equation to a Fick-Jacobs-like equation. From this last equation, we can calculate the effective diffusion coefficient applying Neumann boundary conditions. On one hand, for channels with a straight axis our theoretical approximation for the effective coefficient does coincide with the reported in the literature [D. Reguera and J. M. Rubí, Phys. Rev. E 64, 061106 (2001) and P. Kalinay and J. K. Percus, ibid. 74, 041203 (2006)]. On the other hand, for tubes with a straight axis and circular cross-section our analytical expression does not coincide with the reported by Rubí and Reguera and by Kalinay and Percus, although it is practically identical.
Related Concept Videos
Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates
When a particle moves relative to an inertial frame, the equations of motion can be expressed using rectangular components. If the motion is confined to the x-y plane, the equations having the x and y coordinates only can be used to simplify the mathematical representation.
However, when particles...
Curvilinear Motion: Polar Coordinates
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
Equilibrium Conditions for a Particle
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
First Law: Particles in Two-dimensional Equilibrium
Newton's first law tells us about...
First Law: Particles in One-dimensional Equilibrium
Principle of Linear Impulse and Momentum for a System of Particles
Notably, internal forces between particles, occurring in equal and opposite collinear pairs, cancel out and are not part of the equation of motion. This exclusion simplifies the...

