Related Experiment Video
Updated: May 9, 2026
10:56
Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
Published on: May 20, 2014
Brownian motion in inhomogeneous suspensions.
Mingcheng Yang1, Marisol Ripoll
1Theoretical Soft-Matter and Biophysics, Institute of Complex Systems, Forschungszentrum Jülich, 52425 Jülich, Germany. mcyang@iphy.ac.cn
Summary
This study revisits the Langevin description for Brownian motion in inhomogeneous suspensions. It resolves the Ito-Stratonovich dilemma by ensuring macroscopic force balance, restoring the Langevin framework for particle dynamics.
Area of Science:
- Physics
- Physical Chemistry
- Statistical Mechanics
Background:
- Brownian motion in inhomogeneous suspensions presents challenges due to position-dependent friction.
- The Langevin approach faces difficulties with multiplicative noise interpretation in such systems.
- Existing models struggle with the Ito-Stratonovich dilemma, impacting particle dynamics accuracy.
Purpose of the Study:
- To revisit and refine the Langevin description for Brownian motion in inhomogeneous suspensions.
- To resolve the Ito-Stratonovich dilemma arising from position-dependent friction.
- To restore the self-completeness of the Langevin framework without relying on Fokker-Planck methods.
Main Methods:
- Re-derivation of the extended overdamped Langevin equation from the infradamped Langevin equation.
- Ensuring macroscopic force balance during the elimination of fast variables.
- Direct derivation without invoking the Fokker-Planck formalism.
Main Results:
- The Ito-Stratonovich dilemma in inhomogeneous systems is shown to originate from violated macroscopic force balance.
- A repaired Langevin procedure yields an extended overdamped Langevin equation.
- Generalized drift-force relations and Smoluchowski equations for inhomogeneous suspensions are derived.
Conclusions:
- The study successfully resolves the multiplicative noise interpretation issue in inhomogeneous Brownian motion.
- The self-completeness of the Langevin framework is restored for these complex systems.
- New generalized equations provide a more accurate description of particle dynamics in inhomogeneous suspensions.
Related Concept Videos
01:17Colloids and Suspensions
Children at play often make suspensions such as mixtures of mud and water, flour and water, or a suspension of solid pigments in water known as tempera paint. These suspensions are heterogeneous mixtures composed of relatively large particles visible to the naked eye or seen with a magnifying glass. They are cloudy, and the suspended particles settle out after mixing. The suspended particles in a suspension settle out after some time of mixing. The separation of particles from a suspension is...
01:29The Colloidal State
The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called the...
01:10First Law: Particles in One-dimensional Equilibrium
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
01:18First Law: Particles in Two-dimensional Equilibrium
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Newton's first law tells us about the...
01:27Distribution of Molecular Speeds
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
01:11Relative Velocity in Two Dimensions
Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing vector...