Related Experiment Video
Updated: Apr 3, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
Towards a statistical mechanical theory of active fluids
Umberto Marini Bettolo Marconi1, Claudio Maggi2
1Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, 62032, Camerino, INFN Perugia, Italy. umberto.marinibettolo@unicam.it.
Soft Matter
|September 22, 2015
Summary
We developed a statistical mechanics model for active particles, revealing an effective attraction between them. This model helps understand active fluid behavior and derive their equation of state.
Area of Science:
- Statistical Mechanics
- Soft Matter Physics
- Non-equilibrium Systems
Background:
- Active particles exhibit persistent motion, deviating from equilibrium behavior.
- Modeling these systems requires accounting for correlated noise and inter-particle interactions.
Purpose of the Study:
- To develop a statistical mechanical framework for active particles.
- To characterize steady-state properties and derive macroscopic behavior.
- To investigate the role of particle activity on interactions and phase behavior.
Main Methods:
- Stochastic description of N interacting active particles with correlated Gaussian noise.
- Multidimensional unified colored noise approximation for the many-particle distribution function.
- Extension of Born-Green-Yvon (BGY) equations to active systems.
- Development of a mean-field theory and derivation of an equation of state.
Main Results:
- Obtained the many-particle distribution function analogous to the Gibbs distribution.
- Derived equations for stationary density profiles, pair correlations, and pressure.
- Identified an effective attraction between active particles at low densities.
- Derived a van der Waals-like equation of state for active fluids.
Conclusions:
- The developed statistical mechanical approach accurately describes active particle systems.
- Particle activity induces effective attraction and influences macroscopic properties.
- The mean-field theory provides a simplified yet effective description of active fluid behavior.
More Related Videos
Related Concept Videos
01:28Euler's Equations of Motion
1.1K
In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
1.1K
01:04Pascal's Law
12.4K
In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...
12.4K
01:30Typical Model Studies
684
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
684
01:20Stokes' Law
3.3K
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature.
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only...
3.3K
01:17Accelerating Fluids
2.4K
When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
2.4K
01:28Navier–Stokes Equations
2.7K
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
2.7K