Related Experiment Video
Updated: Jul 19, 2026
08:19
Induction of Microstreaming by Nonspherical Bubble Oscillations in an Acoustic Levitation System
Published on: May 9, 2021
Toy model of hydrodynamic fluctuations
1Department of Materials, Polymer Physics, ETH Zürich, HCI H 543, CH-8093 Zürich, Switzerland. hco@mat.ethz.ch
Physical Review Letters
|October 10, 2006
Summary
This study introduces a new model for hydrodynamic fluctuations in ideal gases, distinguishing between biased and unbiased momentum densities to better describe small systems. This approach enables the formulation of hydrodynamic equations satisfying the fluctuation-dissipation theorem.
Area of Science:
- Thermodynamics
- Fluid Dynamics
- Statistical Mechanics
Background:
- Einstein's theory of equilibrium fluctuations is inadequate for small thermodynamic systems.
- Understanding hydrodynamic fluctuations in ideal gases requires a refined approach.
Purpose of the Study:
- To develop a model for hydrodynamic fluctuations in small volume elements of an ideal gas.
- To distinguish between biased and unbiased momentum densities.
- To formulate hydrodynamic equations consistent with the fluctuation-dissipation theorem.
Main Methods:
- Development of a toy model for correlated fluctuations in neighboring small cells.
- Distinction of biased and unbiased momentum densities.
- Formulation of hydrodynamic equations based on these densities.
Main Results:
- A clear distinction between biased and unbiased momentum densities was established.
- Hydrodynamic equations satisfying the fluctuation-dissipation theorem were derived.
- The model provides a framework for analyzing thermodynamic properties in small systems.
Conclusions:
- The proposed model effectively addresses the limitations of existing theories for small systems.
- The distinction of momentum densities is crucial for accurate hydrodynamic descriptions.
- This work advances the understanding of fluctuation phenomena in non-equilibrium systems.
Related Concept Videos
01:30Typical Model Studies
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.
01:12Modeling and Similitude
Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...
01:21Design Example: Creating a Hydraulic Model of a Dam Spillway
Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
01:04Hydrostatic Pressure Force on a Curved Surface
Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...
01:11Pressure Variation in a Fluid at Rest
In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
When measuring pressure at two different levels within the fluid, the difference in pressure...
When measuring pressure at two different levels within the fluid, the difference in pressure...
01:22Surface Tension of Fluid
Surface tension is a fundamental property of fluids, occurring at the boundary between a liquid and a gas or between two immiscible liquids. This phenomenon arises from the cohesive forces between molecules at the fluid's surface, creating an effect similar to a stretched elastic membrane. Inside each fluid, molecules are equally attracted in all directions by neighboring molecules, but surface molecules experience a net inward force, resulting in surface tension.
Surface tension varies with...
Surface tension varies with...