Elastic properties of dense hard-sphere fluids
1Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 82234 Weßling, Germany and Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow, Russia.
Physical Review. E
|October 24, 2019
Summary
This study reveals that conventional formulas for elastic moduli diverge for hard-sphere (HS) fluids. These formulas are unsuitable for HS systems, necessitating new approaches for understanding their elastic properties.
Area of Science:
- Statistical Physics
- Physics of Fluids
- Soft Condensed Matter
- Granular Materials
Background:
- Conventional expressions for high-frequency elastic moduli in simple systems with continuous potentials diverge at the hard-sphere (HS) repulsive limit.
- The applicability of these expressions to HS systems, crucial in various scientific fields, is questionable.
Purpose of the Study:
- To analyze the elastic properties of dense hard-sphere (HS) fluids.
- To identify the origin of divergence in conventional elastic moduli expressions for HS systems.
- To explore implications for sound wave propagation, Poisson's ratio, and the Stokes-Einstein relation in HS fluids.
Main Methods:
- Analysis based on expressions derived by Miller (1969).
- Investigation of consequences for sound wave propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity.
- Identification of the divergence origin in conventional high-frequency elastic moduli expressions.
Main Results:
- Conventional expressions for high-frequency elastic moduli diverge when approaching the HS repulsive limit.
- These conventional expressions are only valid for soft interactions and not applicable to HS systems.
- The study clarifies the limitations of existing models for HS fluid elasticity.
Conclusions:
- Existing high-frequency elastic moduli expressions are inappropriate for hard-sphere systems.
- A new understanding of elastic properties in dense HS fluids is provided.
- The findings are relevant for statistical physics, fluid dynamics, soft matter, and granular materials research.
Related Concept Videos
00:56Density
18.9K
Density is an important characteristic of substances, crucial in determining whether an object sinks or floats in a fluid. Its SI unit is kg/m3, and its cgs unit is g/cm3. The density of an object helps in identifying its composition, and also reveals information about the phase of the matter and its substructure. The densities of liquids and solids are roughly comparable, consistent with the fact that their atoms are in close contact. However, gases have much lower densities than liquids and...
18.9K
01:31Characteristics of Fluids
913
Fluids differ from solids primarily in their molecular structure and stress response. Solids have tightly packed molecules with strong intermolecular forces, maintaining their shape and resisting deformation. In contrast, fluids have molecules spaced farther apart with weaker forces, allowing them to flow and deform easily.
Fluids, which include both liquids and gases, are substances that deform continuously under shearing stress. For example, water and oil are liquids with molecules that can...
Fluids, which include both liquids and gases, are substances that deform continuously under shearing stress. For example, water and oil are liquids with molecules that can...
913
01:20Characteristics of Fluids
7.5K
When a force is applied parallel to the top surface of a solid, it resists the applied force due to the internal frictional forces between the layers of the solid known as shearing resistance. However, when the force is removed, the shearing forces restore the original shape of the solid. Other deformation forces also cause temporary changes in shape if the forces are not beyond a threshold magnitude. Solids tend to retain their shape, making the study of their rest and motion easier. Beyond...
7.5K
00:51Speed of Sound in Solids and Liquids
3.8K
Most solids and liquids are incompressible—their densities remain constant throughout. In the presence of an external force, the molecules tend to restore to their original positions, which is only possible because the constituents interact. The interactions help the constituents pass on information about external disturbances, like sound waves. Therefore, sound waves travel faster through these media. Compared to solids, the constituents in a liquid are less tightly bound. Thus, sound...
3.8K
02:26Molecular Comparison of Gases, Liquids, and Solids
53.0K
Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no regular arrangement (no fixed shape); in a gas, they are far apart with no regular arrangement (no fixed shape). Particles in a solid vibrate about fixed positions (cannot flow) and do not generally move in relation to one another; in a liquid, they move past each other (can flow) but remain in essentially constant contact; in a gas, they move...
53.0K
01:27Density, Specific Weight, Specific Gravity and Compressibility of Fluid
1.4K
Density, specific weight, specific gravity, and compressibility are fundamental properties of fluids. Density is the mass per unit volume, characterizing the mass of a fluid system. It influences buoyancy, pressure, flow dynamics, viscosity, thermal conductivity, and sound propagation. For instance, in pipeline design, accurate density measurements ensure that the pipeline can handle the fluid's mass.
Specific weight represents the weight per unit volume and is calculated by multiplying...
Specific weight represents the weight per unit volume and is calculated by multiplying...
1.4K