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Elastic Collisions: Introduction

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An elastic collision is one that conserves both internal kinetic energy and momentum. Internal kinetic energy is the sum of the kinetic energies of the objects in a system. Truly elastic collisions can only be achieved with subatomic particles, such as electrons striking nuclei. Macroscopic collisions can be very nearly, but not quite, elastic, as some kinetic energy is always converted into other forms of energy such as heat transfer due to friction and sound. An example of a nearly...

Elastic Collisions: Case Study

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Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

Types Of Collisions - I

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When two objects come in direct contact with each other, it is called a collision. During a collision, two or more objects exert forces on each other in a relatively short amount of time. A collision can be categorized as either an elastic or inelastic collision. If two or more objects approach each other, collide and then bounce off, moving away from each other with the same relative speed at which they approached each other, the total kinetic energy of the system is said to be conserved. This...

Types of Collisions - II

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When two or more objects collide with each other, they can stick together to form one single composite object (after collision). The total mass of the object after the collision is the sum of the masses of the original objects, and it moves with a velocity dictated by the conservation of momentum. Although the system's total momentum remains constant, the kinetic energy decreases, and thus such a collision is an inelastic collision. Most of the collisions between objects in daily life are...

Elasticity

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Elasticity is the ability of an object to withstand the effects of distortion and to return to its original size and shape once the forces causing deformation are removed. When an elastic material deforms under the action of an external force, it experiences internal resistance to the deformation. However, if no external force is applied, it returns to its original state.
The elasticity of an object can be described by a stress-strain curve, which represents the relationship between stress...

Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...

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Sticky elastic collisions.

Jérémie Bec¹, Stefano Musacchio, Samriddhi Sankar Ray

¹Laboratoire Lagrange, UMR 7293, Université de Nice Sophia Antipolis, CNRS, Observatoire de la Côte d'Azur, Bd. de l'Observatoire, 06300 Nice, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 16, 2013

Summary

This summary is machine-generated.

Sticky elastic collisions significantly alter heavy particle behavior in random flows, causing particles to cluster. This study provides a framework and simulations to understand this phenomenon and its relation to hydrodynamic interactions.

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Area of Science:

Fluid dynamics
Particle physics
Statistical mechanics

Background:

Understanding particle dynamics in turbulent flows is crucial for various industrial and environmental applications.
Heavy inertial particles exhibit complex behaviors influenced by fluid flow and interparticle interactions.
Elastic collisions play a significant role in particle clustering and separation dynamics.

Purpose of the Study:

To investigate the effects of purely elastic collisions on the dynamics of heavy inertial particles in a three-dimensional random incompressible flow.
To develop a theoretical framework for describing and quantifying the phenomenon of sticky elastic collisions.
To analyze the impact of hydrodynamic interactions on colliding particle systems.

Main Methods:

Numerical simulations of particle trajectories in a random incompressible flow.
Development of a theoretical model to capture the essence of sticky elastic collisions.
Analysis of statistical properties of interparticle separations and relative velocities.

Main Results:

Sticky elastic collisions lead to a significant influence on interparticle separations and relative velocities.
Particle pairs undergoing numerous collisions remain in close proximity for extended periods.
Hydrodynamic interactions further modify the dynamics of colliding particles.

Conclusions:

Sticky elastic collisions are a key factor in particle clustering and dynamics in random flows.
The developed theoretical framework accurately describes and quantifies the observed phenomena.
Hydrodynamic interactions are important for a comprehensive understanding of particle collision dynamics.