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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
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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.
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Steady, Laminar Flow in Circular Tubes01:23

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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
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When water is poured into a glass, it falls freely and quickly, whereas if honey or maple syrup is poured over a pancake, it flows slowly and sticks to the surface of the container. This difference in the flow of different kinds of liquids arises due to the fluid friction between the liquid layers and the liquid and the surrounding material. This property of fluids is called fluid viscosity. In this example, water has a lower viscosity than honey and maple syrup.
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Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
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Probing bulk viscosity in relativistic flows.

A Gabbana1,2, D Simeoni1,2,3, S Succi4,5

  • 1Università di Ferrara and INFN-Ferrara, 44122 Ferrara, Italy.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|June 23, 2020
PubMed
Summary
This summary is machine-generated.

This study connects kinetic relaxation rate and bulk viscosity in relativistic fluids across various energy regimes. Findings validate theoretical models and explore quark-gluon plasma transport, offering experimental verification possibilities.

Keywords:
bulk viscosityquark-gluon plasmarelativistic hydrodynamics

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Area of Science:

  • * Relativistic fluid dynamics
  • * Kinetic theory
  • * Plasma physics

Background:

  • * Understanding transport coefficients like bulk viscosity is crucial for relativistic fluid dynamics.
  • * Existing theoretical frameworks have limitations in describing fluid behavior across different energy regimes.
  • * Quark-gluon plasma (QGP) exhibits complex transport phenomena.

Purpose of the Study:

  • * To establish an analytical link between kinetic relaxation rate and bulk viscosity for relativistic fluids.
  • * To determine the validity and limitations of the Chapman-Enskog method in different regimes.
  • * To investigate the impact of bulk viscosity on transport processes in QGP.

Main Methods:

  • * Derivation using Chapman-Enskog asymptotic expansion and Grad's method of moments.
  • * Validation against a benchmark relativistic fluid flow.
  • * Numerical simulations of transport phenomena in quark-gluon plasmas.

Main Results:

  • * An analytical connection between kinetic relaxation rate and bulk viscosity was derived, valid from ultra-relativistic to near non-relativistic limits.
  • * The range of validity for the Chapman-Enskog approach was defined, showing departures at higher Knudsen numbers.
  • * Numerical simulations highlighted the significant effects of bulk viscosity on QGP transport.

Conclusions:

  • * The derived analytical connection provides a robust tool for studying relativistic fluid dynamics.
  • * The Chapman-Enskog method's applicability is constrained by the Knudsen number.
  • * Bulk viscosity in QGP is a key factor for transport processes and potentially measurable experimentally.