Undergrad Non-Newtonian fluids at the quantum level

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SUMMARY

The discussion centers on the behavior of Non-Newtonian fluids at the quantum level, specifically how molecular shape and interactions influence their properties. Non-Newtonian fluids consist of nonspherical molecules, which lead to deviations from the Navier-Stokes equations governing Newtonian fluids. Classical mechanics effectively explains these deviations, while quantum mechanics plays a limited role, primarily in determining molecular shapes and the forces involved. The conversation emphasizes that emergent properties of fluids arise from molecular interactions rather than deeper quantum phenomena.

PREREQUISITES
  • Understanding of Non-Newtonian fluid dynamics
  • Familiarity with Navier-Stokes equations
  • Basic knowledge of classical mechanics
  • Concepts of molecular shape and interactions
NEXT STEPS
  • Research the mathematical modeling of Non-Newtonian fluids
  • Explore the implications of molecular shape on fluid behavior
  • Study the Navier-Stokes equations in detail
  • Investigate the role of classical mechanics in fluid dynamics
USEFUL FOR

Researchers in fluid dynamics, physicists studying material properties, and engineers working with complex fluids will benefit from this discussion.

thebosonbreaker
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I am intrigued by the diversity of Non-Newtonian fluids and need to ask a question.

Can anyone provide me with a breakdown of what goes on at the quantum level as the Non-Newtonian fluid bounces up and down on top of the speaker in the video I have embedded.

What I would like to know is essentially what happens in terms of:
  • Molecules and atoms
  • Electrons orbiting the nuclei of the atoms
  • Protons and neutrons in the nuclei of the atoms
  • Quarks and other particles that make up the electrons
  • Even further down the quantum level would be nice (if possible!)
Many thanks in advance.
 
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The properties of a fluid are emergent properties. Anything more fundamental than molecule-molecule interactions will play no role in determining the Newtonian or non-Newtonian behavior of a fluid.
 
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thebosonbreaker said:
What I would like to know is essentially what happens in terms of:
  • Molecules and atoms
A non-Newtonian fluid is composed of molecules whose shape seen from far away is significantly nonspherical. This causes the effective equations derived from a statistical mechanics treatment to be significantly different from the Navier-Stokes equations for Newtonian fluids. One needs additional degrees of freedom to model the deviation from sphericity. That's all.

Given the effective forces of the molecules, classical mechanics suffices to explain the deviations from Newtonian laws. Quantum mechanics, atoms and electrons are only relevant in as far as they determine the possible shapes of the molecules and the effective forces in reshaping them (i.e., their classical molecular force field). Stuff inside atoms works exactly the same as for all matter.
 
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Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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