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When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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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...
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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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Related Experiment Video

Updated: Aug 28, 2025

Fabricating High-viscosity Droplets using Microfluidic Capillary Device with Phase-inversion Co-flow Structure
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Terminal stage of highly viscous flow.

U Buchenau1

  • 1Forschungszentrum Jülich GmbH, Jülich Centre for Neutron Science (JCNS-1) and Institute for Complex Systems (ICS-1), 52425 Jülich, Germany.

Physical Review. E
|September 16, 2022
PubMed
Summary

This study introduces a shear misfit model for viscous flow, predicting a Debye peak in dielectric spectra. The model explains faster thermal expansion equilibration in polymers by accounting for adiabatic density fluctuations.

Area of Science:

  • Rheology and viscoelasticity
  • Glass transition physics
  • Dielectric spectroscopy

Background:

  • Highly viscous flow exhibits complex relaxation behaviors.
  • The terminal stage of viscous flow is theoretically challenging.
  • Experimental evidence suggests a Debye peak in dielectric spectra.

Purpose of the Study:

  • To present a shear misfit model for highly viscous flow.
  • To explain the terminal stage using irreversible Eshelby relaxations.
  • To investigate density fluctuations and compressibility at the glass transition.

Main Methods:

  • Theoretical modeling based on five-dimensional shear space.
  • Analysis of dielectric, shear, and bulk relaxation data.
  • Application to vacuum pump oils and squalane.

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Main Results:

  • The model predicts a Debye peak in dielectric spectra, aligning with experimental data.
  • A relationship between adiabatic and isothermal compressibility jumps at the glass transition is derived.
  • Adiabatic density fluctuations explain faster thermal expansion equilibration in squalane.

Conclusions:

  • The shear misfit model provides a framework for understanding viscous flow and relaxation phenomena.
  • The model successfully explains experimental observations, including dielectric spectra and thermal expansion dynamics.
  • This work offers insights into the interplay between density fluctuations and thermal properties near the glass transition.