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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Irrotational Flow01:28

Irrotational Flow

Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
Shearing Stress01:18

Shearing Stress

Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
Rapidly Varying Flow01:24

Rapidly Varying Flow

Rapidly varying flow (RVF) in open channels is characterized by abrupt changes in flow depth over a short distance, with the rate of depth change relative to distance often approaching unity. These flows are inherently complex due to their transient and multi-dimensional nature, making exact analysis difficult. However, approximate solutions using simplified models provide valuable insights into their behavior.Key Features of Rapidly Varying FlowRVF is commonly observed in scenarios involving...
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...

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Related Experiment Video

Updated: May 24, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Transient-time correlation function applied to mixed shear and elongational flows.

Remco Hartkamp1, Stefano Bernardi, B D Todd

  • 1Multi Scale Mechanics, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. r.m.hartkamp@utwente.nl

The Journal of Chemical Physics
|February 25, 2012
PubMed
Summary
This summary is machine-generated.

The transient-time correlation function (TTCF) method efficiently calculates fluid nonlinear responses. This method is more effective than non-equilibrium molecular dynamics (NEMD) for small deformation rates, enabling rheology studies.

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Area of Science:

  • Fluid dynamics
  • Computational physics
  • Rheology

Background:

  • Non-equilibrium molecular dynamics (NEMD) simulations are crucial for understanding fluid behavior under stress.
  • Calculating nonlinear responses in fluids, especially at low deformation rates, presents computational challenges.

Purpose of the Study:

  • To evaluate the transient-time correlation function (TTCF) method for calculating the nonlinear response of atomic fluids.
  • To compare the efficiency of TTCF with direct NEMD simulations for planar mixed flow.
  • To explore the application of TTCF in studying fluid rheology at small deformation rates.

Main Methods:

  • Utilized the transient-time correlation function (TTCF) method.
  • Performed direct averaging of non-equilibrium molecular dynamics (NEMD) simulations.
  • Calculated the pressure tensor response and generalized viscosity for planar mixed flow.

Main Results:

  • TTCF demonstrated superior efficiency compared to direct NEMD averages for small rates of deformation.
  • The study analyzed the impact of noise in simulations with low deformation rates.
  • Generalized viscosity for planar mixed flow was successfully computed using TTCF.

Conclusions:

  • TTCF is a more efficient method than NEMD for simulating fluids at small deformation rates.
  • TTCF can be applied to systems with deformation rates significantly lower than those typically used in NEMD.
  • TTCF facilitates direct comparison between NEMD simulations and experimental data for molecular systems, aiding in industrial rheology studies.