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Related Concept Videos

Newtonian Fluid: Problem Solving01:18

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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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In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
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For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
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Related Experiment Video

Updated: Aug 16, 2025

High-Contrast and Fast Photorheological Switching of a Twist-Bend Nematic Liquid Crystal
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A Finite Element Approximation for Nematic Liquid Crystal Flow with Stretching Effect Based on Nonincremental

Zhaoxia Meng1, Meng Liu2, Hongen Jia2

  • 1Department of Energy and Power Engineering, Shanxi Energy Institute, Taiyuan 030024, China.

Entropy (Basel, Switzerland)
|December 23, 2022
PubMed
Summary

A novel decoupling method is introduced for nematic liquid crystal flow, enhancing stability and accuracy. This approach uses a new auxiliary variable and projection method for reliable simulation of complex fluid dynamics.

Keywords:
decoupled numerical schemefinite elementsnematic liquid crystalnonincremental pressure-correction projection method

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Area of Science:

  • * Computational fluid dynamics
  • * Continuum mechanics
  • * Materials science

Background:

  • * Nematic liquid crystal (NLC) flow simulations are crucial for understanding materials behavior.
  • * Existing methods face challenges in handling the stretching effect and ensuring numerical stability.
  • * Decoupling velocity and pressure is a common strategy in fluid dynamics.

Purpose of the Study:

  • * To propose a new decoupling method for simulating NLC flow with stretching effects.
  • * To ensure unconditional energy stability and verify the energy dissipation law.
  • * To analyze the impact of various parameters on singularity annihilation, stability, and accuracy.

Main Methods:

  • * Finite element discretization framework.
  • * Introduction of an auxiliary variable 'w' for director vector calculation.
  • * Nonincremental pressure-correction projection method for velocity-pressure decoupling.

Main Results:

  • * The proposed method achieves unconditional energy stability.
  • * Numerical examples demonstrate effective singularity annihilation.
  • * Verification of parameter effects on temporal and spatial accuracy.

Conclusions:

  • * The new decoupling method provides a stable and accurate approach for NLC flow simulation.
  • * The method effectively handles stretching effects and singularity annihilation.
  • * It offers a reliable tool for analyzing NLC material behavior and optimizing device performance.