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Related Concept Videos

Navier–Stokes Equations01:28

Navier–Stokes Equations

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...
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

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.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Euler's Equations of Motion01:28

Euler's Equations of Motion

In fluid mechanics, shear stresses arise from viscosity, which represents a fluid's internal resistance to deformation. For low-viscosity fluids, like water, these stresses are minimal, simplifying flow analysis by allowing the fluid to be treated as inviscid, or frictionless. In an inviscid fluid, shear stresses are absent, leaving only normal stresses, which act perpendicularly to fluid elements. Notably, pressure — defined as the negative of the normal stress — remains uniform across...
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Introduction to Types of Flows01:23

Introduction to Types of Flows

Fluid flows are categorized by dimensionality and behavior, with one-dimensional flow being the simplest form, where properties like velocity and pressure change only along a single axis. Water moving through straight pipes exemplifies this flow type, as variations in other directions are minimal. One-dimensional analysis helps simplify understanding such flows, focusing solely on changes along the pipe's length.
Two-dimensional flow involves changes in both length and height, as seen in air...

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Related Experiment Video

Updated: Jul 6, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Shear-induced particle migration in one-, two-, and three-dimensional flows.

C Gao1, J F Gilchrist

  • 1Department of Chemical Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed
Summary

This study examines how particle migration and flow dynamics affect suspension behavior in open channels. Herringbone channels and chaotic flows show unique concentration profiles and limited mixing at higher particle concentrations.

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Area of Science:

  • Fluid dynamics
  • Multiphase flow
  • Particle migration

Background:

  • Shear-induced migration is a key phenomenon in multiphase flows.
  • Understanding particle behavior in open channel flows is crucial for various applications.

Purpose of the Study:

  • To investigate the interplay between advection and shear-induced migration in steady open flows.
  • To analyze particle focusing and concentration profiles in different channel geometries.
  • To examine transient phenomena during migration onset and mixing in chaotic flows.

Main Methods:

  • Simulations of suspension flow in straight and herringbone channels.
  • Analysis of particle concentration profiles and migration dynamics.
  • Investigation of chaotic flow mixing at varying bulk volume fractions.

Main Results:

  • Herringbone channels create concentration profiles distinct from straight channels.
  • Buckling instability can cause transients during migration onset.
  • Mixing in chaotic flows is less effective at higher bulk volume fractions.

Conclusions:

  • Channel geometry significantly influences particle segregation.
  • Flow instabilities can lead to transient particle redistribution.
  • Static mixers have limited efficacy in mitigating shear-induced migration in chaotic flows at higher concentrations.