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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.
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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...
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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...
Turbulent Flow01:24

Turbulent Flow

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 spots,...
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Fluid dynamics is the study of fluids in motion. Velocity vectors are often used to illustrate fluid motion in applications like meteorology. For example, wind—the fluid motion of air in the atmosphere—can be represented by vectors indicating the speed and direction of the wind at any given point on a map. Another method for representing fluid motion is a streamline. A streamline represents the path of a small volume of fluid as it flows. When the flow pattern changes with time, the streamlines...
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Related Experiment Video

Updated: Jun 14, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Chemically driven hydrodynamic instabilities.

C Almarcha1, P M J Trevelyan, P Grosfils

  • 1Nonlinear Physical Chemistry Unit, CP 231, Faculté des Sciences, Université Libre de Bruxelles (ULB), Campus Plaine, 1050 Brussels, Belgium.

Physical Review Letters
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Chemical reactions can destabilize fluid systems, creating complex patterns. This study shows how simple reactions influence buoyancy-driven instabilities in stratified solutions, both numerically and experimentally.

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Area of Science:

  • Fluid dynamics
  • Chemical kinetics
  • Pattern formation

Background:

  • Density changes in a gravity field can trigger buoyancy-driven instabilities.
  • Reaction-diffusion-convection models describe systems where chemical reactions, diffusion, and fluid flow interact.
  • Understanding pattern formation in reactive systems is crucial for various scientific fields.

Purpose of the Study:

  • To analyze how chemical reactions can destabilize stable density stratifications.
  • To investigate the effect of reactions on pattern symmetry in unstable systems.
  • To demonstrate these phenomena using a specific acid-base neutralization reaction.

Main Methods:

  • Development of a general reaction-diffusion-convection model.
  • Numerical simulations to observe instability and pattern evolution.
  • Experimental validation using a specific chemical reaction.

Main Results:

  • Chemical reactions can induce or affect buoyancy-driven instabilities.
  • Reactions can destabilize otherwise stable density stratifications.
  • Even in initially unstable systems, reactions break pattern symmetry.

Conclusions:

  • Chemical reactions play a significant role in fluid instabilities and pattern formation.
  • The interplay between reaction kinetics and fluid dynamics can lead to complex behaviors.
  • Both numerical and experimental approaches confirm the destabilizing and symmetry-breaking effects of reactions.