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Related Concept Videos

Steady, Laminar Flow Between Parallel Plates01:17

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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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Couette Flow01:22

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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...
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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 purely axial,...
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Capillarity describes the movement of liquid in small spaces without external forces acting on it. The capillarity is driven by surface tension and adhesive interactions between the liquid and surrounding solid surfaces. This effect is often seen in narrow tubes, porous materials, and fine particles.
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Related Experiment Video

Updated: Apr 12, 2026

Chemotactic Response of Marine Micro-Organisms to Micro-Scale Nutrient Layers
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Wavelength Selection in Gyrotactic Bioconvection.

S Ghorai1, R Singh, N A Hill

  • 1Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India, sghorai@iitk.ac.in.

Bulletin of Mathematical Biology
|May 13, 2015
PubMed
Summary

This study models micro-organism bioconvection patterns, finding numerical simulations align with experiments when cell diffusion is low. It confirms the gyrotaxis model

Area of Science:

  • Fluid dynamics
  • Microbiology
  • Pattern formation

Background:

  • Bioconvection involves pattern formation by motile microorganisms.
  • Gyrotaxis describes orientation influenced by gravity and viscosity in bottom-heavy cells.

Purpose of the Study:

  • To numerically investigate pattern formation in micro-organism bioconvection.
  • To analyze the influence of key parameters on wavelength selection in bioconvection patterns.
  • To validate a mathematical model against experimental observations.

Main Methods:

  • Solving coupled Navier-Stokes and micro-organism conservation equations numerically.
  • Utilizing a large cross-section chamber with periodic horizontal boundary conditions.
  • Investigating parameter influence on pattern wavelength.

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Last Updated: Apr 12, 2026

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Main Results:

  • Computed wavelengths agree with experimental observations for small cell diffusion.
  • Refutes claims of mathematical model inaccuracy at long times.
  • Provides first 3D simulation evidence of 'bottom-standing' plumes.

Conclusions:

  • The gyrotaxis model accurately predicts bioconvection patterns under specific conditions.
  • Numerical simulations support the validity of the mathematical model for bioconvection.
  • 3D simulations reveal novel plume structures in bioconvection.