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Related Concept Videos

Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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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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:
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.
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...
Poiseuille's Law and Reynolds Number01:10

Poiseuille's Law and Reynolds Number

Any fluid in a horizontal tube can flow due to pressure differences—fluid flows from high to low pressure. The flow rate (Q) is the ratio of pressure difference and resistance through a horizontal tube. The greater the pressure difference, the higher the flow rate. The flow resistance is expressed as:
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...

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The Diffusion of Passive Tracers in Laminar Shear Flow
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Published on: May 1, 2018

Unbiased diffusion in tubes with corrugated walls.

Leonardo Dagdug1, Marco-Vinicio Vazquez, Alexander M Berezhkovskii

  • 1Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, 09340 Mexico DF, Mexico.

The Journal of Chemical Physics
|July 24, 2010
PubMed
Summary

We studied the unbiased motion of Brownian particles in corrugated tubes. A new formula predicts the effective diffusion coefficient, validated by simulations, defining its applicability limits.

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Area of Science:

  • Physics
  • Physical Chemistry
  • Statistical Mechanics

Background:

  • Brownian motion describes random particle movement.
  • Confined particle diffusion is crucial in microfluidics and biophysics.
  • Corrugated geometries introduce complex transport dynamics.

Purpose of the Study:

  • To analyze unbiased Brownian particle motion in a tube with corrugated walls.
  • To derive an effective one-dimensional model for particle diffusion.
  • To establish a formula for the effective diffusion coefficient and its validity.

Main Methods:

  • Utilized an effective one-dimensional description via the generalized Fick-Jacobs equation.
  • Derived a formula for the effective diffusion coefficient based on geometric parameters.
  • Employed Brownian dynamics simulations for validation.

Main Results:

  • A formula for the effective diffusion coefficient was derived.
  • The study determined the applicable range for the 1D model.
  • Simulation results confirmed the derived formula within its domain.

Conclusions:

  • The generalized Fick-Jacobs equation provides a valid 1D model for particle diffusion in corrugated tubes.
  • The derived formula accurately predicts the effective diffusion coefficient.
  • The study clarifies the limitations of the 1D approach for confined Brownian motion.