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Related Concept Videos

Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
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...
Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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.
Irrotational Flow01:28

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 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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Related Experiment Video

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Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Coexistence of two singularities in dewetting flows: regularizing the corner tip.

Ivo Peters1, Jacco H Snoeijer, Adrian Daerr

  • 1Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France.

Physical Review Letters
|October 2, 2009
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Summary

Corner singularities in fluid dynamics drive entrainment in wetting and dewetting flows. This study reveals a sharp tip formation before entrainment, with nanometric length deduced from macroscopic measurements.

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Last Updated: Jun 19, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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Published on: February 22, 2018

Area of Science:

  • Fluid dynamics
  • Surface science
  • Rheology

Background:

  • Entrainment in wetting and dewetting flows is often initiated by sharp corner singularities.
  • Viscous stress divergence near the contact line is a key factor, regularized at molecular scales.

Purpose of the Study:

  • Investigate the fine structure of corners formed at the rear of sliding drops.
  • Develop and validate a lubrication model for corner singularity phenomena.

Main Methods:

  • Experimental observation of sliding drops.
  • Development of a lubrication model.
  • Macroscopic measurements to deduce microscopic length scales.

Main Results:

  • Observed a sudden decrease in tip radius, down to 20 micrometers, preceding entrainment.
  • Proposed lubrication model shows good agreement with experimental data.
  • Deduced a nanometric length scale for the tip size from macroscopic measurements.

Conclusions:

  • The tip size in corner singularities is governed by the classical viscous singularity.
  • Macroscopic measurements can effectively probe nanometric length scales in fluid interfaces.