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Related Concept Videos

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,...
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.
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 Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
During this process, the momentum of the fluid within the control volume remains constant over the time interval dt. By applying the...
Plane Potential Flows01:23

Plane Potential Flows

Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform Flow
Uniform flow...

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Related Experiment Video

Updated: May 26, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Diffuse-interface approach to rotating Hele-Shaw flows.

Ching-Yao Chen1, Yu-Sheng Huang, José A Miranda

  • 1Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China. chingyao@mail.nctu.edu.tw

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
PubMed
Summary
This summary is machine-generated.

In a rotating Hele-Shaw cell, fluid interfaces become unstable, forming complex patterns. Viscosity contrast and Coriolis forces drive interface singularities and topological changes like droplet pinch-off.

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Uncoupling Coriolis Force and Rotating Buoyancy Effects on Full-Field Heat Transfer Properties of a Rotating Channel

Published on: October 5, 2018

Area of Science:

  • Fluid dynamics
  • Complex systems
  • Nonlinear physics

Background:

  • Two-phase flow in rotating Hele-Shaw cells exhibits centrifugal instability.
  • Interface deformation depends on viscosity contrast, leading to complex patterns.
  • Interfacial singularities and topological changes can emerge from these deformations.

Purpose of the Study:

  • To numerically simulate pattern formation in rotating Hele-Shaw cells.
  • To investigate the influence of viscosity contrast and Coriolis forces on interface dynamics.
  • To analyze the development of interface singularities and topological changes.

Main Methods:

  • Utilizing a diffuse-interface model for two-phase displacement.
  • Employing a Boussinesq Hele-Shaw-Cahn-Hilliard approach.
  • Incorporating inertial effects from the Coriolis force and considering all viscosity contrasts.

Main Results:

  • The simulations capture a variety of pattern-forming behaviors.
  • Distinct complex patterns arise at the fluid-fluid boundary based on viscosity contrast.
  • The study illustrates and discusses the role of viscosity contrast and Coriolis forces in interface singularity development.

Conclusions:

  • The Boussinesq Hele-Shaw-Cahn-Hilliard model effectively simulates complex fluid interface dynamics.
  • Viscosity contrast and Coriolis forces are key factors in generating interfacial singularities.
  • Understanding these phenomena is crucial for predicting fluid behavior in rotating systems.