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Couette Flow

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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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Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, distinguishing it from closed conduit or pipe flow. In open channels such as rivers, canals, and artificial channels, energy analysis provides valuable insights into flow behavior and the relationship between depth, velocity, and slope.Specific Energy and Flow DepthIn open channel flow, the specific energy, E, combines the gravitational potential...

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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...

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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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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...

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Related Experiment Video

Updated: Jun 5, 2026

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

Published on: August 27, 2013

Transverse flow in thin superhydrophobic channels.

François Feuillebois¹, Martin Z Bazant, Olga I Vinogradova

¹LIMSI, UPR 3251, CNRS, B.P. 133, 91403 Orsay, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|January 15, 2011

Summary

Optimizing superhydrophobic surfaces enhances transverse flow in microfluidic channels. Theoretical results guide the design of textured surfaces for improved passive mixing and electrokinetic amplification.

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Last Updated: Jun 5, 2026

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics

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Published on: August 27, 2013

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Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method

Measuring the Interaction Force Between a Droplet and a Super-hydrophobic Substrate by the Optical Lever Method

Published on: June 14, 2019

Area of Science:

Fluid dynamics
Surface science
Microfluidics

Background:

Superhydrophobic surfaces offer reduced friction and unique flow control in micro- and nanofluidic devices.
Optimizing surface texture is crucial for maximizing desired hydrodynamic phenomena.

Purpose of the Study:

To provide theoretical guidance for optimizing transverse hydrodynamic phenomena in superhydrophobic channels.
To maximize transverse flow by optimizing surface texture parameters.

Main Methods:

Analysis of rigorous bounds on permeability for parallel-plate channels with two-component textures.
Optimization of area fractions, slip lengths, geometry, and orientation of surface textures.

Main Results:

Theoretical framework for optimizing transverse flow in superhydrophobic channels.
Demonstration that specific surface textures, like aligned stripes, can achieve very strong transverse flows.
Identification of optimal parameters for maximizing transverse flow.

Conclusions:

Optimized superhydrophobic surfaces can significantly enhance transverse flow.
Potential applications include passive microfluidic mixing and amplification of transverse electrokinetic phenomena.