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Related Concept Videos

Velocity Potential01:20

Velocity Potential

In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:
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...
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:
Stream Function01:20

Stream Function

In two-dimensional incompressible fluid flow, the continuity equation is essential for ensuring mass conservation, meaning that any change in fluid entering or exiting a region is balanced by a corresponding change elsewhere. For incompressible flow, where density remains constant, this requirement simplifies to the condition that the divergence of the velocity field must be zero. Mathematically, this is expressed as,
Capillarity in Fluid01:19

Capillarity in Fluid

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.
Surface tension is crucial to capillarity. It results from cohesive forces between liquid molecules at the liquid-air boundary, forming a skin that resists external forces. When the capillary tube...
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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Protocol for Biofilm Streamer Formation in a Microfluidic Device with Micro-pillars
07:19

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Published on: August 20, 2014

Streaming potential generated by two-phase flow in a polygonal capillary.

J D Sherwood1, Etienne Lac

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK. jds60@cam.ac.uk

Journal of Colloid and Interface Science
|June 18, 2010
PubMed
Summary
This summary is machine-generated.

Streaming potential in polygonal capillaries with two-phase flow is theoretically predicted. Ions are convected by fluid flow, generating streaming potentials that increase linearly with pressure gradients.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Electrochemistry

Background:

  • Two-phase flow in confined geometries can generate electrical potentials.
  • Understanding streaming potential is crucial for various applications, including microfluidics and geological processes.

Purpose of the Study:

  • To theoretically predict the streaming potential generated by two-phase flow in a polygonal capillary.
  • To investigate the role of fluid flow and ion convection in streaming potential generation.

Main Methods:

  • Theoretical modeling of fluid flow and ion transport within a polygonal capillary.
  • Analysis of charge cloud convection and current return pathways.

Main Results:

  • Streaming potentials are generated due to ion convection by the flowing fluid.
  • The presence of a thin fluid film between the oil drop and capillary walls facilitates ion movement.
  • Current returns via conduction along the menisci in the capillary corners.
  • Predicted streaming potentials grow linearly with the applied pressure gradient.

Conclusions:

  • The study provides a theoretical framework for understanding streaming potential in complex two-phase flow systems.
  • The findings highlight the importance of capillary geometry and fluid properties in electrokinetic phenomena.