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Related Concept Videos

Boundary Layer Characteristics01:18

Boundary Layer Characteristics

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
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,
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:
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.
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Boundary Conditions for Current Density

Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Moving boundary approximation for curved streamer ionization fronts: solvability analysis.

Fabian Brau1, Benny Davidovitch, Ute Ebert

  • 1Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
PubMed
Summary
This summary is machine-generated.

This study refines the minimal density model for negative streamer ionization fronts by introducing a curvature correction. This advancement moves beyond ideal conductivity approximations, offering a more accurate understanding of streamer dynamics.

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Area of Science:

  • Plasma Physics
  • Fluid Dynamics
  • Computational Electromagnetics

Background:

  • Investigating the minimal density model for negative streamer ionization fronts.
  • Building upon earlier moving boundary approximations and Laplacian growth models.

Purpose of the Study:

  • Derive a curvature correction to the moving boundary approximation, analogous to surface tension.
  • Explore the implications of this correction for streamer dynamics and modeling.

Main Methods:

  • Employing solvability analysis with unique features, including unconventional zero modes of the adjoint operator.
  • Performing analytical calculations with inner-outer matching on a line.
  • Investigating the relationship between fields, curvature, and conductivity.

Main Results:

  • A curvature correction resembling surface tension was derived for the minimal density model.
  • The analysis revealed a necessary shift from ideal conductivity to a charge neutrality approximation.
  • The electric potential within the streamer interior was shown to satisfy a Laplace equation, leading to a Muskat-type problem.

Conclusions:

  • The derived curvature correction enhances the accuracy of streamer front modeling.
  • Replacing ideal conductivity with charge neutrality provides a more realistic description of streamer interiors.
  • The study introduces a new framework for analyzing streamer ionization fronts with improved physical fidelity.