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Boundary Layer Characteristics01:18

Boundary Layer Characteristics

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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...
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Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

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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...
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Solid–Solid Solutions01:24

Solid–Solid Solutions

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The temperature-composition phase diagram of two solids, A and B, which are immiscible in the solid phase but form miscible liquids, shows that when the temperature is low, these two exist as separate, pure solids (A and B). As the temperature increases, they transition into a single-phase liquid solution where A and B coexist. Moving from point a1 to a2 in the phase diagram, the composition changes such that solid B begins to separate from the solution, enriching the remaining liquid with A.
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Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

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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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Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

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An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...
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Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model01:09

Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model

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Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the...
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Related Experiment Video

Updated: May 2, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Stability of a directional solidification front in subdiffusive media.

Mohammad Abu Hamed1, Alexander A Nepomnyashchy2

  • 1Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel and Department of Mathematics, The college of Sakhnin-Academic College for Teacher Education, Sakhnin 30810, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 4, 2014
PubMed
Summary

Crystal growth instability in alloys is affected by anomalous diffusion, deviating from normal Brownian motion. This study generalizes the Mullins-Sekerka criterion for directional solidification under anomalous diffusion conditions.

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Area of Science:

  • Materials Science
  • Solidification Physics
  • Non-equilibrium Thermodynamics

Background:

  • Crystal growth efficiency is often limited by morphological instability.
  • This instability arises from a feedback loop between interface deformation and solute diffusion.
  • Normal diffusion models assume Brownian motion, but anomalous diffusion occurs in complex media.

Purpose of the Study:

  • To investigate the impact of anomalous diffusion on directional solidification fronts.
  • To generalize the Mullins-Sekerka stability criterion for anomalous diffusion scenarios.
  • To derive a nonlinear evolution equation describing interface cellular structures.

Main Methods:

  • Linear stability analysis of a moving planar solidification front.
  • Derivation of a generalized stability criterion.
  • Asymptotic analysis to obtain a nonlinear evolution equation.

Main Results:

  • A generalized Mullins-Sekerka stability criterion for anomalous diffusion was obtained.
  • A Sivashinsky-type nonlinear evolution equation governing interface cellular structures was derived.
  • The study demonstrates how anomalous diffusion modifies solidification front stability.

Conclusions:

  • Anomalous diffusion significantly impacts crystal growth stability.
  • The derived generalized criterion and evolution equation provide new tools for understanding alloy solidification.
  • This work extends classical solidification theory to include memory effects from anomalous diffusion.