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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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,...
Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

Newtonian fluids exhibit a constant viscosity, meaning their shear stress and shear strain rate are directly proportional. This property ensures a predictable and stable response to applied forces, maintaining a linear relationship between force and flow. Examples include water, air, and light oils, consistently demonstrating this proportional behavior regardless of external conditions.
A velocity gradient forms within the fluid when a Newtonian fluid is placed between two parallel plates, with...
Relation Between the Distributed Load and Shear01:23

Relation Between the Distributed Load and Shear

Understanding the relationship between the distributed load and shear force in structural analysis is crucial for analyzing beams subjected to various loading conditions. Consider the case of a beam experiencing a distributed load, two concentrated loads, and a couple moment.
Shearing Stress01:18

Shearing Stress

Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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...

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Related Experiment Video

Updated: Jul 6, 2026

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
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Wall shear rate distribution for flow in random sphere packings.

Patrick B Warren1, Frantisek Stepanek

  • 1Unilever R&D Port Sunlight, Bebington, Wirral, CH63 3JW, United Kingdom.

Physical Review Letters
|March 21, 2008
PubMed
Summary

This study analyzes wall shear rate distribution in Stokes flow through random sphere arrangements. For dense packings, the distribution is exponential, while dilute packings reveal flow patterns around isolated spheres.

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Area of Science:

  • Fluid dynamics
  • Rheology
  • Computational physics

Background:

  • Understanding fluid flow through porous media is crucial in various scientific and engineering fields.
  • Stokes flow describes low-Reynolds-number fluid motion, relevant for microfluidics and porous media.
  • Wall shear rate is a key parameter in characterizing fluid behavior at interfaces.

Purpose of the Study:

  • To investigate the wall shear rate distribution in pressure-driven Stokes flow through random sphere arrangements.
  • To analyze how packing fraction influences the shear rate distribution.
  • To develop a simple expression for the mean wall shear rate.

Main Methods:

  • Simulations of pressure-driven Stokes flow through random sphere packings.
  • Analysis of wall shear rate distribution P(gamma) across various packing fractions (0.1 <= phi <= 0.64).
  • Derivation of an approximate analytical expression for the mean wall shear rate.

Main Results:

  • For dense packings (high phi), P(gamma) is monotonic and approximately exponential.
  • At low packing fractions (phi --> 0.1), P(gamma) exhibits additional structure linked to isolated sphere flow.
  • An exact result for isolated spheres and a simple mean wall shear rate expression were obtained.

Conclusions:

  • The wall shear rate distribution is highly dependent on the packing fraction of spheres.
  • The study provides insights into fluid behavior in porous media, bridging dense and dilute regimes.
  • A simplified model for mean wall shear rate is proposed based on force-balance principles.