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Related Concept Videos

Viscosity of Fluid01:19

Viscosity of Fluid

Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
Pressure Variation in a Fluid at Rest01:11

Pressure Variation in a Fluid at Rest

In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
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Stokes' Law01:20

Stokes' Law

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Newtonian Fluid: Problem Solving01:18

Newtonian Fluid: Problem Solving

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Static and Kinetic Frictional Force

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Related Experiment Video

Updated: Jun 25, 2026

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

Flapping motion and force generation in a viscoelastic fluid.

Thibaud Normand1, Eric Lauga

  • 1Département de Mécanique, Ecole Polytechnique, 91128 Palaiseau Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

Reciprocal motion in complex polymeric fluids can generate forces, unlike in simple Newtonian fluids where it

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Related Experiment Videos

Last Updated: Jun 25, 2026

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
10:28

Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

Published on: January 3, 2014

Studying Large Amplitude Oscillatory Shear Response of Soft Materials
06:07

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Published on: April 25, 2019

Area of Science:

  • Fluid Dynamics
  • Biophysics
  • Rheology

Background:

  • Swimming cells and mucociliary clearance involve movement in complex fluids.
  • Purcell's scallop theorem states reciprocal motion in Newtonian fluids cannot generate net force.
  • Exploiting complex fluid properties for microscale force generation remains an area of interest.

Purpose of the Study:

  • To investigate if complex fluids can be exploited for force generation via reciprocal motion.
  • To determine the validity of Purcell's scallop theorem in polymeric fluids.
  • To calculate forces generated by flapping motion in various confined geometries.

Main Methods:

  • Considered a prototypical reciprocal motion: periodic flapping of a tethered semi-infinite plane.
  • Analyzed fluid dynamics in polymeric fluids (Oldroyd-B model and generalizations).
  • Calculated forces for small-amplitude sinusoidal motion in three setups: near a wall, in a wedge, and a scallop-like flapper.

Main Results:

  • Reciprocal flapping motion induces net forces in polymeric fluids, contradicting the scallop theorem.
  • No average flow is generated, only net forces at quadratic order in oscillation amplitude.
  • Viscoelastic properties, specifically normal-stress differences, are key to this force generation.

Conclusions:

  • The scallop theorem is not valid in polymeric fluids.
  • Reciprocal motion of biological appendages like cilia can generate forces in complex fluids (e.g., mucus).
  • Viscoelastic force generation offers a novel propulsion method for microscale systems.