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Related Concept Videos

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.
When measuring pressure at two different levels within the fluid, the difference in pressure...
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...
Deriving the Speed of Sound in a Liquid01:09

Deriving the Speed of Sound in a Liquid

As with waves on a string, the speed of sound or a mechanical wave in a fluid depends on the fluid's elastic modulus and inertia. The two relevant physical quantities are the bulk modulus and the density of the material. Indeed, it turns out that the relationship between speed and the bulk modulus and density in fluids is the same as that between the speed and the Young's modulus and density in solids.
The speed of sound in fluids can be derived by considering a mechanical wave propagating...
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.
Accelerating Fluids01:17

Accelerating Fluids

When a fluid is in constant acceleration, the pressure and buoyant force equations are modified. Suppose a beaker is placed in an elevator accelerating upward with a constant acceleration, a. In the beaker, assume there is a thin cylinder of height h with an infinitesimal cross-sectional area, ΔS.
The motion of the liquid within this infinitesimal cylinder is considered to obtain the pressure difference. Three vertical forces act on this liquid:
Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
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Protocol for Relative Hydrodynamic Assessment of Tri-leaflet Polymer Valves
11:12

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Published on: October 17, 2013

Pumping by flapping in a viscoelastic fluid.

On Shun Pak1, Thibaud Normand, Eric Lauga

  • 1Department of Mechanical and Aerospace Engineering, University of California-San Diego, 9500 Gilman Drive, La Jolla, California 92093-0411, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Viscoelastic fluids can overcome the scallop theorem

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Area of Science:

  • Fluid dynamics
  • Rheology
  • Biophysics

Background:

  • Purcell's scallop theorem states that time-reversible motion in Newtonian fluids yields no net flow.
  • Nonlinear rheological properties of viscoelastic fluids may offer a way to circumvent this limitation.
  • Understanding fluid transport in micro-devices is crucial for various applications.

Purpose of the Study:

  • To investigate if viscoelasticity can enable net fluid flow via reciprocal motion, breaking the scallop theorem constraints.
  • To explore the potential of biologically inspired geometries for fluid pumping in complex fluids.
  • To analytically characterize and optimize the fluid flow and pumping performance.

Main Methods:

  • Asymptotic analysis of a flapper model in a polymeric (Oldroyd-B) fluid.
  • Calculation of time-average net fluid flow based on flapping amplitude.
  • Analytical characterization and optimization of induced flow fields.

Main Results:

  • Net fluid flow is achieved at fourth order in flapping amplitude, defying the scallop theorem.
  • Reciprocal flapping motion can induce significant fluid transport in viscoelastic fluids without inertia.
  • Flow field and pumping efficiency were successfully characterized and optimized.

Conclusions:

  • Nonlinear viscoelasticity allows for net fluid transport using reciprocal motion, challenging the scallop theorem.
  • Biologically inspired flapping geometries are effective for pumping complex fluids in micro-devices.
  • The findings offer valuable insights for designing novel micropumps for polymeric and complex fluids.