Viscosity

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Viscosity

• 2005/4/24
• Dept. Physics, Tunghai Univ.
• Biophysics?C. T. Shih

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Elasticity Hookean Solid

• An ideal elastic solid
• An applied shear stress (??) produces a shear
  strain in response
• The shear strain is proportional to shear stress
• The constant of proportionality is the shear
  modulus

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(No Transcript)
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Viscosity Newtonian Liquid

• An ideal viscous liquid
• An applied shear stress produces a flow with a
  constant shear strain rate in response
• The strain rate is proportional to the shear
  stress, and the constant of proportionality is
  the viscosity
• Inverse of the proportional constant ? is the
  dynamical viscosity and r is the kinematic
  viscosity

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Some Value of Viscosity
Liquids (at 20 C)
viscosity (Pas)
ethyl alcohol 0.248 10-3
acetone 0.326 10-3
methanol 0.59 10-3
benzene 0.64 10-3
water 1.025 10-3
nitrobenzol 2.0 10-3
mercury 17.0 10-3
sulfuric acid 30 10-3
olive oil 81 10-3
castor oil 0.985
glycerol 1.485
pitch 107
Gases (at 0 C)
viscosity (Pas)
hydrogen 8.4 10-6
air 17.4 10-6
xenon 21.2 10-6
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Newtonian Liquid (conti.)

• Imagine some liquid sandwiched between parallel
  plates of area A separated by a distance y
• The plates are moved with a relative velocity v
• The force resisting the relative motion of the
  plates FA?v/y
• ? is the viscosity
• v/y is just the time derivative of shear strain,
  or g, so it can be written as s?g

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Real Material Viscoelastic

• Hookean solid and Newtonian liquid are two
  limiting cases of elasticity and viscosity
• The behavior of real materials is in between
  viscoelastic
• There is a particular timescale to determine
  which kind of response elastic or viscous
• The material responds at first in an elastic way,
  after a certain time t it begins to flow like a
  liquid

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Relaxation Time
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Viscoelasticity

• When the Hookean regime is gradually replaced by
  the Newtonian regime
• The relaxation time constant can be regard as
  determining the time interval over which the
  elastic regime is replaced by the viscos regime

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shear-thinning fluid faster-moving, less
viscous Ex clay, milk, blood
shear-thickening fluid faster-moving, more
viscous Ex sugar in water, rice starch
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Problem

• ?? 20???????1.010-3Ns/m2,??????,????????????????