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Viscosity

Viscosity. 2005/4/24 Dept. Physics, Tunghai Univ. Biophysics‧C. T. Shih. Elasticity: Hookean Solid. An ideal elastic solid An applied shear stress (剪力) produces a shear strain in response The shear strain is proportional to shear stress

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Viscosity

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  1. Viscosity 2005/4/24 Dept. Physics, Tunghai Univ. Biophysics‧C. T. Shih

  2. Elasticity: Hookean Solid • An ideal elastic solid • An applied shear stress (剪力) produces a shear strain in response • The shear strain is proportional to shear stress • The constant of proportionality is the shear modulus

  3. 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 η is the dynamical viscosity and r is the kinematic viscosity

  4. Some Value of Viscosity Liquids (at 20 °C): Gases (at 0 °C):

  5. 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 F=Aηv/y • η is the viscosity • v/y is just the time derivative of shear strain, or g’, so it can be written as σ=ηg’

  6. 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

  7. Relaxation Time

  8. 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

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

  10. Problem • 水在 20℃時黏滯係數為1.0×10-3Ns/m2,當溫度升高時,黏滯係數會變大還是變小?為什麼?

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