Viscosity

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

4. 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

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

6. 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’

7. 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

8. Relaxation Time

9. 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

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

11. 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？