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 The constant of proportionality is the shear modulus

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  is the kinematic viscosity

GasesGases (at 0 °C):C viscosity (Pa·s) hydrogen8.4 × air17.4 × xenon21.2 × LiquidsLiquids (at 20 °C):C viscosity (Pa·s) ethyl alcohol0.248 × acetone0.326 × methanol0.59 × benzene0.64 × water1.025 × nitrobenzol2.0 × mercury17.0 × sulfuric acid30 × olive oil81 × castor oil0.985 glycerol1.485 pitch10 7 Some Value of Viscosity

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  ’, so it can be written as σ=η  ’

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  it begins to flow like a liquid

Relaxation Time

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

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

Problem 水在 20 ℃時黏滯係數為 1.0×10 -3 Ns/m 2 ， 當溫度升高時，黏滯係數會變大還是變 小？為什麼？