Viscosity 2005424 Dept Physics Tunghai Univ BiophysicsC T

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

Elasticity: Hookean Solid n n 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 n n 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

Some Value of Viscosity Liquids (at 20 °C): viscosity (Pa·s) ethyl alcohol 0. 248 × 10 -3 Gases (at 0 °C): acetone 0. 326 × 10 -3 methanol 0. 59 × 10 -3 benzene 0. 64 × 10 -3 hydrogen 8. 4 × 10 -6 water 1. 025 × 10 -3 air 17. 4 × 10 -6 nitrobenzol 2. 0 × 10 -3 xenon 21. 2 × 10 -6 mercury 17. 0 × 10 -3 sulfuric acid 30 × 10 -3 olive oil 81 × 10 -3 castor oil 0. 985 glycerol 1. 485 pitch 107 viscosity (Pa·s)

Newtonian Liquid (conti. ) n n n 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’

Real Material: Viscoelastic n n 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

Relaxation Time

Viscoelasticity n n 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