KATEDRA MATERIÁLOVÉHO INŽENÝRSTVÍ A CHEMIE
123MED – viscosity
Viscosity
• Property of fluid characterized by “internal friction”.
• Viscosity is depended on internal forces between atoms or
molecules. Fluids with higher internal forces possess
higher viscosities.
• Indicates the relationship between the shear stress and
change of velocity in dependence on the distance between
the adjacent layers of flowing liquid.
• Ideal liquid has no viscosity
and its dynamic viscosity = 0.
η = 0 Pa s
n = 0 m2 s-1
Viscosity explanation
Simple imagination:
• We have two plates with large area S. The first is fixed and
the second one is assumed moving due to application of
the force F.
• The space between these two place if filled by fluid.
• The fluid is moving with velocity u in close proximity to
moving plate. With increasing distance from this plate the
velocity decreases up to 0.
Expression of dynamic viscosity
For keeping of upper plate in equilibrium movement to lower fixed plate we have to apply force F that is directly proportional to area of pulled plate (Newtonian fluids).
velocity gradient (shear rate)
F - applied force, S – area of plate, v – velocity, y – distance from the plate.
For calculation the problem can be rewritten to the form
Dynamic viscosity – η (éta) [N.s/m2] or [Pa.s]
dy
dv
S
F xxy
dy
dv
d
v x
dy
dvSF x
Viscosity
Newtonian fluids – constant viscosity (water, oil, glycerol,…)
Bingham plastic – material that behaves as a solid at low
stresses but flows as a vicious fluid at high stresses.
Shear thickening – viscosity increases with the shear rate,
Shear thinning – viscosity decreases with the shear rate.
Dynamic viscosity vs. kinematic viscosity
Dynamic viscosity – η (eta) [N.s/m2] or [Pa.s]
Kinematic viscosity – ν [m2 s-1]
dy
dvxxy
n
Liquid .10-3 [Pa.s]
Benzin 0,53
Ethanol 1,2
Glycerol 1480
Blood (37°C) 3,0 – 3,6
Water (25°C) 0,8937
Dependence od dynamic viscosity on temperature – an example for water
Viscosity increases with increasing pressure.
Viscosity decreases with increasing temperature.
Anomaly of water: maximum density at 3,98°C. Reference: Čmelík, M., Machonský, L., Šíma, Z. Fyzikální tabulky. Liberec: TU Liberec,
2001.
Dependence of dynamic viscosity on concentration of liquids – water salt solution
Viscosity increases with increasing concentration of salt.
Density of solution increases with increasing concentration of salt.
Measurement of viscosity
- Hoppler's viscometer – method of falling ball
measurement of ball's fall in tube (slope 10°) full fill by
liquid. Ball has defined density and its movement has to be
slow enough to assure there is no existence of vortex flow
(minimum falling time).
Viscosity calculation
K – constant of ball from device producer,
t – falling time,. ρ1 – ball density, ρ2 – liquid density.
Kt 21 -
With slope of 10°:
Dynamic viscosity calculation
K – constant of ball from device producer, t – falling time,. ρ1 – ball density,
ρ2 – liquid density, r – sphere radius.
grFA 23
3
4
rvFStokes 6
grgVmgG 1
3
13
4
cosmgG