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

Non-newtonian fluids

Change of velocity dv on dependence on distance dy (d) is

not linear.

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

Measurement of viscosity

YOUR TASK

Measure density of water and glycerol (pycnometer).

Measure falling times with Hoppler's viscometer and calculate dynamic viscosity of water and glycerol.

Calculate kinematic viscosity of water and glycerol.

Compare results with tabular values.