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Zuzana Balázsiová
Comenius University in Bratislava, Medical Faculty, Dpt. Medical Physics,
Biophysics, Informatics and Telemedicine
year: 2016
Mechanical properties of
liquids
Viscosity and its measurement
Why viscosity?
• The viscosity of the saliva, sweat, bile, synovial
fluid...
• Blood viscosity is a direct indicator of the ability
of blood to flow through the vessel
• The increased blood viscosity is one of the
parameters that is associated with other risk
factors for cardiovascular diseases (high blood
pressure, cholesterol, diabetes, smoking, ...) *
• Blood viscosity is also influenced by lifestyle
(lack of exercise, dehydration...)
http://bloodflowonline.com/content/blood-viscosity
*Recommended: Whole Blood Viscosity: Links to Cardiovascular Disease http://youtu.be/sWfCKdjxLc0
http://bloodflowonline.com/content/blood-viscosityhttp://youtu.be/sWfCKdjxLc0
Properties of liquid
Real fluids:
• Molecular structure
• Internal liquid friction
• Slightly compressible
• Capillary
phenomenon
Ideal fluids:
• Molecular structure is
neglected
• It is continuum (flow is
smooth, no turbulence)
• Absent internal friction
• incompressibility
Real fluid flow
V > V1 > V2 > ... >Vmin=0 m.s-1
v2
vv1
Vmin=0 m.s-1
V=max
dx
dv Coeff. of internal friction
dx
dv If flowrate varies and = const Newtonian liquids
Dynamic viscosity –
If flowrate varies and const Non Newtonian liquids
Lines of flow dv
dx
dx
dvFlow velocity gradient
Blood viscosity
http://meridianvalleylab.com/wp-content/uploads/2012/03/Picture8.png
http://meridianvalleylab.com/wp-content/uploads/2012/03/Picture8.png
Body fluids (examples)Name Relative viscosity Type of liquid
blood 4,0 - 5,3Non Newtonian fluids
Synovial fluid* Very high
Blood plasma 1,5 – 2,0
Newtonian fluidsSaliva 1,63 - 2,38
urine 1
Distilled water 1 Newtonian fluid
Relative viscosity – ratio of
the viscosity of the solution
to the viscosity of watter
*Viscosity of synovial fluidhttps://netterimages.com/images/vpv/000/000/008/8298-0550x0475.jpg
Methods for viscosity measuring
• Rotatory viscometers -
viscosity is determined
by the resistance which
fluid put to the rotary
movement of
appropriately selected
bodies.
• Measurement of
Newtonian and Non-
Newtonian fluidsObrazok prebraty z: AD Chemia S.r.p
http://www.pragolab.cz/files/download/Seminar_reologie_2015.pdf
• Vibrating viscometers use
for determining viscosity
damping capacity of fluid
as a consequence its
viscosity
• Measurement of
Newtonian and Non-
Newtonian fluids
Obrázok prebratý z: http://www.helago-cz.cz/product/sv-10-
vibracni-viskozimetr/
Methods for viscosity measuring
http://www.pragolab.cz/files/download/Seminar_reologie_2015.pdf
• Falling-ball viscometer
– measurement is
based on the
measuring of the speed
of the ball which
dimension is known
• Measurement of
Newtonian liquidsStoke’s falling-ball viscometer
• Stoke’s law (blood sedimentation)
F = 6 η π r v F – frictional force, η – dynamic viscosity of medium, π = 3,14, r –
radius of the particle, v –particle´s velocity
Obrázok prebratý z:
http://www.google.sk/imgres?imgurl=http://people.tuke.sk/zuzana.gibova/pohyboverovnice/obr2.6.3.gif&imgrefurl
Methods for viscosity measuring
http://www.google.sk/imgres?imgurl=http://people.tuke.sk/zuzana.gibova/pohyboverovnice/obr2.6.3.gif&imgrefurl
• Capilar tube viscometer –
based on measuring the
time t during which a
constant volume of liquid V
flows through a capillary at
constant pressure and
temperature
• Measurement of Newtonian
liqiudsUbbelohde´s viscometer
Prevzaté z: www.srovnanicen.cz/q/Ubbelohdeho/
Methods for viscosity measuring
http://www.pragolab.cz/files/download/Seminar_reologie_2015.pdf
http://www.srovnanicen.cz/q/Ubbelohdeho/
Capillary tube viscometer
• Poiseuille´s law – indicates the volume of
liquid (V), which flows through capillary in
time (t)
tl
prV
8
4
r – capillary radius, Δ p –the hydrostatic pressure difference between the
two ends of the capillary, l – lenght of capillary, t – time, in which flows
liquid through capillary, η - dynamic viscosity, g – gravity acceleration, Δ h
–the difference between the liquid level in a upper reservoir, ρ – density of
liquid
tl
gh
V
r
8
4
What are you going to do
Viscometer constant specified by
manufacturer (overwrite K =...mm2 s-2)
Dynamic viscosity of measurement fluid (calculate)
ρ density of measured fluid (overwrite ρ = ...kg m-3 )
t the time required to empty the upper reservoir (measure)
r – capillary radius, Δ p –the hydrostatic pressure difference between the two ends
of the capillary, l – lenght of capillary, t – time, in which flows liquid through capillary,
η - dynamic viscosity, g – gravity acceleration, Δ h –the difference between the
liquid level in a upper reservoir, ρ – density of liquid
1. Dynamic viskosity
η [ Pa s]Other units: 1P(Poise) = 0,1 Pa.s
Viscosity fluids
tK
2. Kinematic viskosity
ν [ m2 s-1]Other units 1St(Stokes) = 0,0001 m2.s-1
ν = K t
3. Relative viscosity – ratio of the viscosity of the
solution to the viscosity of watter (dimensionless
number)
Ubbelohde´s capillary tube
viscometer
Capillary
Marks for
fulfillment
Marks for measuring
Measuring condition:
V = const.
t = const.
p = const.
Laminar flow in tube
Blood viscosity
Brozmanová, M. Poruchy termoregulácie. https://portal.jfmed.uniba.sk/download.php?fid=559
Sangho, K. et al. A new method for blood viscosity measurement. Journal of Non-Newtonian Fluid Mechanics
Volume 94, Issue 1, 10 November 2000, Pages 47–56
Meridian Valley LabMeridian Valley Lab. The Relationship Between Blood Pressure and Blood Viscosity. http://meridianvalleylab.com/the-
relationship-between-blood-pressure-and-blood-viscosity#
Blood viscosity
Haematocrit(the ratio between the
volume of red cells and
plasma )
Body temperature Blood flow velocity
Blood viscosity Blood pressure
The viscosity of blood is increased in infections e.g.
Measurement blood viscosity uses Hagen-Poiseuille law
https://portal.jfmed.uniba.sk/download.php?fid=559http://www.sciencedirect.com/science/journal/03770257http://www.sciencedirect.com/science/journal/03770257/94/1http://meridianvalleylab.com/the-relationship-between-blood-pressure-and-blood-viscosity
Relationship between blood
pressure and blood viscosity
Meridian Valley LabMeridian Valley Lab. The Relationship Between Blood Pressure and Blood Viscosity.
http://meridianvalleylab.com/the-relationship-between-blood-pressure-and-blood-viscosity#
1. Constant cardiac output
2. Blood
viscosity
increases
(dehydration,
infection...)
3. Total peripheral resistance increases
(thereby reducing blood flow)
4.
Blo
od
pre
ssu
re
incre
ases
(card
iac
outp
ut
must
be
main
tain
ed)
http://meridianvalleylab.com/the-relationship-between-blood-pressure-and-blood-viscosity
Effect of temperature on blood
viscosity
Obrázok upravený. Prevzaté z:
https://www.hindawi.com/journals/bmri/2014/840379.fig.002.jpg
https://www.hindawi.com/journals/bmri/2014/840379.fig.002.jpg
Prevzaté z: Baldeo, a kol. Colorimetric determination of haemoglobin.
http://image.slidesharecdn.com/hemoglobinandhematocritdetermination-130626105718-phpapp02/95/hemoglobin-and-
hematocrit-determination-1-638.jpg?cb=1372244301
Effect of haematocrit on blood
viscosity
http://image.slidesharecdn.com/hemoglobinandhematocritdetermination-130626105718-phpapp02/95/hemoglobin-and-hematocrit-determination-1-638.jpg?cb=1372244301
Effect of gender on blood viscosity
Prevzaté z: Rosenson, R. S, McCormix, A., Uretz, E., F. Distribution of blood viscosity values and biochemical correlates in healthy adults.
Clinical Chemistry 42(8),1996, p.1189-1195. Dostupné na:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.528.2325&rep=rep1&type=pdf
Blood viscosity values were significantly higher in men than in women at
each of the shear rates evaluated. Normalized blood viscosity is blood
viscosity at haematocrit 45%. Plasma viscosity and serum viscosity is
independent on gender.
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.528.2325&rep=rep1&type=pdf
Recommended:
Ubbelohde Glass Capillary Kinematic Viscometer Demonstration
http://www.youtube.com/watch?v=pIoYM5F14xI
http://www.youtube.com/watch?v=pIoYM5F14xI