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