Dynamic viscosity

A presentation on viscosity(Dynamic Viscosity)

1. Department of Mechanical Engineering
Don BoscoCollege of Engineering and
Technology, ADBU
By DipjyotiDeka
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2. INTRODUCTION
The two aspects of fluid mechanics:-
1.Thenatureofafluidismuchdifferenttothatofsolid.
2.Influids,weusuallydealwithcontinuousstreamsoffluidwithoutabeginningorend.
Wenormallyrecognizethreestatesofmatter:solid,liquidandgas.However,liquidandgas
arebothfluids;incontrasttosolidstheylacktheabilitytodeformation.Becauseafluid
cannotresistthedeformationforce,itmovesup,itflowsundertheactionoftheforce.
Itsshapewillchangecontinuouslyaslingasforceisapplied.
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3. Thedeformationiscausedbyshearingforceswhichacttangentiallytoasurface.Aswe
canseetheforceFactingtangentiallyonarectangularelementABCD.Thisisa
shearingforceandproducestherhombuselementA’B'
A
D
B
B’
C
A’
Shearing force F, acting on the fluid element.
Hence, we can say that A fluid is a substance which deforms continuously when subjected
to shearing forces.
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4. VISCOSITY
Apropertyoffluidtoresisttherateofdeformation-aquantitivemeasureofafluid’s
resistancetoflow(waterv/ssyrup).Ittakesplacewhenafluidisacteduponbyashear
stress.
Itisanimportantfluidpropertywhenanalyzingliquidbehaviorandfluidmotionnear
solidboundaries.Theshearresistanceinafluidiscausedbyintermolecularfriction
exertedwhenlayersoffluidattempttoslidebyoneanother.
Therearetworelatedmeasuresoffluidviscosity:
•DynamicorAbsolute
•Kinematic
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5. Why does viscosity exist in fluid flow
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Molecular collisions –the molecules of the fluid bump into each other,
slowing down their motion
Momentum transfer from higher momentum to lower -momentum is mass
times velocity, mu. During a collision, momentum will be transferred.
Measured by shear stressτ,, which is the tangential force divided by the
area

6. Fluidwithlowviscosity Fluidwithhighviscosity
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7. Newton’s law of Viscosity
Viscosityisthephysicalpropertythatcharacterizestheflowresistanceofsimplefluids.
Newton’slawofviscositydefinestherelationshipbetweentheshearstressandshearrateof
afluidsubjectedtoamechanicalstress.Theratioofshearstresstoshearrateisconstant,
foragiventemperatureandpressure,andisdefinedastheviscosityorcoefficientof
viscosity.Newtonian’sfluidsobeyNewton’slawofviscosity.
Thus,Viscosityisindependentoftheshearrate.Similarly,Non-Newtonianfluidsdonot
followNewton’slawandthus,theirviscosity(ratioofshearstresstoshearrate)isnot
constantandisdependentontheshearrate.
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8. Dynamicviscosity:-Itisthetangentialforceperunitarearequiredtomoveone
horizontalplanewithrespecttoanotherplane-atanunitvelocity-whenmaintainingan
unitdistanceapartinthefluid.Theshearingstressbetweenthelayersofanon-turbulent
fluidmovinginstraightparallellinescanbedefinedforaNewtonianFluidas:
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9. Fig shows two fluid layers at distance y and y+dyfrom the surface. They move with different
velocities u and u+du as shown in fig. The top layer causes a shear stress on lower while lower
layer causes shear stress on the top layer. The shear stress τ is proportional to the rate of change
of velocity with respect y.
Mathematically,??????α
????????????
????????????
??????=μ
????????????
????????????
Here constant of proportionality μ is known as the coefficient of dynamic viscosity
????????????
????????????
known as
the velocity gradient.
From the above equation μ=
??????
????????????
????????????
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10. Causes of Viscosity in Fluids
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Viscosity in Gasses
The molecules of gasses are only weakly kept in position by molecular cohesion (as they
are so far apart). As adjacent layers move by each other there is a continuous exchange of
molecules. Molecules of a slower layer move to faster layers causing a drag, while
molecules moving the other way exert an acceleration force. Mathematical considerations
of this momentum exchange can lead to Newton law of viscosity.
If temperature of a gas increases the momentum exchange between layers will
increase thus increasing viscosity.
Viscosity will also change with pressure -but under normal conditions this change
is negligible in gasses.

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Viscosity in Gasses

12. Viscosity in Liquids
There is some molecular interchange between adjacent layers in liquids -but as the
molecules are so much closer than in gasses the cohesive forces hold the molecules in place
much more rigidly. This cohesion plays an important roll in the viscosity of liquids.
Increasing the temperature of a fluid reduces the cohesive forces and increases the molecular
interchange. Reducing cohesive forces reduces shear stress, while increasing molecular
interchange increases shear stress. Because of this complex interrelation the effect of
temperature on viscosity has something of the
form:
where is the viscosity at temperature T°C, and is the viscosity at temperature 0°C. A
and B are constants for a particular fluid.
High pressure can also change the viscosity of a liquid. As pressure increases the relative
movement of molecules requires more energy hence viscosity increases.
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Viscosity in Liquids

14. ViscosityMeasurements
•Theseviscometergivethevalueofthe‘dynamicviscosity’.
•Itisbasedontheprinciplethatthefluidwhoseviscosityisbeingmeasuredissheared
betweentwosurfaces.
•Intheseviscometersoneofthesurfacesisstationaryandtheotherisrotatedbyanexternal
driveandthefluidfillsthespaceinbetween.
•Themeasurementsareconductedbyapplyingeitheraconstanttorqueandmeasuringthe
changesinthespeedofrotationorapplyingaconstantspeedandmeasuringthechangesin
thetorque.
•Therearetwomaintypesoftheseviscometers:rotatingcylinderandcone-on-plate
viscometers.
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15. Viscosity Measurementscontinue…..
Rotating cylinder viscometer
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16. Cone-on-plate viscometer
Viscosity Measurementscontinue…..
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17. Fluid flow between two parallel plates
The bottom plate is fixed and the top plate is accelerated by applying
some force that acts from left to right.
The upper plate will be accelerated to some terminal velocity and the
fluid between the plates will be set into motion.
Terminal velocity is achieved when the applied force is balanced by a
resisting force (shown as an equal but opposite force applied by the
stationary bottom plate).
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18. As the upper plate begins to accelerate the velocity of the fluid molecules
in contact with the plate is equal to the velocity of the plate (a no slip
condition exists between the plate and the fluid).
Fluid molecules in contact with those against the plate will be
accelerated due to the viscous attraction between them... and so on
through the column of fluid.
The viscosity of the fluid ( , is the attraction between fluid molecules)
results in layers of fluid that are increasingly further from the moving
plate being set into motion.
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19. The velocity gradient (the rate of change in velocity between plates;
du/dy) will be constant and the velocity will increase linearly from zero
at the bottom plate to U
termat the top plate.
Terminal velocity is achieved when the resisting force (the force shown
applied by the bottom plate) is equal but opposite to the force applied to
the top plate (forces are equal so that there is no change in velocity with
time).
The bottom plate and water molecules attached to it are stationary (zero
velocity; no slip between molecules of fluid and the plate) so that
eventually the velocity will vary from zero at the bottom to U
termat the
top which is equal to the terminal velocity of the upper plate.
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22. Effect of viscosity on velocity profile
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Fluid flow is highly dependent on the viscosity of fluids. At the same time for a non-Newtonian
fluid, the viscosity is determined by the flow characteristics . Looking at Figure , we can
observe three very different velocity profiles depending on the fluid behavior. For all these
fluids, the shear rate at the walls (i.e. the slope of the velocity profile near the wall) is going to
determine viscosity. Successful characterization of viscosity is key in determining if a fluid is
Newtonian or non-Newtonian, and what range of shear rates needs to be considered for an
specific application.

23. Several fundamental effects are produced by viscosity:
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Drag: Skin friction drag caused by shear stresses at the surface contribute a majority of
the drag of most airplanes.
The pressure distribution: is changed by the presence of a boundary layer, even when no
significant separation is present.
Flow separation: Viscosity is responsible for flow separation which causes major
changes to the flow patterns and pressures.

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Viscosity and Navier–Stokes equations
The Navier–Stokes equations, describe the motion of viscous fluid substances. These
balance equations arise from applying Newton's second law to fluid motion, together with the
assumption that the stress in the fluid is the sum of a diffusing viscous term and a pressure
term—hence describing viscous flow.
Viscosity and Coutette’sflow
Couetteflow is the laminar flow of a viscous fluid in the space between two parallel plates,
one of which is moving relative to the other. The flow is driven by virtue of viscous drag
force acting on the fluid and the applied pressure gradient parallel to the plates.

25. Viscosity Effects In Dynamic Light Scattering Measurements
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•Dynamic light scattering (DLS) is a method for monitoring crystallization processes, solutions.
•DLS measures how fast the particles diffuse through the liquid.
•Smaller particles diffuse faster than larger ones.
•Solvent viscosity effect the measurement.
•For precise determination of particle size, it is essential to know the exact viscosity value of
the solvent.

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