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VISCOSIMETRIA����

MÉTODOS INSTRUMENTAIS - Q3008Licenciatura em Química 2018/2019

MÓDULO 2

Viscosity as a Rheological Property

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ABOLUTE or DYNAMIC VISCOSITY

Where v = dx/dt

ABOLUTE or DYNAMIC VISCOSITY

SI unit: Pa. s = kg. m-1. s-1CGS unit : P (Poise) = g. cm-1. s-11mPa. s= 1cP

(Taxa de deformação )

(Tensão cisalhante ou de deformação)

dv/dy

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Consider a fluid between two plates, one moving and the other stationary.

If the speed of the top plate is small enough, the fluid particles will move parallel to it, and their speed will vary linearly from zero at the bottom to u at the top. Each layer of fluid will move faster than the one just below it, and friction between them will give rise to a  force τ  resisting their relative motion. In particular, the fluid will apply on the top plate a force in the direction opposite to its motion, and an equal but opposite one to the bottom plate. An external force F is therefore required in order to keep the top plate of area A moving at constant speed u.

ABOLUTE or DYNAMIC VISCOSITY

ABOLUTE or DYNAMIC VISCOSITYA second interpretation of viscosity is obtained fromthe equation of Newton multiplying both sides by dv/dy:

Writing v as dx/dt and rearranging left side of equation:

The rate change of volume energy is proportional to the square of the velocity gradient, with the viscosity as the factor of proportionality:

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KINEMATIC VISCOSITY

SI unit : m2. s-1

CGS unit : cm2. s-1 = Stoke (St) mm2. s-1 = centiStoke (cSt)

EFFECT OF PRESSURE ON VISCOSITY

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•  Lubrificantsviscosityincreaseswithpressure.•  Formost lubricants this effect is considerably larger than the

other effects when the pressure is significantly aboveatmospheric.

•  The Barus equation:

EFFECT OF PRESSURE ON VISCOSITY

Gases

EFFECT OF TEMPERATURE ON VISCOSITY•  The viscosity of liquids decreases with increasing temperature.•  The viscosity of gases increases with increasing the temperature.

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SAE (Society of Automotive Engineers)

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VISCOSITY OF WATER AND TEMPERATURE

Some Empirical Viscosity-Temperature Equations

Arrhenius

https://www.hindawi.com/journals/jchem/2015/163262/

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EFFECT OF TEMPERATURE AND MOLECULAR WEIGHT ON VISCOSITY

http://www.scielo.br/pdf/cta/v28n3/a10v28n3.pdf

VISCOSITY - COMPOSITION - TEMPERATURE

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NEWTONIAN FLUIDS

NON-NEWTONIAN FLUIDS

http://polymerdatabase.com/polymer%20physics/Viscosity2.html

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NON-NEWTONIAN FLUIDS

Viscosity for� NEWTONIAN AND �

NON-NEWTONIAN FLUIDS

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The viscosity spectrum, in which the viscosities of various viscous samples (20 °C, atmospheric pressure) are presented.

http://www.nature.com/nprot/journal/v6/n7/fig_tab/nprot.2011.337_F2.html

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ctehgP =++ ρρ 2v21

FLOW OF AN IDEAL FLUID THROUGH A PIPEBernoulli equation

http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

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FLOW OF VISCOUS NEWTONAIN FLUID THROUGH A PIPE

http://www.physics.usyd.edu.au/teaching/Ag/fluids/wviscosity.htm

FLOW OF VISCOUS NEWTONAIN FLUID THROUGH A PIPE

http://www.physics.usyd.edu.au/teaching/Ag/fluids/wviscosity.htm

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The velocity through the tube has a quasi-parabolic profile, with the maximum velocity along the center line and the minimum velocity at the wall of the tube. The shear stress varies linearly and the shear rate varies non-linearly from zero at the central axis to a maximum at the wall of the tube.

FLOW OF VISCOUS NEWTONAIN FLUID THROUGH A PIPE

The Reynolds number is the ratio of inertial forces to viscous forces.

In ideal fluids, turbulence can be predicted on the basis of the calculated value of a dimensionless parameter known as the Reynolds number (Re)

where ρ and η are the fluid's density and viscosity, d is the diameter of the vessel, and v is the flow velocity. 

The Reynolds Number, Viscosity and Flow

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The Reynolds Number, Viscosity and Flow

The Reynolds number is the ratio of inertial forces to viscous forces.

The Reynolds Number, Viscosity and Flow

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The Reynolds Number, Viscosity and Flow

WHY TO MEASURE VISCOSITY

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VISCOSITY MEASUREMENTS

VISCOSITY MEASUREMENTS

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VISCOSITY MEASUREMENTS

where ρ1 and ρ2 are the densities of the two liquids

VISCOSITY MEASUREMENTS

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η

OSTWALD VISCOSITY MEASUREMENTS

VISCOSITY MEASUREMENTS

Capillary Viscometers

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VISCOSITY MEASUREMENTS

η = K ( σ - ρ ) t

Consider a sphere falling through a viscous fluid. As the sphere falls so its velocity increases until it reaches a constant velocity known as the terminal velocity. At this velocity the frictional drag due to viscous forces is just balanced by the gravitational force.

Effective gravitational force = = weight – buoyancy force =4/3πr 3(ρ – σ) g

Frictional force (Fd) = 6 π η r Stokes Law

Frictional force =- Effective gravitational force

η = K ( σ - ρ ) t

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Rotational Viscometers •  These viscometer give the value of the ‘dynamic viscosity’. •  It is based on the principle that the fluid whose viscosity is

being measured is sheared between two surfaces. •  In these viscometers one of the surfaces is stationary and the

other is rotated by an external drive and the fluid fills the space in between.

•  The measurements are conducted by applying either a constant torque and measuring the changes in the speed of rotation or applying a constant speed and measuring the changes in the torque.

•  There are two main types of these viscometers: rotating cylinder and cone-on-plate viscometers

VISCOSITY MEASUREMENTS �

VISCOSITY MEASUREMENTS

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Cone-on-plate viscometer

VISCOSITY MEASUREMENTS �

VISCOSITY MEASUREMENTSThe Rotational Viscometer

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VISCOSITY MEASUREMENTS

Rotating cylinder viscometer

Rotation of the inner cylinder/ spindler generates shear on the fluid, causing the fluid to flow within the viscometer. The torque required to produce a given angular velocity, or the angular velocity resulting from a given torque, are measures of the viscosity of the fluid.

ROTARY VISCOMETERS Rotational viscometers are made up of two parts: One that rotates, and another that remains stationary. The two parts may be: concentric cylinders (cup and bob), parallel plates, a low angle cone and plate, or a spindle inside of a cylinder..  

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x

ROTARY VISCOMETER

  Óleo parafínico de origem mineral (Edwards® Ultragrade 19)

Óleo sintético: polidimetilsiloxano (Rhodorsil® Oil 47 V100)

Estudar a influencia da temperatura na viscosidade de um óleo lubrificante,

usando o viscosímetro rotacional MYR V2-R.

TrabalhoPrá=coaRealizar

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usandooviscosímetrorotacionalMYRV2-R.

Estudaroefeitoda temperaturanaviscosidadedeálcoois de cadeia curta (etanol, propanol,butanol....) usando um viscosímetro capilardevidro,Cannon-FenskAnalisando os resultados ob=dos pela globalidadedosestudantesparaosdiferentesalcoóis,poder-se-àverificararelaçãoentreosvaloresdaviscosidadee o comprimento da cadeia carbonada dosdiferentesalcoóis

TrabalhoPrá=coaRealizar

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Usandoumviscosímetrocapilardevidro,Cannon-Fensk

BibliographyHiemenz, P.C.; Rajagopalan, R. Principles of Colloidal and Surface Chemistry, 3rd ed. Marcel Dekker. New York, 1997, cap 4 Viswanath, D. S; Ghosh, T.K; Prasad, D. H. L.; Dutt, N.V. K. Viscosity of Liquids: Theory, Estimation, Experiment and Data, Springer, 2007 Haynes, W.M. et al. CRC Handbook of Chemistry and Physcs, 95th ed, 2014-2015 https://www.tqc.eu/rsrc/artikel_downloads/rotational-viscometer-vr3000-dv1305--m44.pdf http://www.prrc.nmt.edu/groups/petrophysics/media/pdf/viscometer.pdf http://onlinelibrary.wiley.com/store/10.1002/app.1984.070291274/asset/070291274_ftp.pdf?v=1&t=ivh9v94m&s=39da008b6a556992ccafc1cf62c319981070c76f